From 3dcd42a220b256ab07736c0da13ab5d73d2546dd Mon Sep 17 00:00:00 2001 From: jdebecdelievre Date: Tue, 29 May 2018 20:39:11 -0700 Subject: [PATCH 1/5] changes to add verifications --- ...igenvalue problem - tests-checkpoint.ipynb | 869 +++ .../How it works (modif)-checkpoint.ipynb | 5112 +++++++++++++++++ .../How it works-checkpoint.ipynb | 938 +++ Eigenvalue problem - tests.ipynb | 864 +++ How it works (modif).ipynb | 4991 ++++++++++++++++ How it works.ipynb | 938 +++ src/pyfme/aircrafts/__init__.py | 3 +- src/pyfme/aircrafts/boeing_linear.py | 87 + src/pyfme/aircrafts/cessna_172.py | 215 +- src/pyfme/models/euler_flat_earth.py | 50 +- src/pyfme/models/state/acceleration.py | 12 + src/pyfme/models/state/aircraft_state.py | 24 + src/pyfme/models/state/angular_velocity.py | 11 + src/pyfme/models/state/attitude.py | 11 + src/pyfme/models/state/position.py | 11 + src/pyfme/models/state/velocity.py | 12 + src/pyfme/utils/anemometry.py | 4 +- src/pyfme/utils/coordinates.py | 24 + 18 files changed, 14169 insertions(+), 7 deletions(-) create mode 100644 .ipynb_checkpoints/Eigenvalue problem - tests-checkpoint.ipynb create mode 100644 .ipynb_checkpoints/How it works (modif)-checkpoint.ipynb create mode 100644 .ipynb_checkpoints/How it works-checkpoint.ipynb create mode 100644 Eigenvalue problem - tests.ipynb create mode 100644 How it works (modif).ipynb create mode 100644 How it works.ipynb create mode 100644 src/pyfme/aircrafts/boeing_linear.py diff --git a/.ipynb_checkpoints/Eigenvalue problem - tests-checkpoint.ipynb b/.ipynb_checkpoints/Eigenvalue problem - tests-checkpoint.ipynb new file mode 100644 index 0000000..3b5f60d --- /dev/null +++ b/.ipynb_checkpoints/Eigenvalue problem - tests-checkpoint.ipynb @@ -0,0 +1,869 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Python Flight Mechanics Engine " + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.aircrafts import LinearB747, SimplifiedCessna172\n", + "from pyfme.models import EulerFlatEarth\n", + "import numpy as np\n", + "nl = np.linalg\n", + "import matplotlib.pyplot as plt\n", + "from pyfme.environment.atmosphere import ISA1976\n", + "from pyfme.environment.wind import NoWind\n", + "from pyfme.environment.gravity import VerticalConstant\n", + "from pyfme.environment import Environment\n", + "from pyfme.utils.trimmer import steady_state_trim\n", + "from pyfme.models.state.position import EarthPosition\n", + "from pyfme.simulator import Simulation\n", + "from pyfme.models import EulerFlatEarth" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Test on Boeing" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "aircraft = LinearB747()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Aircraft mass: 288660.5504587156 kg\n", + "Aircraft inertia tensor: \n", + " [[ 24700000. 0. -2120000.]\n", + " [ 0. 44900000. 0.]\n", + " [ -2120000. 0. 67300000.]] kg/m²\n" + ] + } + ], + "source": [ + "print(f\"Aircraft mass: {aircraft.mass} kg\")\n", + "print(f\"Aircraft inertia tensor: \\n {aircraft.inertia} kg/m²\")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "state, environment = aircraft.trimmed_conditions()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system = EulerFlatEarth(t0=0, full_state=state)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "A_long, A_lat = system.linearized_model(state, aircraft, environment, None)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ -6.86619629e-03 1.39437135e-02 0.00000000e+00 -9.80665000e+00]\n", + " [ -9.04964592e-02 -3.14906754e-01 2.35892792e+02 -0.00000000e+00]\n", + " [ 3.89092422e-04 -3.36169904e-03 -4.28171388e-01 0.00000000e+00]\n", + " [ 0.00000000e+00 0.00000000e+00 1.00000000e+00 0.00000000e+00]]\n" + ] + } + ], + "source": [ + "print(f\"{A_long}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "d = aircraft.calculate_derivatives(None, None, None)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "val, vec = nl.eig(A_long)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-0.37168337+0.88692454j, -0.37168337-0.88692454j,\n", + " -0.00328880+0.0671904j , -0.00328880-0.0671904j ])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "val" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ -5.57748538e-02 0.00000000e+00 -2.35900000e+02 9.80665000e+00]\n", + " [ -1.27028796e-02 -4.35107741e-01 4.14335937e-01 0.00000000e+00]\n", + " [ 3.56656916e-03 -6.05604146e-03 -1.45800775e-01 0.00000000e+00]\n", + " [ 0.00000000e+00 1.00000000e+00 0.00000000e+00 0.00000000e+00]]\n" + ] + } + ], + "source": [ + "print(f\"{A_lat}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "val, vec = nl.eig(A_lat)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-0.03309986+0.94696989j, -0.03309986-0.94696989j,\n", + " -0.56322438+0.j , -0.00725928+0.j ])" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "val" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Eigen values are the same as the ones in Etkin. So the matrix was copy-pasted right in EulerFlatEarth.linearize()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Simplified Cessna: compare response with eigenvalue analysis" + ] + }, + { + "cell_type": "code", + "execution_count": 463, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "aircraft = SimplifiedCessna172()" + ] + }, + { + "cell_type": "code", + "execution_count": 464, + "metadata": {}, + "outputs": [], + "source": [ + "atmosphere = ISA1976()\n", + "gravity = VerticalConstant()\n", + "wind = NoWind()\n", + "environment = Environment(atmosphere, gravity, wind)" + ] + }, + { + "cell_type": "code", + "execution_count": 465, + "metadata": {}, + "outputs": [], + "source": [ + "pos = EarthPosition(x=0, y=0, height=1000)\n", + "psi = 0.5 # rad\n", + "TAS = 45 # m/s\n", + "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}\n", + "trimmed_state, trimmed_controls = steady_state_trim(\n", + " aircraft,\n", + " environment,\n", + " pos,\n", + " psi,\n", + " TAS,\n", + " controls0\n", + ")\n", + "environment.update(trimmed_state)" + ] + }, + { + "cell_type": "code", + "execution_count": 466, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" + ] + }, + { + "cell_type": "code", + "execution_count": 467, + "metadata": {}, + "outputs": [], + "source": [ + "A_long, A_lat = system.linearized_model(trimmed_state, aircraft, environment, trimmed_controls)" + ] + }, + { + "cell_type": "code", + "execution_count": 468, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "longitudinal eigenvalues : [[-2.61877991+4.03883858j -2.61877991-4.03883858j -0.02858402+0.26539636j\n", + " -0.02858402-0.26539636j]]\n" + ] + } + ], + "source": [ + "long_val, long_vec=nl.eig(A_long)\n", + "long_val = np.expand_dims(long_val, axis = 0)\n", + "print(f\"longitudinal eigenvalues : {long_val}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 469, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "lat eigenvalues : [[-5.64040610+0.j -0.22741980+1.12082018j -0.22741980-1.12082018j\n", + " 0.02242997+0.j ]]\n" + ] + } + ], + "source": [ + "lat_val, lat_vec=nl.eig(A_lat)\n", + "lat_val = np.expand_dims(lat_val, axis = 0)\n", + "print(f\"lat eigenvalues : {lat_val}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Longitudinal checks" + ] + }, + { + "cell_type": "code", + "execution_count": 490, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.utils.coordinates import wind2body, body2wind" + ] + }, + { + "cell_type": "code", + "execution_count": 491, + "metadata": {}, + "outputs": [], + "source": [ + "alpha = np.arctan2(trimmed_state.velocity.w, trimmed_state.velocity.u)\n", + "u = trimmed_state.velocity.u*1.0" + ] + }, + { + "cell_type": "code", + "execution_count": 492, + "metadata": {}, + "outputs": [], + "source": [ + "perturbation = (long_vec.T[0] + long_vec.T[1])/10" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Eigenvalue approach" + ] + }, + { + "cell_type": "code", + "execution_count": 493, + "metadata": {}, + "outputs": [], + "source": [ + "C = nl.lstsq(a=long_vec,b=perturbation.real)[0].real" + ] + }, + { + "cell_type": "code", + "execution_count": 494, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0.00068044+0.j, 0.19898677+0.j, -0.00221646+0.j, 0.00352200+0.j])" + ] + }, + "execution_count": 494, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "perturbation" + ] + }, + { + "cell_type": "code", + "execution_count": 495, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 4.47131754e+01 +9.11776957e-18j,\n", + " -7.57841343e-13 +2.78656422e-19j, 3.58117832e+00 +7.30262577e-19j])" + ] + }, + "execution_count": 495, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1" + ] + }, + { + "cell_type": "code", + "execution_count": 496, + "metadata": {}, + "outputs": [], + "source": [ + "t = np.linspace(0,10,100)\n", + "N = len(t)\n", + "X = np.zeros((N,4))\n", + "xx = []\n", + "for i in range(N):\n", + " x_stab = (long_vec*np.exp(long_val*t[i])).dot(C)\n", + " xx.append(x_stab[1])\n", + " x1 = wind2body(np.array([x_stab[0] + trimmed_state.velocity.u, x_stab[1], 0]), alpha=alpha, beta=0)\n", + " X[i,:2] = x1.real[2:]" + ] + }, + { + "cell_type": "code", + "execution_count": 497, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\numpy\\core\\numeric.py:531: ComplexWarning: Casting complex values to real discards the imaginary part\n", + " return array(a, dtype, copy=False, order=order)\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(xx,'.')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 498, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(t,X[:,1],'.')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 499, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.utils.input_generator import Constant" + ] + }, + { + "cell_type": "code", + "execution_count": 500, + "metadata": {}, + "outputs": [], + "source": [ + "controls = {\n", + " 'delta_elevator': Constant(trimmed_controls['delta_elevator']),\n", + " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", + " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", + " 'delta_t': Constant(trimmed_controls['delta_t'])\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 501, + "metadata": {}, + "outputs": [], + "source": [ + "# Perturbate\n", + "trimmed_state.cancel_perturbation()\n", + "p = perturbation.real\n", + "trimmed_state.perturbate(np.array([p[0],p[1],0]), 'velocity',reference_frame = 'stability_axis')\n", + "trimmed_state.perturbate(np.array([0,p[2],0]), 'angular_vel',reference_frame = 'stability_axis')\n", + "trimmed_state.perturbate(np.array([0,p[3],0]), 'attitude',reference_frame = 'stability_axis')" + ] + }, + { + "cell_type": "code", + "execution_count": 502, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "environment.update(trimmed_state)\n", + "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" + ] + }, + { + "cell_type": "code", + "execution_count": 503, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "sim = Simulation(aircraft, system, environment, controls)" + ] + }, + { + "cell_type": "code", + "execution_count": 484, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n", + "\n", + "time: 0%| | 0/10 [00:00" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(t,X[:,1] - max(X[:,1]),'.')\n", + "plt.plot(r.w - max(r.w))\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 487, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Aircraft State \n", + "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", + "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", + "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", + "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", + "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", + "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " + ] + }, + "execution_count": 487, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trimmed_state" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/.ipynb_checkpoints/How it works (modif)-checkpoint.ipynb b/.ipynb_checkpoints/How it works (modif)-checkpoint.ipynb new file mode 100644 index 0000000..7557a20 --- /dev/null +++ b/.ipynb_checkpoints/How it works (modif)-checkpoint.ipynb @@ -0,0 +1,5112 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Python Flight Mechanics Engine " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Aircraft " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import pyfme\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy import stats" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.aircrafts import SimplifiedCessna172, Cessna172" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "aircraft = SimplifiedCessna172()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "ename": "AttributeError", + "evalue": "'SimplifiedCessna172' object has no attribute 'full_state'", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mAttributeError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0maircraft\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfull_state\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[1;31mAttributeError\u001b[0m: 'SimplifiedCessna172' object has no attribute 'full_state'" + ] + } + ], + "source": [ + "aircraft.full_state" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Aircraft will provide the simulator the forces, moments and inertial properties in order to perform the integration of the dynamic system equations:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(f\"Aircraft mass: {aircraft.mass} kg\")\n", + "print(f\"Aircraft inertia tensor: \\n {aircraft.inertia} kg/m²\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(f\"forces: {aircraft.total_forces} N\")\n", + "print(f\"moments: {aircraft.total_moments} N·m\")" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Stability Derivatives : \n", + "CL_0 = 0.148;\n", + "CM_0 = 0.012068670774609398;\n", + "CL_alpha = 5.44;\n", + "CL_q = 7.281999999999999;\n", + "CL_delta_elev = 0.005677366997294861;\n", + "CM_alpha2 = -0.0008829539354397849;\n", + "CM_alpha = -0.01230758597735665;\n", + "CM_q = -12.464;\n", + "CM_delta_elev = -0.014180595130748421;\n", + "CD_K1 = 0.04394233763124108;\n", + "CD_0 = 0.029537580994030695;\n", + "CL_MAX = 1.889;\n", + "CY_beta = -0.26799999999999996;\n", + "CY_p = -0.05993333333333333;\n", + "CY_r = 0.2143333333333333;\n", + "CY_delta_rud = -0.561;\n", + "Cl_beta = -0.022292500000000003;\n", + "Cl_p = -0.3025083333333333;\n", + "Cl_r_cl = 0.17341925931518656;\n", + "Cl_delta_rud = -0.0027193749999999996;\n", + "Cl_delta_aile = 0.0044410237288135595;\n", + "CN_beta = 0.0126;\n", + "CN_p_al = -0.007206294994140298;\n", + "CN_r_cl = -0.00957535593543321;\n", + "CN_r_0 = -0.027354917660317425;\n", + "CN_delta_rud = 0.016818749999999997;\n", + "CN_delta_aile_cl = -0.0004745447361550377;\n" + ] + } + ], + "source": [ + "print(\"Stability Derivatives : \")\n", + "for k,val in aircraft.__dict__.items():\n", + " if k.startswith('C') and \"data\" not in k and \"_\" in k:\n", + " print(f\"{k} = {val};\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the aircraft, in order to calculate its forces and moments it is necessary to set the controls values within the limits: " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0}\n" + ] + } + ], + "source": [ + "print(aircraft.controls)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'delta_elevator': (-0.4537856055185257, 0.48869219055841229), 'delta_aileron': (-0.26179938779914941, 0.3490658503988659), 'delta_rudder': (-0.27925268031909273, 0.27925268031909273), 'delta_t': (0, 1)}\n" + ] + } + ], + "source": [ + "print(aircraft.control_limits)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "but also to provide and environment (ie. atmosphere, winds, gravity) and the aircraft state, which will also determine the aerodynamic contribution." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Environment " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.environment.atmosphere import ISA1976\n", + "from pyfme.environment.wind import NoWind\n", + "from pyfme.environment.gravity import VerticalConstant" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "atmosphere = ISA1976()\n", + "gravity = VerticalConstant()\n", + "wind = NoWind()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The atmosphere, wind and gravity model make up the environment:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.environment import Environment" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "environment = Environment(atmosphere, gravity, wind)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The environment has an update method which given the state (ie. position, altitude...) updates the environment variables (ie. density, wind magnitude, gravity force...)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Help on method update in module pyfme.environment.environment:\n", + "\n", + "update(state) method of pyfme.environment.environment.Environment instance\n", + "\n" + ] + } + ], + "source": [ + "help(environment.update)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## State " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Even if the state can be set manually by giving the position, attitude, velocity, angular velocities... Most of the times, the user will want to trim the aircraft in a stationary condition. The aircraft controls to flight in that condition will be also provided by the trimmer." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.utils.trimmer import steady_state_trim" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Help on function steady_state_trim in module pyfme.utils.trimmer:\n", + "\n", + "steady_state_trim(aircraft, environment, pos, psi, TAS, controls, gamma=0, turn_rate=0, exclude=None, verbose=0)\n", + " Finds a combination of values of the state and control variables\n", + " that correspond to a steady-state flight condition.\n", + " \n", + " Steady-state aircraft flight is defined as a condition in which all\n", + " of the motion variables are constant or zero. That is, the linear and\n", + " angular velocity components are constant (or zero), thus all\n", + " acceleration components are zero.\n", + " \n", + " Parameters\n", + " ----------\n", + " aircraft : Aircraft\n", + " Aircraft to be trimmed.\n", + " environment : Environment\n", + " Environment where the aircraft is trimmed including atmosphere,\n", + " gravity and wind.\n", + " pos : Position\n", + " Initial position of the aircraft.\n", + " psi : float, opt\n", + " Initial yaw angle (rad).\n", + " TAS : float\n", + " True Air Speed (m/s).\n", + " controls : dict\n", + " Initial value guess for each control or fixed value if control is\n", + " included in exclude.\n", + " gamma : float, optional\n", + " Flight path angle (rad).\n", + " turn_rate : float, optional\n", + " Turn rate, d(psi)/dt (rad/s).\n", + " exclude : list, optional\n", + " List with controls not to be trimmed. If not given, every control\n", + " is considered in the trim process.\n", + " verbose : {0, 1, 2}, optional\n", + " Level of least_squares verbosity:\n", + " * 0 (default) : work silently.\n", + " * 1 : display a termination report.\n", + " * 2 : display progress during iterations (not supported by 'lm'\n", + " method).\n", + " \n", + " Returns\n", + " -------\n", + " state : AircraftState\n", + " Trimmed aircraft state.\n", + " trimmed_controls : dict\n", + " Trimmed aircraft controls\n", + " \n", + " Notes\n", + " -----\n", + " See section 3.4 in [1] for the algorithm description.\n", + " See section 2.5 in [1] for the definition of steady-state flight\n", + " condition.\n", + " \n", + " References\n", + " ----------\n", + " .. [1] Stevens, BL and Lewis, FL, \"Aircraft Control and Simulation\",\n", + " Wiley-lnterscience.\n", + "\n" + ] + } + ], + "source": [ + "help(steady_state_trim)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.models.state.position import EarthPosition" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "pos = EarthPosition(x=0, y=0, height=1000)\n", + "psi = 0.5 # rad\n", + "TAS = 45 # m/s\n", + "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "trimmed_state, trimmed_controls = steady_state_trim(\n", + " aircraft,\n", + " environment,\n", + " pos,\n", + " psi,\n", + " TAS,\n", + " controls0\n", + ") " + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Aircraft State \n", + "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", + "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", + "u: 44.86 m/s, v: 0.00 m/s, w: 3.61 m/s \n", + "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", + "u_dot: -0.80 m/s², v_dot: 0.00 m/s², w_dot: -0.80 m/s² \n", + "P_dot: -0.00 rad/s², Q_dot: 0.00 rad/s², R_dot: 0.00 rad/s² " + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trimmed_state" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'delta_aileron': 4.8196779769121189e-07,\n", + " 'delta_elevator': -0.077707734980732135,\n", + " 'delta_rudder': -3.746264248090009e-06,\n", + " 'delta_t': 4.2875481736583809e-17}" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trimmed_controls" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, all the necessary elements in order to calculate forces and moments are available " + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Environment conditions for the current state:\n", + "environment.update(trimmed_state)\n", + "\n", + "# Forces and moments calculation:\n", + "forces, moments = aircraft.calculate_forces_and_moments(trimmed_state, environment, controls0)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "NDIM forces : \n", + "CL : 0.5590400736551502\n", + "CD : 0.043270695389780164\n", + "Cm : 0\n", + "CY : 5.022312452897911e-07\n", + "Cl : -2.164295485216534e-10\n", + "Cn : 0\n", + "Ct : 0\n", + "CAS : 42.87850158964442\n", + "CM : 3.8407025219899804e-07\n", + "CN : 4.86337495461688e-09\n" + ] + } + ], + "source": [ + "print(\"NDIM forces : \")\n", + "for k,val in aircraft.__dict__.items():\n", + " if k.startswith('C') and \"data\" not in k and \"_\" not in k:\n", + " print(f\"{k} : {val}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([ -8.33931929e+02, 4.44894756e-03, -2.59679525e+01]),\n", + " array([ -4.30622210e-05, 1.04593235e-02, 9.67648497e-04]))" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "forces, moments" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The aircraft is trimmed indeed: the total forces and moments (aerodynamics + gravity + thrust) are zero" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simulation " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to simulate the dynamics of the aircraft under certain inputs in an environment, the user can set up a simulation using a dynamic system:" + ] + }, + { + "cell_type": "code", + "execution_count": 739, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.models import EulerFlatEarth" + ] + }, + { + "cell_type": "code", + "execution_count": 740, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Constant Controls " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values." + ] + }, + { + "cell_type": "code", + "execution_count": 741, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.utils.input_generator import Constant" + ] + }, + { + "cell_type": "code", + "execution_count": 742, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "controls = {\n", + " 'delta_elevator': Constant(trimmed_controls['delta_elevator']),\n", + " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", + " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", + " 'delta_t': Constant(trimmed_controls['delta_t'])\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 743, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.simulator import Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 744, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "sim = Simulation(aircraft, system, environment, controls)" + ] + }, + { + "cell_type": "code", + "execution_count": 745, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system = EulerFlatEarth(t0=0, full_state=trimmed_state)\n", + "sim = Simulation(aircraft, system, environment, controls)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once the simulation is set, the propagation can be performed:" + ] + }, + { + "cell_type": "code", + "execution_count": 767, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n", + "\n", + "time: 10.0it [00:00, ?it/s]\n", + "\n" + ] + } + ], + "source": [ + "results = sim.propagate(5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The results are returned in a DataFrame:" + ] + }, + { + "cell_type": "code", + "execution_count": 747, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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FxFyFzMachMxMyMzTASaaileron...thrustuvv_downv_eastv_northwx_earthy_earthz_earth
time
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-1.701269e-14 5.456968e-12 0.133756 -2.123358e-13 \n", + "0.14 1.523404e-11 -1.969178e-14 7.275958e-12 0.133756 -2.025612e-13 \n", + "0.15 1.568878e-11 -2.252049e-14 1.273293e-11 0.133756 -1.931933e-13 \n", + "0.16 1.580247e-11 -2.549911e-14 1.273293e-11 0.133756 -1.842518e-13 \n", + "0.17 1.557510e-11 -2.861302e-14 1.637090e-11 0.133756 -1.756801e-13 \n", + "0.18 1.557510e-11 -3.185448e-14 1.818989e-11 0.133756 -1.674601e-13 \n", + "0.19 1.557510e-11 -3.522797e-14 1.818989e-11 0.133756 -1.596367e-13 \n", + "0.20 1.568878e-11 -3.873125e-14 1.818989e-11 0.133756 -1.522040e-13 \n", + "0.21 1.568878e-11 -4.234649e-14 1.818989e-11 0.133756 -1.450822e-13 \n", + "0.22 1.546141e-11 -4.605667e-14 2.182787e-11 0.133756 -1.382001e-13 \n", + "0.23 1.568878e-11 -4.985191e-14 2.182787e-11 0.133756 -1.315377e-13 \n", + "0.24 1.568878e-11 -5.373557e-14 2.182787e-11 0.133756 -1.251340e-13 \n", + "0.25 1.568878e-11 -5.770391e-14 2.364686e-11 0.133756 -1.189899e-13 \n", + "0.26 1.557510e-11 -6.175787e-14 2.546585e-11 0.133756 -1.131234e-13 \n", + "0.27 1.580247e-11 -6.588990e-14 2.546585e-11 0.133756 -1.075064e-13 \n", + "0.28 1.568878e-11 -7.008588e-14 2.728484e-11 0.133756 -1.020786e-13 \n", + "0.29 1.557510e-11 -7.434394e-14 2.910383e-11 0.133756 -9.685431e-14 \n", + "0.30 1.568878e-11 -7.867110e-14 2.910383e-11 0.133756 -9.187934e-14 \n", + "... ... ... ... ... ... \n", + "9.71 1.479066e-10 -5.311047e-12 4.729372e-11 0.133756 -4.807148e-15 \n", + "9.72 1.480203e-10 -5.318273e-12 4.729372e-11 0.133756 -4.794496e-15 \n", + "9.73 1.482476e-10 -5.325504e-12 4.729372e-11 0.133756 -4.781638e-15 \n", + "9.74 1.483613e-10 -5.332739e-12 4.729372e-11 0.133756 -4.768578e-15 \n", + "9.75 1.484750e-10 -5.339978e-12 4.729372e-11 0.133756 -4.755319e-15 \n", + "9.76 1.485887e-10 -5.347222e-12 4.729372e-11 0.133756 -4.741864e-15 \n", + "9.77 1.488161e-10 -5.354470e-12 4.729372e-11 0.133756 -4.728216e-15 \n", + "9.78 1.489298e-10 -5.361722e-12 4.729372e-11 0.133756 -4.714378e-15 \n", + "9.79 1.490434e-10 -5.368978e-12 4.729372e-11 0.133756 -4.700354e-15 \n", + "9.80 1.491571e-10 -5.376239e-12 4.729372e-11 0.133756 -4.686147e-15 \n", + "9.81 1.493845e-10 -5.383504e-12 4.729372e-11 0.133756 -4.671759e-15 \n", + "9.82 1.494982e-10 -5.390773e-12 4.729372e-11 0.133756 -4.657195e-15 \n", + "9.83 1.496119e-10 -5.398046e-12 4.729372e-11 0.133756 -4.642458e-15 \n", + "9.84 1.497256e-10 -5.405323e-12 4.911271e-11 0.133756 -4.627550e-15 \n", + "9.85 1.498393e-10 -5.412605e-12 4.911271e-11 0.133756 -4.612476e-15 \n", + "9.86 1.498393e-10 -5.419890e-12 4.911271e-11 0.133756 -4.597238e-15 \n", + "9.87 1.500666e-10 -5.427180e-12 4.911271e-11 0.133756 -4.581839e-15 \n", + "9.88 1.501803e-10 -5.434473e-12 4.911271e-11 0.133756 -4.566283e-15 \n", + "9.89 1.502940e-10 -5.441771e-12 4.911271e-11 0.133756 -4.550574e-15 \n", + "9.90 1.504077e-10 -5.449072e-12 4.911271e-11 0.133756 -4.534714e-15 \n", + "9.91 1.506351e-10 -5.456378e-12 4.911271e-11 0.133756 -4.518707e-15 \n", + "9.92 1.507487e-10 -5.463687e-12 4.911271e-11 0.133756 -4.502555e-15 \n", + "9.93 1.508624e-10 -5.471000e-12 4.911271e-11 0.133756 -4.486263e-15 \n", + "9.94 1.509761e-10 -5.478317e-12 4.911271e-11 0.133756 -4.469834e-15 \n", + "9.95 1.510898e-10 -5.485638e-12 4.911271e-11 0.133756 -4.453270e-15 \n", + "9.96 1.514309e-10 -5.492963e-12 4.911271e-11 0.133756 -4.436576e-15 \n", + "9.97 1.515446e-10 -5.500291e-12 4.911271e-11 0.133756 -4.419754e-15 \n", + "9.98 1.516582e-10 -5.507624e-12 4.911271e-11 0.133756 -4.402808e-15 \n", + "9.99 1.517719e-10 -5.514960e-12 4.911271e-11 0.133756 -4.385742e-15 \n", + "10.00 1.519993e-10 -5.522300e-12 4.911271e-11 0.133756 -4.368557e-15 \n", + "\n", + " My Mz TAS a aileron ... \\\n", + "time ... \n", + "0.01 -1.355845e-11 -1.585097e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.02 -1.314636e-11 -1.347614e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.03 -1.274679e-11 -1.121474e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.04 -1.235936e-11 -9.062203e-15 45.0 336.434581 -9.644866e-18 ... \n", + "0.05 -1.198371e-11 -7.014180e-15 45.0 336.434581 -9.644866e-18 ... \n", + "0.06 -1.161948e-11 -5.066498e-15 45.0 336.434581 -9.644866e-18 ... \n", + "0.07 -1.126632e-11 -3.215162e-15 45.0 336.434581 -9.644866e-18 ... \n", + "0.08 -1.092389e-11 -1.456347e-15 45.0 336.434581 -9.644866e-18 ... \n", + "0.09 -1.059187e-11 2.136113e-16 45.0 336.434581 -9.644866e-18 ... \n", + "0.10 -9.889790e-12 1.798616e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.11 -9.209049e-12 2.315148e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.12 -8.548998e-12 2.316617e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.13 -8.289160e-12 2.445525e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.14 -7.664615e-12 3.206469e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.15 -7.059053e-12 2.645450e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.16 -6.844501e-12 2.752624e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.17 -6.263865e-12 2.954086e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.18 -5.700878e-12 3.081479e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.19 -4.782397e-12 1.923424e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.20 -4.637041e-12 2.008599e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.21 -4.496103e-12 2.088193e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.22 -3.986845e-12 3.475211e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.23 -3.865669e-12 3.540318e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.24 -3.375572e-12 4.004200e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.25 -2.900371e-12 3.721343e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.26 -2.439613e-12 3.636619e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.27 -2.365464e-12 3.682321e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.28 -1.920964e-12 4.699768e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.29 -1.489974e-12 4.060594e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.30 -1.444688e-12 4.092412e-14 45.0 336.434581 -9.644866e-18 ... \n", + "... ... ... ... ... ... ... \n", + "9.71 1.651500e-25 -3.956346e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.72 1.597792e-25 -3.952250e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.73 1.544085e-25 -3.948197e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.74 1.503805e-25 -3.944187e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.75 1.463524e-25 -3.940220e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.76 1.409817e-25 -3.936298e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.77 1.369536e-25 -3.932421e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.78 1.315829e-25 -3.928590e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.79 1.275549e-25 -3.924805e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.80 1.248695e-25 -3.921066e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.81 1.208414e-25 -3.917374e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.82 1.181561e-25 -3.913730e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.83 1.154707e-25 -3.910134e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.84 1.114427e-25 -3.906587e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.85 1.074146e-25 -3.903089e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.86 1.047292e-25 -3.899641e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.87 1.007012e-25 -3.896243e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.88 9.801583e-26 -3.892896e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.89 9.533047e-26 -3.889600e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.90 9.130242e-26 -3.886355e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.91 8.861705e-26 -3.883162e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.92 8.458901e-26 -3.880022e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.93 8.324632e-26 -3.876934e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.94 8.056096e-26 -3.873900e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.95 7.921828e-26 -3.870920e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.96 7.653291e-26 -3.867993e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.97 7.519023e-26 -3.865121e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.98 7.250486e-26 -3.862304e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.99 7.116218e-26 -3.859542e-14 45.0 336.434581 -9.644866e-18 ... \n", + "10.00 6.847682e-26 -3.856835e-14 45.0 336.434581 -9.644866e-18 ... \n", + "\n", + " thrust u v v_down v_east v_north \\\n", + "time \n", + "0.01 0.577997 44.87164 -3.511938e-15 4.440892e-16 21.574149 39.491215 \n", + "0.02 0.577997 44.87164 -3.512042e-15 4.440892e-16 21.574149 39.491215 \n", + "0.03 0.577997 44.87164 -3.512218e-15 4.440892e-16 21.574149 39.491215 \n", + "0.04 0.577997 44.87164 -3.512470e-15 4.440892e-16 21.574149 39.491215 \n", + "0.05 0.577997 44.87164 -3.512798e-15 4.440892e-16 21.574149 39.491215 \n", + "0.06 0.577997 44.87164 -3.513206e-15 4.440892e-16 21.574149 39.491215 \n", + "0.07 0.577997 44.87164 -3.513695e-15 4.440892e-16 21.574149 39.491215 \n", + "0.08 0.577997 44.87164 -3.514266e-15 4.440892e-16 21.574149 39.491215 \n", + "0.09 0.577997 44.87164 -3.514923e-15 0.000000e+00 21.574149 39.491215 \n", + "0.10 0.577997 44.87164 -3.515665e-15 -4.440892e-16 21.574149 39.491215 \n", + "0.11 0.577997 44.87164 -3.516503e-15 -8.881784e-16 21.574149 39.491215 \n", + "0.12 0.577997 44.87164 -3.517460e-15 -8.881784e-16 21.574149 39.491215 \n", + "0.13 0.577997 44.87164 -3.518540e-15 -4.440892e-16 21.574149 39.491215 \n", + "0.14 0.577997 44.87164 -3.519743e-15 -4.440892e-16 21.574149 39.491215 \n", + "0.15 0.577997 44.87164 -3.521077e-15 0.000000e+00 21.574149 39.491215 \n", + "0.16 0.577997 44.87164 -3.522536e-15 0.000000e+00 21.574149 39.491215 \n", + "0.17 0.577997 44.87164 -3.524120e-15 0.000000e+00 21.574149 39.491215 \n", + "0.18 0.577997 44.87164 -3.525830e-15 4.440892e-16 21.574149 39.491215 \n", + "0.19 0.577997 44.87164 -3.527666e-15 4.440892e-16 21.574149 39.491215 \n", + "0.20 0.577997 44.87164 -3.529612e-15 8.881784e-16 21.574149 39.491215 \n", + "0.21 0.577997 44.87164 -3.531666e-15 8.881784e-16 21.574149 39.491215 \n", + "0.22 0.577997 44.87164 -3.533831e-15 8.881784e-16 21.574149 39.491215 \n", + "0.23 0.577997 44.87164 -3.536124e-15 1.332268e-15 21.574149 39.491215 \n", + "0.24 0.577997 44.87164 -3.538548e-15 1.332268e-15 21.574149 39.491215 \n", + "0.25 0.577997 44.87164 -3.541109e-15 1.776357e-15 21.574149 39.491215 \n", + "0.26 0.577997 44.87164 -3.543804e-15 1.776357e-15 21.574149 39.491215 \n", + "0.27 0.577997 44.87164 -3.546629e-15 1.776357e-15 21.574149 39.491215 \n", + "0.28 0.577997 44.87164 -3.549585e-15 2.220446e-15 21.574149 39.491215 \n", + "0.29 0.577997 44.87164 -3.552685e-15 2.220446e-15 21.574149 39.491215 \n", + "0.30 0.577997 44.87164 -3.555922e-15 2.664535e-15 21.574149 39.491215 \n", + "... ... ... ... ... ... ... \n", + "9.71 0.577997 44.87164 -6.664932e-15 5.875300e-13 21.574149 39.491215 \n", + "9.72 0.577997 44.87164 -6.666790e-15 5.884182e-13 21.574149 39.491215 \n", + "9.73 0.577997 44.87164 -6.668652e-15 5.888623e-13 21.574149 39.491215 \n", + "9.74 0.577997 44.87164 -6.670518e-15 5.897505e-13 21.574149 39.491215 \n", + "9.75 0.577997 44.87164 -6.672389e-15 5.901946e-13 21.574149 39.491215 \n", + "9.76 0.577997 44.87164 -6.674264e-15 5.906386e-13 21.574149 39.491215 \n", + "9.77 0.577997 44.87164 -6.676144e-15 5.915268e-13 21.574149 39.491215 \n", + "9.78 0.577997 44.87164 -6.678028e-15 5.919709e-13 21.574149 39.491215 \n", + "9.79 0.577997 44.87164 -6.679916e-15 5.928591e-13 21.574149 39.491215 \n", + "9.80 0.577997 44.87164 -6.681810e-15 5.933032e-13 21.574149 39.491215 \n", + "9.81 0.577997 44.87164 -6.683708e-15 5.937473e-13 21.574149 39.491215 \n", + "9.82 0.577997 44.87164 -6.685612e-15 5.946355e-13 21.574149 39.491215 \n", + "9.83 0.577997 44.87164 -6.687520e-15 5.950795e-13 21.574149 39.491215 \n", + "9.84 0.577997 44.87164 -6.689434e-15 5.964118e-13 21.574149 39.491215 \n", + "9.85 0.577997 44.87164 -6.691353e-15 5.968559e-13 21.574149 39.491215 \n", + "9.86 0.577997 44.87164 -6.693277e-15 5.968559e-13 21.574149 39.491215 \n", + "9.87 0.577997 44.87164 -6.695207e-15 5.973000e-13 21.574149 39.491215 \n", + "9.88 0.577997 44.87164 -6.697142e-15 5.981882e-13 21.574149 39.491215 \n", + "9.89 0.577997 44.87164 -6.699083e-15 5.986323e-13 21.574149 39.491215 \n", + "9.90 0.577997 44.87164 -6.701029e-15 5.995204e-13 21.574149 39.491215 \n", + "9.91 0.577997 44.87164 -6.702982e-15 5.999645e-13 21.574149 39.491215 \n", + "9.92 0.577997 44.87164 -6.704940e-15 6.004086e-13 21.574149 39.491215 \n", + "9.93 0.577997 44.87164 -6.706904e-15 6.012968e-13 21.574149 39.491215 \n", + "9.94 0.577997 44.87164 -6.708875e-15 6.017409e-13 21.574149 39.491215 \n", + "9.95 0.577997 44.87164 -6.710851e-15 6.026291e-13 21.574149 39.491215 \n", + "9.96 0.577997 44.87164 -6.712834e-15 6.030731e-13 21.574149 39.491215 \n", + "9.97 0.577997 44.87164 -6.714823e-15 6.035172e-13 21.574149 39.491215 \n", + "9.98 0.577997 44.87164 -6.716819e-15 6.044054e-13 21.574149 39.491215 \n", + "9.99 0.577997 44.87164 -6.718821e-15 6.048495e-13 21.574149 39.491215 \n", + "10.00 0.577997 44.87164 -6.720829e-15 6.057377e-13 21.574149 39.491215 \n", + "\n", + " w x_earth y_earth z_earth \n", + "time \n", + "0.01 3.396464 0.394912 0.215741 -1000.0 \n", + "0.02 3.396464 0.789824 0.431483 -1000.0 \n", + "0.03 3.396464 1.184736 0.647224 -1000.0 \n", + "0.04 3.396464 1.579649 0.862966 -1000.0 \n", + "0.05 3.396464 1.974561 1.078707 -1000.0 \n", + "0.06 3.396464 2.369473 1.294449 -1000.0 \n", + "0.07 3.396464 2.764385 1.510190 -1000.0 \n", + "0.08 3.396464 3.159297 1.725932 -1000.0 \n", + "0.09 3.396464 3.554209 1.941673 -1000.0 \n", + "0.10 3.396464 3.949122 2.157415 -1000.0 \n", + "0.11 3.396464 4.344034 2.373156 -1000.0 \n", + "0.12 3.396464 4.738946 2.588898 -1000.0 \n", + "0.13 3.396464 5.133858 2.804639 -1000.0 \n", + "0.14 3.396464 5.528770 3.020381 -1000.0 \n", + "0.15 3.396464 5.923682 3.236122 -1000.0 \n", + "0.16 3.396464 6.318594 3.451864 -1000.0 \n", + "0.17 3.396464 6.713507 3.667605 -1000.0 \n", + "0.18 3.396464 7.108419 3.883347 -1000.0 \n", + "0.19 3.396464 7.503331 4.099088 -1000.0 \n", + "0.20 3.396464 7.898243 4.314830 -1000.0 \n", + "0.21 3.396464 8.293155 4.530571 -1000.0 \n", + "0.22 3.396464 8.688067 4.746313 -1000.0 \n", + "0.23 3.396464 9.082980 4.962054 -1000.0 \n", + "0.24 3.396464 9.477892 5.177796 -1000.0 \n", + "0.25 3.396464 9.872804 5.393537 -1000.0 \n", + "0.26 3.396464 10.267716 5.609279 -1000.0 \n", + "0.27 3.396464 10.662628 5.825020 -1000.0 \n", + "0.28 3.396464 11.057540 6.040762 -1000.0 \n", + "0.29 3.396464 11.452452 6.256503 -1000.0 \n", + "0.30 3.396464 11.847365 6.472245 -1000.0 \n", + "... ... ... ... ... \n", + "9.71 3.396464 383.459700 209.484989 -1000.0 \n", + "9.72 3.396464 383.854613 209.700731 -1000.0 \n", + "9.73 3.396464 384.249525 209.916472 -1000.0 \n", + "9.74 3.396464 384.644437 210.132214 -1000.0 \n", + "9.75 3.396464 385.039349 210.347955 -1000.0 \n", + "9.76 3.396464 385.434261 210.563697 -1000.0 \n", + "9.77 3.396464 385.829173 210.779438 -1000.0 \n", + "9.78 3.396464 386.224085 210.995180 -1000.0 \n", + "9.79 3.396464 386.618998 211.210921 -1000.0 \n", + "9.80 3.396464 387.013910 211.426663 -1000.0 \n", + "9.81 3.396464 387.408822 211.642404 -1000.0 \n", + "9.82 3.396464 387.803734 211.858146 -1000.0 \n", + "9.83 3.396464 388.198646 212.073887 -1000.0 \n", + "9.84 3.396464 388.593558 212.289628 -1000.0 \n", + "9.85 3.396464 388.988471 212.505370 -1000.0 \n", + "9.86 3.396464 389.383383 212.721111 -1000.0 \n", + "9.87 3.396464 389.778295 212.936853 -1000.0 \n", + "9.88 3.396464 390.173207 213.152594 -1000.0 \n", + "9.89 3.396464 390.568119 213.368336 -1000.0 \n", + "9.90 3.396464 390.963031 213.584077 -1000.0 \n", + "9.91 3.396464 391.357943 213.799819 -1000.0 \n", + "9.92 3.396464 391.752856 214.015560 -1000.0 \n", + "9.93 3.396464 392.147768 214.231302 -1000.0 \n", + "9.94 3.396464 392.542680 214.447043 -1000.0 \n", + "9.95 3.396464 392.937592 214.662785 -1000.0 \n", + "9.96 3.396464 393.332504 214.878526 -1000.0 \n", + "9.97 3.396464 393.727416 215.094268 -1000.0 \n", + "9.98 3.396464 394.122329 215.310009 -1000.0 \n", + "9.99 3.396464 394.517241 215.525751 -1000.0 \n", + "10.00 3.396464 394.912153 215.741492 -1000.0 \n", + "\n", + "[1000 rows x 35 columns]" + ] + }, + "execution_count": 747, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 749, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "kwargs = {'marker': '.',\n", + " 'subplots': True,\n", + " 'sharex': True,\n", + " 'figsize': (12, 6)}" + ] + }, + { + "cell_type": "code", + "execution_count": 750, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\plotting\\_core.py:1716: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n", + " series.name = label\n" + ] + }, + { + "data": { + "image/png": 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Y4VlSecsZjmfB7i3QsbEwddh3LEmTrpAbBmOYY2m/QREtQAvAwoULJ7smSRpd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\nRK5CYII=\n", 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GZkmSJptKgXpaR2OWGodCu0f3ApcaV1swMEuSNJVUWmp8sB92DTQmUO9zYGEh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\nFTfdkZnnVjvGwCyplVQL1I2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1M4OqVcnDsCRJyt2ZoXdXLx3dI7QhK0LYde2ussAwLElSEeQKu9PqptH+Sjtb\ne7e+enABOjOMtJTBzgxSHsJwRNQCrcCGlNL7Jl6SJEmVpxzbkLmFsDS6fMwMfwJYBxyah2tJklS2\ncu2qlnML4QK0IauN2j337hvoY8aUGS5lkCZgQmE4IhqB/wD8LfDJvFQkSVIJ5fqw2oidGYq0nMHO\nDFLhTHRm+CvAXwINuQ6IiEuASwCampomeDtJkiYm13KG7T3b2dG3Y+/lDLvlMfS6dlcqL+MOwxHx\nPmBzSml1RLwt13EppRXACoCWlha3UpMkFVSumd2+gT56+nvY8PKG/U+yDZmUWROZGX4LcGZEvBeo\nBw6NiJtSSufmpzRJkkaWsw1Zfy8dPYVvQzbSrmq2IZMq07jDcErp08CnAYZmhq80CEuS8iFnG7JJ\n09i8czPbere9erCdGSRNgH2GJUlFVw5tyMDlDJLyFIZTSvcB9+XjWpKk6pCrDVl3f/f+XRmgKG3I\n6mrq/LCapL04MyxJGpeRwm7fQB+TYhLtr7SzpXfL3ifYhkxSGTIMS5JyKseeu87sSsonw7AkZViu\ntbt9A31s79lOR3fhOzO4bldSKRmGJanK5erMUEMNbS+37X+CbcgkZYhhWJIq3O61u+u3r6eupm5P\n4JxeN532ne1s6Rm2drcASxmGh93dH1KzDZmkSmEYlqQKMHzt7vDAmbMzQ57t25nBsCupWhiGJakM\n5GpDRoLeXTl2Vcuz4Wt3dwduOzNIqnaGYUkqkn3X7u4OnHZmkKTSMQxLUp7kakO2vWc7O/p2FGVX\ntX23EDbsStKBGYYlaYzKoQ3ZEYccwbS6aXt9UM7ODJI0foZhSRomV2eG2ppaXuh6Yf8TitCGzF3V\nJKlwDMOSMifXcoaOVzro7Oks+P13r921DZkklZ5hWFLVGb6cYUvPlr1meHt39RZ8OcNIbcjAXdUk\nqRwZhiVVpIPeVS3PbEMmSdXBMCypLO27dnfPkoKeLrr6ugremcE2ZJKUDYZhSSWRqzODu6pJkorJ\nMCypYHLtqtbT3zPyB9UKMMN75LQj7cwgScpp3GE4Io4G/hfwWmAAWJFS+mq+CpNUGXJ1ZnBXNUlS\nJZjIzHA/cEVK6bGIaABWR8RPU0q/yVNtkspAruUM23u209XbxY7+HfuflOfQ29TQxKSaSXt1hbAz\ngyQpH8YdhlNKLwIvDj3uioh1wFGAYViqMLk2msjZmSHPYXd4ZwZ3VZMkFVNe1gxHRDOwCFg1wtcu\nAS4BaGpqysftJB2kXGF3et102ne2s6VnS0HvP9KuaoZdSVI5mHAYjojpwPeAy1NK2/f9ekppBbAC\noKWlJU30fpJGlmvt7raebWybp0gkAAAKhklEQVR6ZVPB79/U0ET/QP+e+9qZQZJUCSYUhiOijsEg\nfHNK6fb8lCQpl5E2mkgp0berj46ewu6qBiMvZ3DtriSpkk2km0QA1wPrUkpfyl9JUjblakMGUD+p\nns6dnWzr3fbqCXZmkCRpwiYyM/wW4DxgbUSsGXrtr1JKP5p4WVJ1Gmkpw/TJ0+l4paMobcjA5QyS\nJA03kW4SDwGRx1qkipdr3W4x25Dtu6ta30AfM6bM8MNqkiSNwB3opIMwvOfulp4te3Vm6O3vLcq6\nXRh5OYO7qkmSdPAMw9I+Drrnbp6N1IbMtbuSJBWGYViZkyvs2oZMkqTsMQyrKuXqzNDT30NnT+fI\nJ+VxOcO+63ZtQyZJUnkyDKtijdRzFyAINry8Ye+DC7Bu98hpR+63lMF1u5IkVRbDsMrWQXVmKFIb\nMtftSpJUXQzDKpnhnRlefPlF4NUlBV29XXT1de1/Up5D70hh1zZkkiRlh2FYBZMr7PYN9NHb3zty\nZ4Y8h92ROjPMmTbHsCtJkgDDsCYoV2eG2qjlhR0v7H+CPXclSVIZMQxrVLlmeEvZhgzszCBJkibO\nMCwgd2eGnBtN5HmGd1b9LCbXTjbsSpKkojIMZ0Su5QzT66bT/ko7W3q3vHpwgZYy7A67fQN91NXU\n2ZlBkiSVnGG4SuwbdncHzq7eLrr7u/l9z+8LXoNtyCRJUqUxDFeQce2qlmf7zvDahkySJFUyw3CZ\n2Xftbt9AH5NqJtHxSsf+s7tF6szgDK8kSapWhuEic1c1SZKk8jGhMBwR7wa+CtQC304pfS4vVVWw\nnBtN7Opje892Ono69j+pALuqTaqZtNcH5dxoQpIkaX/jDsMRUQtcC/wx0Ab8MiJ+kFL6Tb6KKxe5\nZnOHf0gNIAg2vLxh/wu4q5okSVJZmsjM8CnAMymlZwEi4v8AfwqUVRh+7KXH+MFvf8BzW5/bs0HE\n8BC5b6hNKTGtbho7+nYwwAD9u/pH7sRQoCUMu+1euzu8tvpJ9Zx7wrnuqiZJkpQnEwnDRwHD99tt\nA06dWDn5tWbzGi76yUXsSrv2/sLLOR4X0RGHHEFt1ALuqiZJklQqEwnDMcJrab+DIi4BLgFoamqa\nwO0OXutLrQykgaLec7iRNpqoq63jrGPPcnZXkiSpDEwkDLcBRw973ghs3PeglNIKYAVAS0vLfmG5\nkFqOaKGupo7egd68XG/f2dx91wzbmUGSJKmyTCQM/xL4w4iYC2wAlgIfyUtVebLw8IVc/67rR+zu\ncKAPwu37dWdzJUmSqtO4w3BKqT8iPg78hMHWajeklH6dt8ryZOHhC52hlSRJ0ogipeKtXIiIduD5\not3wVU3A70pwXxWX45wNjnP1c4yzwXHOhlKO8zEppdmjHVTUMFwqEdE+lm+GKpvjnA2Oc/VzjLPB\ncc6GShjnmlIXUCRbS12AisJxzgbHufo5xtngOGdD2Y9zVsLwtlIXoKJwnLPBca5+jnE2OM7ZUPbj\nnJUwvKLUBagoHOdscJyrn2OcDY5zNpT9OGdizbAkSZI0kqzMDEuSJEn7MQxLkiQps6omDEfERHbT\nU4WIGNoPW1UtIg4tdQ0qvIiYExFzSl2HCicippW6BhVWRESpa5ioig/DETEpIq4BvhgR7yx1PSqM\noXH+O+DvIuKPS12PCici/hNwf0QsHnpe8T9otbeIqBn673kVsCAiJpe6JuXXsJ/Zd0TExRFxTKlr\nUsFM3f2gUn9eV3QYHvqmfw2YAzwKXBUR/ykippS2MuVTRLwVWA3MAJ4G/jYi3lzaqpRvw36INgCv\nAJcAJD/lW43OA+YBC1JKd6WUektdkPInImYA/wwcBnwZ+CBwfEmLUt5FxDsi4iHg2og4Fyr353Wl\nLy1oABYC70opdUVEB/BeYAlwU0krUz4NANeklL4LEBELgDOBX5S0KuVVSilFRA1wBPAt4PSIOCel\ndHNE1KaUdpW4ROXB0C89fwh8LaW0LSJagB7gKUNx1ZgONKeU/iNARCwpcT3Ks4h4DfA/gS8CncAn\nImJuSulvIqImpTRQ2goPTkWH4ZTS9ohYDywDvg78nMFZ4jdFxN0ppU0lLE/5sxp4dFggegRYVOKa\nlGe7f4AO/VL7MnAv8P6IeBDYTgXsYqTRDf3SMws4a+gX2/OB54COiPhCSum50laoiUopvRARr0TE\nd4BGoBmYGREnAv/s/5sr09BkBUNB90hgLXBHSmlXRLQBj0TEt1NKL0ZEVNIscUUvkxhyB7AwIuak\nlHYwODi9DIZiVYGU0isppZ5hM4PvAn5XypqUf8NmEhYAPwHuBN7A4C+5J1bqWjSN6FpgMTA/pXQy\n8JcMzi4tL2lVyqclDP7t3caU0rHAl4DXAmeVtCqNS0RcCLQBfzP00g7gTcAsgJTS08DNwDdKUuAE\nVUMYfojBH6LLAFJKq4GTGbagW9UhImqH/TX6j4dem28nkarzOPBN4D4GZ4SfBH5TSbMMGtXTwP8D\nTgFIKa0HnmfwZ7mqQEqpncGJqY6h5/cPfamnZEVpXCJiOvCnwOeB90TE8UP/zT4GfGXYof8daIyI\nP6y0n9cVH4ZTSi8C/5fBAVoSEc1AN9BfyrpUEANAHYM/XE+KiB8CV+IvPtWmBjgc+M8ppTMY/IH7\nF6UtSfmUUuoGPgXURsSHIuIE4M8Y/OVH1eMZBsPRaRFxOHAqsLPENekgDf2t+39OKX0VuItXZ4cv\nBd4REW8aev4yg5MZ3cWvcmKqZjvmiHgPg38t82bgGymlipyq14FFxGkM/tXbL4AbU0rXl7gk5VlE\nTE0p7Rx6HMDhKaWXSlyWCiAi/h3wduB9wD+mlP6xxCUpjyKiHvgY8H4Gf8H9WkppRWmr0kRExGuB\nHwCfTSn961ArzPcCK4GmocfvSSn9voRlHrSqCcMAEVHH4OcznBWuUhHRyGBbpi+llPzrtioWEZP8\nbzkb7BZS3SJiLtCWUuordS2auIj4KHBuSun0oefvAf49cBTwqZTSC6WsbzyqKgxLkiSpMIZ1/VkJ\nbGJw+eK3gbWVtk54uIpfMyxJkqTCGwrChzC47OXDwDMppX+r5CAMFd5nWJIkSUV1KYMfbP7jalmu\n6DIJSZIkjUkl7jA3GsOwJEmSMss1w5IkScosw7AkSZIyyzAsSZKkzDIMS1IJRMRhEXHp0OMjh/p2\nSpKKzA/QSVIJREQz8C8ppRNLXIokZZp9hiWpND4HvD4i1gBPAyeklE6MiGXAB4Ba4ETgi8BkBrch\n7wHem1L6fUS8HrgWmA28AlycUnqy+G9DkiqbyyQkqTQ+Bfw2pbQQ+K/7fO1E4CPAKcDfAq+klBYB\nDwPnDx2zArgspbQYuBL4ZlGqlqQq48ywJJWfe1NKXUBXRGwDfjj0+lrgpIiYDrwZuC0idp8zpfhl\nSlLlMwxLUvkZvsXpwLDnAwz+3K4Btg7NKkuSJsBlEpJUGl1Aw3hOTCltB56LiCUAMeiN+SxOkrLC\nMCxJJZBS6gR+HhFPAF8YxyX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511ZgK0BfX18Rl66RI4Nkv6yU/fPR22rcIEmSJFXarME5pfSSEu8xAKzOe9wL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\nAElFTkSuQmCC\n", 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TQwTniJgC/Az4XGZ+Z5D9zgDOANh3330PXrVq1VCfQaq/yl/Pb9kEG35XnePu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\nSQUYnCVJkqQCDM6SJElSAQZ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kCpr2YcAnKnddZ5pVh/IIxl8GPgR8FegyGEuSlJPx0Lz74WdmfJ1pVhOrajCO\niIuAP0gpXR0Rv8FgLElSbXKmWU0o82AcEd8BVpV46f3AfwVekVLaP10wjogrgCsA1qxZs2Hbtm2z\nurYkSaqCyTPN1VzgxJlmVVDVZowjYh3wXeDpsV2rgR3AuSmlsj96OmMsSVIdqaWZZlcE1Bzl1q7N\nUgpJkppMXjPNk3s0Dw/C8jMNzZpitsG4rRqDkSRJDezUc+ENN5d+rZIzzaUeJNz9EPziNli8CtoW\nPnM9SzM0Cy7wIUmS8pHHTPPik2DxSh8AbDKufCdJkupXuZnmSq4I6PLZDctgLEmSGlP3jXDf5wrl\nGNXo0bzkWbBwycSe0D4AWFcMxpIkqblsvwd+ejP0/RL2bX9m5reapRkG5prkw3eSJKm5nHpu+UBa\najXALB4APLiz8Gvcvm2Fh/8sy6hLzhhLkqTmVW757JEh6N+R/fWWPAta2mwxV2WWUkiSJM1HcS3z\neMeMSj4AePxpLmRSIQZjSZKkSum+Ee76FAwPVL5jhnXM82YwliRJqrZSHTMqVZYxHpjHZ7OtYy7L\nYCxJklQrqtlibnIds4HZYCxJklTzilvMPbW7snXMk/sxN9Ey2QZjSZKkelatOuZFJ8DCpc9cowED\ns8FYkiSpEU0OzMODcLg/+zrm4sBc523lDMaSJEnNpFoP/tVhlwyDsSRJkkr3Y67EMtk1HJgNxpIk\nSSpvfNW/x+9/poNFJQLz+PLYOdYuzzYYt1VjMJIkSaoxp54Lb7h56v6sA3NxS7rbri78t0Yf7DMY\nS5Ik6RnlAnNWXTIe/KrBWJIkSXWs69LSgXaugfnZr6vgIOfHYCxJkqSjN11gLu6SUQf9kQ3GkiRJ\nyl65wFzDcutKERF9wLYcLr0GeDSH66q6vM/NwfvcHLzPjc973BzyvM+npZRWzHRQbsE4LxHRN5s/\nGNU373Nz8D43B+9z4/MeN4d6uM8teQ8gB/vyHoCqwvvcHLzPzcH73Pi8x82h5u9zMwbj/XkPQFXh\nfW4O3ufm4H1ufN7j5lDz97kZg/F1eQ9AVeF9bg7e5+bgfW583uPmUPP3uelqjCVJkqRSmnHGWJIk\nSZoi12AcEZsiYldEPJDR+b4VEfsi4rZJ+6+KiIcjIkXE8iyuJUmSpMaS94zxjcArMzzfNcCbS+z/\nEfAy8umbLEmSpDqQazBOKd0BTFhIOyLOGJv53RIRd0bE2XM433eB/hL770sp/WbeA5YkSVLDqsUl\noa8Drkwp/SoiXgh8CnhpzmOSJElSg6upYBwRi4EXA5sjYnz3wrHXLgY+WOJtj6WULqzOCCVJktSo\naioYUyjt2JdSWj/5hZTSV4Dt7+/vAAATe0lEQVSvVH9IkiRJagZ5P3w3QUrpALA1IjYCRMHzcx6W\nJEmSmkDe7dq+APw7cFZE9EbE24A3Am+LiJ8CPwNeN4fz3QlsBv5g7HwXju3/i4joBVYD/xER12f9\ne5EkSVJ9c+U7SZIkiRorpZAkSZLyktvDd8uXL0+dnZ15XV6SJElNYsuWLbtTSitmOi63YNzZ2Ul3\nd3del5ckSVKTiIhZrX5ca+3aJEmSVEc2P7SZmx68iYHhAZYsWEL/YGER4iULljA0OkR7Szv9g/10\ntHXwpme/iY1nbcx5xOUZjCVJknRUNj+0mQ/eVbT+2lOU/nrM+LG1Go59+E6SJElH5au//uqc3/Od\nR79TgZFko6ZmjIeGhujt7WVgYCDvocxJR0cHq1evpr29Pe+hSJJUNT27evj6r7/Or/f9msefehyY\n+vH5+L7ZfD2X91XjGo5t5vftHdhb9u9HOS9b87I5v6dacutj3NXVlSY/fLd161aWLFnCsmXLiIhc\nxjVXKSX27NlDf38/a9euzXs4kiRVRc+uHt56+1sZGh3KeyiqEcs7lrNs0bKarDGOiC0ppa6Zjqup\nGeOBgQE6OzvrJhQDRATLli2jr68v76FIklQ13Tu7DcWa4I3PeSOXr7s872HMS00FY6CuQvG4ehyz\nJGl+enb1cMMDN/CbA7+hvaW9pj8+r8TH7m0tNRchlKO2lja6TppxQrbm+bdakqQ56tnVw6XfvJQR\nRsofVO7p/Bme2q/J9023b8zyjuUsaF1QE6E97/c129jOPvFsLjvnMtavXF/270e9MBhP0trayrp1\n645s33rrrbhCnySpWPfO7ulDcRNqhI/RJYPxJIsWLaKnpyfvYUiqA5Ob2uc9a1PLM0qNNrbBkcHp\n/mo0nUb5GF2q+2Dcs6uH7p3ddJ3UVbEp/Msvv/zI8tWPPfYYV111FR/4wAcqci1J9eGff/HPfOju\nDz2zI8uPqGvlfY5t+vcVWbNkDW0tbTUR2rN830zHDo0O0bm0s2E+RpdqNhh/9J6P8osnfzHtMQcH\nD/LQ3odIJILgrBPOYvGCxWWPP/vEs/mrc/9q2nMeOnSI9esL/7jXrl3LLbfcwvXXXw/Atm3buPDC\nC7n00kvn9puR1HC+9sjX8h6CakQQ/NGZf2QZgdQAajYYz0b/UD+JQh/mRKJ/qH/aYDwb5UopBgYG\n2LhxI5/4xCc47bTT5nUN1b/ND23mlodvYXBksC4/Bs7yfc06ticHniz790PNpb2l3TICqUFkGowj\nohXoBh5LKb1mPueaaWYXCmUUb//224/8T+wj53+kYh/lXHnllVx88cW87GW1u1qLqmPKuvCT1cvH\nwI340Xa1rzFmvKl9rYT2+b7Psc3ufScfezKnH386F51xkWUEUoPIesb4auBBYGnG5y1p/cr1fOYV\nn6l4jfEnP/lJ+vv7ed/73leR86u+fHvbt/MegmqMT+NLUmPILBhHxGrgfwU+DPzvWZ13JutXrq/4\nT+p/8zd/Q3t7+5Ha4yuvvJIrr7yyotesdeON7cfrwJtpRmlgeCDLP0rVOZ/Gl6TGkeWM8ceA9wJL\nMjxn1R08eHDKvq1bt+YwktrVs6uHt3zzLUfqu4Gm/Pgc4KRjTuLY9mNrJrQ34g8itTy2RmpqL0nK\nKBhHxGuAXSmlLRFxwTTHXQFcAbBmzZosLq0cdO/snhiKm9gZx5/BP778H/MehiRJykBLRuc5D7go\nIn4DfBF4aUTcNPmglNJ1KaWulFLXihUrMrq0qu35K56f9xBqxsvW+DCmJEmNIpMZ45TSfwH+C8DY\njPF7UkpvOspzERFZDKtqUmqu2dNVx64C4OwTzubA4AGguT4+X7JgCe2t7Vz8ny5m41kbM/tzlSRJ\n+aqpPsYdHR3s2bOHZcuW1U04TimxZ88eOjo68h5K1ex6ehcA797wbl58yotzHo0kSVI2Mg/GKaXv\nA98/mveuXr2a3t5e+vr6Mh1TpQ3GIDftuImfdv8UqK+Zz6N533h98X277jMYS5KkhhF5lQF0dXWl\n7u7uXK6dpZ5dPbz5m2/Oexi5+esX/bXlBJIkqaZFxJaU0oy9NbN6+K5p3f343XkPIVffefQ7eQ9B\nkiQpEwbjebhv133cvvX2vIeRK7sySJKkRlFTD9/Vk55dPfzZN/9sQj/f4xYcx7HtxzZ8jbFdGSRJ\nUiMyGB+lUotcPHf5c13sQZIkqU5ZSnGUuk6aWr9tWYEkSVL9csb4KK1fuZ7F7YtZumApJy460bIC\nSZKkOmcwPkqHRw5zcOgg5yw/h3etfxfrV67Pe0iSJEmaB0spjtIPtv8AKLRre/u3307Prp6cRyRJ\nkqT5MBgfpR899iOgsArc0OgQ3Tvrf7ESSZKkZmYwPgqbH9rM97d/H4AWWmhvaS/5MJ4kSZLqhzXG\nc7T5oc188K4PPrMj4L0veK81xpIkSXXOGeM5+sbWb0zYHk2j7B/cn9NoJEmSlBWD8RwtXbB0wnZb\nS5tlFJIkSQ3AYDwHPbt6+EHvD45sb1i5gRsuvMEyCkmSpAZgMJ6D7p3djKQRAFqjld9d/buGYkmS\npAZhMJ6DA4cPHPnaThSSJEmNxWA8S5sf2swNP7vhyPYlZ1/ibLEkSVIDMRjP0re3fXvC9kN7H8pp\nJJIkSaoEg/EsrTpm1YTtl615WU4jkSRJUiW4wMcs9Ozq4battwEQBJc+91I2nrUx51FJkiQpS84Y\nz0L3zm6GR4cBaIkWli5cOsM7JEmSVG8MxjPo2dXD/X33H9lujVa7UUiSJDWgzEopIuJU4HPAKmAU\nuC6l9PGszp+Hnl09vPX2tzI0OnRk32gazXFEkiRJqpQsZ4yHgf8jpfRs4EXAuyLiORmev+q6d3ZP\nCMUAI2mE7p3dOY1IkiRJlZJZME4pPZ5S+snY1/3Ag8ApWZ0/D10nddFK64R9LuwhSZLUmCrSlSIi\nOoHfBu6uxPmrZf3K9Vyw5gLu6L2D8085n2WLlnHRGRe5sIckSVIDyjwYR8Ri4F+Av0wpHZj02hXA\nFQBr1qzJ+tIVMZJG6Dyuk4+/tK7LpSVJkjSDTLtSREQ7hVD8+ZTSVya/nlK6LqXUlVLqWrFiRZaX\nzlzPrh6u/t7V/PixH7P76d307OrJe0iSJEmqoMyCcUQE8FngwZTStVmdNw89u3p4yzffwve2f4/B\n0UH2Ht7LZbdfZjiWJElqYFnOGJ8HvBl4aUT0jP16dYbnr5p7n7iXRJqwb3h02G4UkiRJDSyzGuOU\n0g+ByOp8uUpTd7W1tNmNQpIkqYFVpCtFPevZ1cOn/+PTAATByceezNknns1l51xmNwpJkqQGZjCe\npHtnN8OjwwBEBBvP2sjl6y7PeVSSJEmqtEy7UjSCrpO6aInCH8uClgWWT0iSJDUJg/Ek61euZ8NJ\nGzh+4fF85hWfsXxCkiSpSRiMSxgaHeLME840FEuSJDURg/Ek9z5xL/ftuo+dT+20b7EkSVITMRgX\n6dnVw+W3Fx60e7T/Ud52+9s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000/X/v37PTs3wXkojVulPVv61wOF0jmf8a89AAAA2aZxq7T5m54OrrBixQo9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\n3KTbF92ecNSNuuY6ffbJz9L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8imOjh23ZQ/9bAXsALcCvI2JiZr4AjMvMpyLincCtEfEw8FIFfZY2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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "results.plot(y=['elevator', 'aileron', 'rudder', 'thrust'], **kwargs);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Doublet " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values." + ] + }, + { + "cell_type": "code", + "execution_count": 291, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.utils.input_generator import Doublet" + ] + }, + { + "cell_type": "code", + "execution_count": 292, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "de0 = trimmed_controls['delta_elevator']" + ] + }, + { + "cell_type": "code", + "execution_count": 293, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "controls = controls = {\n", + " 'delta_elevator': Doublet(t_init=2, T=1, A=0.1, offset=de0),\n", + " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", + " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", + " 'delta_t': Constant(trimmed_controls['delta_t'])\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 294, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "sim = Simulation(aircraft, system, environment, controls)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once the simulation is set, the propagation can be performed:" + ] + }, + { + "cell_type": "code", + "execution_count": 295, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n", + "time: 0%| | 0/90 [00:00" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "results.plot(y=['x_earth', 'y_earth', 'height'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": 297, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\plotting\\_core.py:1716: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n", + " series.name = label\n" + ] + }, + { + "data": { + "image/png": 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kSaqSMyDW265DzEUz988aW4ckSZJqzjBdb0e8b/D10wd93lKSJEltxDBdb4Zm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\nmA8wY8aMRtUkSZKkOrntlNv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5RI899ph23z1GqA8IPcyZ0LWHuUdP6bNnSo3zO+9f8VT22gQAAEpXjJ7gHd5d\nKv3mDKlte6ijb9JtaS+0dvbZZ2vBggX64IMPNGXKlIjHuLsuv/xyfetb3+q0/+mnn9b//d//6fnn\nn9duu+2m4447Ts3NzRowYIBeeeUVPf7447r55ps1f/58/frXv06rnfEQmDOhaw9z63Zp0q3dAzPT\nywEAgHyxz3jpgj9JK/8q1RwTyKrEU6ZM0UUXXaR169bpL3/5S8RjTj75ZP34xz/Wueeeq759++q9\n995TRUWFNm7cqAEDBmi33XbT66+/rhdeeEGStG7dOvXs2VOTJk3Sfvvtp6lTp0qSqqqqtGnTprTb\nHAmBORMi9TBLoXqgjlsdHeZNlKY9mZ12AQAAxLLP+ECCcodRo0Zp06ZN2nvvvTVkyJCIx5x00kla\nvny5jjjiCElS37599bvf/U6nnHKKbrnlFh166KE66KCDdPjhh0uS3nvvPX39619Xe3soU/30pz+V\nJE2dOlXTp09X79699fzzz6t3796BfR/msZZwzpG6ujqvr6/PdTNSd8Mo6ZOmnduDDpK+szRUs7wi\nQjielV6NEAAAQFfLly/XwQcfnOtm5I1IPw8zW+bucUcJMugvaO8u7RyWJanPoND/z38g8nMY/AcA\nAJC3KMkI2iv/233f4AN3fl3eM1RMv6tIvc4AAABFpLGxUeedd16nfb169dKSJUty1KLEEZiDtvaN\nLjtMOuycnZuHXyw9O6f782b1ozQDAAAUrdGjR6uhoSHXzUgJJRlB67qCX799OhfPn3hVaF7mSGb1\ny1y7AAAAkBICc9A66pU79N+n+zFffyT68wnNAAAgIPk4uUMupPtzIDDnwj7jpdFfif44oRkAAKSp\nsrJS69evL/nQ7O5av369KisrUz4HNcxB61qS0XW7w6RbpfVvS6uXRX6cmmYAAJCG6upqNTU1ae3a\ntbluSs5VVlaquro65ecTmIPWZ5C07o3O29FMe1L6w0URVgAMIzQDAIAUVVRUaPjw4bluRlGgJCPX\nJt0qXbgo+uOUZwAAAOQUgTlon67pvB2tJGNX+4yP3ZP8swOjPwYAAICMIjAHraW583aPnok/N1pP\n8+YPpfo7U24SAAAAUkdgDtK7S6VP3u28rzyJwLzPeGnExMiPPfzd1NsFAACAlBGYg/Tsjd33jTk/\nuXOc/4DUY7fIj10zJPk2AQAAIC0E5iCte7Pzdp+9pLqpyZ/nR+9H3t+6JTSrBgAAALKGwBykrvXK\nVXumfq7TI/RWS9GnoAMAAEBGMA9zkFq3x95ORt1U6a/XSxvf6f7YtdXSD5tSPzfy07XV0vZN6Z/n\nqBnSiVelfx4AACCJwBysrj1XJRYAAAAgAElEQVTMycyQEcl/NEqz+kvqsqTl9k3SoisJRYVu0ZXS\ns3OCP++zc3aet7yX9OM1sY8HAAAxEZiDFGQPc4cLn5BuP7H7/mfnEJgL1TVDQvXo2dC2befiNz12\ni14fDwAAoqKGOUhB9zBLoanm+g2L/Ni1qa+Jjhy4ao9QeM1WWO6qdUt4ufV+DB4FACAJBOYgbf6o\n83bzJ8Gc9z8aI+/vKM1Afrt6UCikeluuW7JT4/xQm1hFEgCAuCjJCNK2LgHZPfJxqTj9xsiLl1Ca\nkb9m10jNHyf/vNFfkSbdmvzzUhk0uPnDUHDus5f0g38k/5oAAJSAuD3MZraPmT1lZsvN7O9m9t3w\n/snh7XYzq4vx/P5mtsDMXg+f44ggv4G8UX9n97AyZHRw56+bGgo1kfxXGtPXIXh3nRUKoYmG5R67\nSbM27vyTSliWQjOndJwj2rSE0XQEZ3qcAQDoJpGSjFZJl7r7wZIOl/RvZvZZSa9K+rKkxXGef6Ok\nx9x9pKTDJC1Po735a8nc7vuOmhHsa0TrAWzbRk1qvpjVT1rxZGLHHjUjFG4zMRCvburO8JzMddgR\nnG8aH3ybAAAoUHEDs7u/7+4vhb/epFDg3dvdl7v7G7Gea2a7SzpW0u3h52939w3pNzsPbe3ybfXe\nIzRgL2gXLoq8nwVNcmvexJ2zUcRUtjPIZquU5sSrdr5m5YDEnrPujdD3c9dZmW0bAAAFIKlBf2ZW\nI2mMpCUJPmWEpLWS7jCzl83sNjPrE+Xc08ys3szq165dm0yz8lN5ADNkRLLPeGnQQZEfozQjN2b1\nl1Yvi3/chYukWSnUNAdp5spQcB46NrHjVzwZCs7vLs1oswAAyGcJB2Yz6yvpD5JmuHui0z/0kPQ5\nSXPdfYykzZJmRjrQ3ee5e5271w0ePDjRZpWm7yyVZN33U5qRXe8uDfcqxxncOforoZCaiTsOqZr2\nZHLB+fYT+UAGAChZCc2SYWYVCoXl37v7/Umcv0lSk7t39EgvUJTAXPCCnBEjEdEWNGmcn/qgMSRu\n3sT4vcqFsFDItHC9dSLfT8ciKP2GRZ/qEIXhZweG6tWz4fQbQzX1AFDA4gZmMzOFapCXu/sNyZzc\n3T8ws3fN7KBwvfPxkl5Lral5ruuUcm3bMvt6HaUZ6yKUkV89SLpiXWZfv5RdPUhqb4l9TKGFhI7g\n/PPR0sZ3Yh+78Z1QcC6077EUZWr59WQ8/N3IU2IOHbvzugOAPGcep2fUzI6W9FdJjZLaw7t/KKmX\npP+RNFjSBkkN7n6ymQ2VdJu7nxp+fq2k2yT1lLRC0tfdPWYhZ11dndfX16f8TWVd/Z3dfyHsNkj6\nf29n/rVn9VfEkoARE6XzH8j865eaeAP7yntJP16TnbZkUqJzSJdV8OEsn9x1VuKztOQjQjSALDOz\nZe4edXrkHcfFC8y5UHCBec5oaUOXXrmjZmRnFoR3l0YuzZBCNaoITrywnOqCI/ks2geyrijTyJ2r\n9sivVSSDxAcyABlGYM6ma/aSWpt3blu5dOVH0Y8PWrT602y3o1hFuoPQVTF/OEnmtj5lGpn3h4tK\nexrJbHVGIHg3jY9cRphJfOhCHATmbOraw1PWQ7pifW7b0IFbnOmJ9wZfSh9KEv1lxy+o4GUqJGfy\n/eG/9sz8WA6J8rNcy0UIzrRiKa1DQgjM2RKpJMLKpCtzMN9utJKBCxfl15RmheLa6u7Lne+qz17R\nV18sZrMGaOdwhhhK9ecTlETubCQqn2ZsyfQMHYMOCk+9iUAUel18pvGBreARmJOVyOwAiaroI/3n\n6mDOlYxYb2zFXDKQCfFmwij128LJlGkUY213JgXRM1toH1aCfP/tKp8+LOSrfJhNpdiV0t3IeGKN\nu8jB7wsCczKCfrPOZZiKdiFWDgit8ob44g1048PHTsncjqW+Obp034OK7Zfxu0ul209WQncyUlGq\npWrx7poh/+RTeUgmP9juKsuhmcCcjERnAkj4fDkOVNFKM0q9VzQR8WbCyPXfbb5KdKaGYgt26Ui3\nV69nlfTDpuDak+8yHfaKpZQjkUWIci0bs+q8u1S6/SQF+rsd2dF7gHTZyqy9HIE5GUF+asqHnotY\nv4gJfNERltOTTM1tqYW9XV0zRGrdktpzS/nn1lWic4WnKx/vziWyeFK2FcMHDkJ2fqCHOXEFW8Oc\nD2G5Q7TeGGYwiCxmWC6TZuVgEGehSqaHq1TqS9OZSSCfbsnms2zdLo7IpNPnpFdylO+zTeTjB4dc\nytYHtlJDDXNyCmqWjHwWLQQyqrezWGG5VAJdJiRzC70Yf87pllxQ850eBrIlrxj/HeaDYl5cKFV5\nVJ5HYEbsW+SUF4TECsuFNtNAvkrql4VJFz5R2NMgpnO7PJ/uUhWjTE9pVyiYuSb/BTmtZNCKofxm\nFwRmhMS6TVnKoTnWkuJS0b0h5Fwqb/6FFB7TmQqOXr3cymkpRwaxXD2QEAIzdoq20ESp1jPHC2+U\nrGROqrfJ8608IYhpz/Lte0Jneb8EeRHcjQHyAIEZnUUrPSi1ntR4gY1bldmRTn1prqZHDOJ2Pr1+\nxSfoJcBL7T0ZyDECMzqL1ataKj1d8WZvKJWfQz5Jd2BWJu+SBBWEKLkAgLxFYEZ3pVzPHK93sNi/\n/0IQ5NyyiQbpTM2kYGXSNx7ndjkA5DkCMyKLVs8sFW9ojDe9WbF+34WqkGcy4C4FABQUAjOii1bP\nXIyDAOPdVics57eg60ODVoz/ZgCghCQamHtkozHIM6ffGLmeub0ltHpRsazmFG/+X8Jy/tt1hbt0\nlpQOErOoAEDJITCXorqp0kt3RR4A1/xxaInWQh+lHXOpaxGWC9GuA+eCmNYtIQEseQwAKHiUZJSy\n2TWhgBxJIU+vRlguXe8ulW4/SVKS72vMZAEAJYmSDMQ3c2X0soXG+dK+RxVWz1q81ftk0qwNWWsO\ncmCf8fwdAwACV5brBiDHrvwo+mMPfzc0f3MhuOus2GG5rIIgBQAAUkJgRuwShUIIzdcMkVY8Gf3x\nygHMZAAAAFJGYEZIvND8h4uy15ZkzOoXe+aEoWOLZ9YPAACQEwRm7BQrNDfOD82ekS/q74w/uO/0\nG6VpMXqeAQAAEsCgP3Q2a2P0ILrujdBCErvOjZsL8Vbuk5gJAwAABIYeZnQXK2y2bYvfs5sp7y4N\nvXbMsGyEZQAAECgCMyKLFzpn9ctuXfO11XGmjFNocB8zYQAAgIARmBFdvNDcOF+a1T+zbbhpfAK9\nypKOmsHgPgAAkBHUMCO2WRulWQMUfQliDwXaygHBBtZ5EyMv3R0JJRgAACCDCMyIb9bH0s9HSxvf\niX5M88eh4JzuEsOJDOjrMHQss2AAAICMIzAjMf/RGJrK7eHvxj6udcvOQYHlvRKbUePqQVJ7S3Lt\noVcZAABkibl7rtvQTV1dndfX1+e6GYjmmiGxFwvJpBETpfMfyM1rAwCAomJmy9y9Lt5xcQf9mdk+\nZvaUmS03s7+b2XfD+yeHt9vNLOoLmdlKM2s0swYzIwUXgx+9H1oUJJv6DQv1KhOWAQBAliVSktEq\n6VJ3f8nMqiQtM7NFkl6V9GVJv0rgHF9w93VptBP5pm5q6M9dZ0krMlhH3Gcv6Qf/yNz5AQAA4ogb\nmN39fUnvh7/eZGbLJe3t7oskycwy20Lkt44e30Tqm5Nx1AzpxKuCOx8AAECKkhr0Z2Y1ksZIWpLE\n01zSE2bmkn7l7vOinHuapGmSNGzYsGSahXzQ0eMspRaerUz6xuPSPuMDbhgAAEB6Eg7MZtZX0h8k\nzXD3T5J4jaPcfbWZ7SlpkZm97u6Lux4UDtLzpNCgvyTOj3yza3gGAAAocAkFZjOrUCgs/97d70/m\nBdx9dfj/a8zsAUnjJXULzLtatmzZOjNblczrBGSYpBiTDaOEcW0gFq4PRMO1gWi4NvLDvokcFDcw\nW6hI+XZJy939hmRaYGZ9JJWFa5/7SDpJ0tXxnufug5N5naCY2dpEphZB6eHaQCxcH4iGawPRcG0U\nlrjTykk6StJ5kiaGp4ZrMLNTzewsM2uSdISkhWb2uCSZ2VAzeyT83L0kPWNmr0haKmmhuz+Wge8j\nKBty3QDkLa4NxML1gWi4NhAN10YBSWSWjGckRZsKo9ukuOESjFPDX6+QdFg6Dcwylo9DNFwbiIXr\nA9FwbSAaro0CkkgPcymJOIMHIK4NxMb1gWi4NhAN10YByculsQEAAIB8QQ8zAAAAEAOBGQAAAIiB\nwAwAAADEQGAGAAAAYiAwAwAAADEQmAEAAIAYCMwAAABADARmAAAAIAYCMwAAABADgRkAAACIgcAM\nAAAAxNAj1w2IZNCgQV5TU5PrZgAAAKCILVu2bJ27D453XF4G5pqaGtXX1+e6GQAAAChiZrYqkeMo\nyciAG+pv0An3naCpj05Vw5qGXDcHAAAAaSAwB+yG+ht0x9/v0IdbPtSyNct03qPnEZoBAAAKGIE5\nYPe+cW+3fde8cE0OWgIAAIAg5GUNcyHb1rqt2763N7ydg5YAAIBS0NLSoqamJjU3N+e6KXmrsrJS\n1dXVqqioSOn5BOaAVfao1ObWzZ32lZeV56g1AACg2DU1Namqqko1NTUys1w3J++4u9avX6+mpiYN\nHz48pXNQkhGwfr36ddu312575aAlAACgFDQ3N2vgwIGE5SjMTAMHDkyrB57AHLA+Pfp029ejjI58\nAACQOYTl2NL9+RCYA7axZWO3fQN6DchBSwAAABAEAnOAGtY0aM2WNbluBgAAAAJEYA7Qn97+U8T9\nL695mbmYAQAAupg6daoWLFiQ62bERWAO0Pqt6yPub1e7Hnr7oSy3BgAAILKGNQ26rfE2OvQSxGi0\nLFm3dV2umwAAAIrcfy/9b73+0esxj/l0+6d64+M35HKZTAcNOEh9e/aNevzIPUbqsvGXxTznZZdd\npn333VcXX3yxJGnWrFmqqqrSpZde2uk4d9cll1yiJ598UsOHD5e773jsz3/+s77//e+rtbVV48aN\n09y5c/XKK69o9uzZuv/++/XHP/5RU6ZM0caNG9Xe3q7PfvazWrFihY477jhNmDBBTz31lDZs2KDb\nb79dxxxzTLwfVVLoYQYAACghm1o2yRUKqi7XppZNaZ9zypQpuvfenasdz58/X5MnT+523AMPPKA3\n3nhDjY2NuvXWW/Xcc89JCk2NN3XqVN17771qbGxUa2ur5s6dq8997nN6+eWXJUl//etfdcghh+jF\nF1/UkiVLNGHChB3nbW1t1dKlSzVnzhxdddVVaX8/XdHDDAAAUCTi9QRLoXKMi564SC3tLaooq9Ds\nY2ards/atF53zJgxWrNmjVavXq21a9dqwIABGjZsWLfjFi9erK9+9asqLy/X0KFDNXHiREnSG2+8\noeHDh+vAAw+UJF1wwQW6+eabNWPGDO2///5avny5li5dqu9973tavHix2traOvUif/nLX5YkjR07\nVitXrkzre4mEwAwAAFBCaves1a0n3ar6D+tVt1dd2mG5w9lnn60FCxbogw8+0JQpU6IeF2lO5F1L\nM7o65phj9Oijj6qiokInnHCCpk6dqra2Nl133XU7junVq5ckqby8XK2trWl8F5FRkgEAAFBiaves\n1TdHfzOwsCyFyjLuueceLViwQGeffXbEY4499ljdc889amtr0/vvv6+nnnpKkjRy5EitXLlSb731\nliTpt7/9rT7/+c/veM6cOXN0xBFHaPDgwVq/fr1ef/11jRo1KrC2x0MPc4AG9R6U6yYAAADkxKhR\no7Rp0ybtvffeGjJkSMRjzjrrLD355JMaPXq0DjzwwB2huLKyUnfccYcmT568Y9Df9OnTJUkTJkzQ\nhx9+qGOPPVaSdOihh2rPPffM6uqGBOYAjdxjZNTHBvYemMWWAAAAZF9jY2PMx81MN910U8THjj/+\n+B0D/HbVu3dvbdu2bcf2vHnzOj3+9NNP7/h60KBBGalhpiQjQMs/Wh71sYP3ODiLLQEAAEBQ6GEO\nULSFSyTFnRMRAACgWDQ2Nuq8887rtK9Xr15asmRJjlqUHgJzgGLVMLNwCQAAyBR3z2pNbzyjR49W\nQ0P+rCIYaxaORFCSEaBYNcwAAACZUFlZqfXr16cdCouVu2v9+vWqrKxM+Rz0MAfotfWvRX2MQX8A\nACATqqur1dTUpLVr1+a6KXmrsrJS1dXVKT+fwByglvaWqI8x6A8AAGRCRUWFhg8fnutmFDVKMgI0\nvF/0i5VBfwAAAIWJwByg599/PupjDPoDAAAoTBkPzGb2azNbY2avZvq1cqlhTYNefP/FXDcDAAAA\nActGD/Odkk7JwuvkVP2H9WpX+47tsvB/HRY3LVbDmvyZXgUAAACJyXhgdvfFkj7K9OvkWr+e/Tpt\nXzDqAo37zLgd263eqofefijbzQIAAECa8qaG2cymmVm9mdUX4rQoXZfF/rTlU/Uo6zwJCXXMAAAA\nhSdvArO7z3P3OnevGzx4cK6bkzSTddvuYczaBwAAUOhIdAHpusrfyD1GytV5xR0WLwEAACg8edPD\nXOg2bt+442uTaeP2jd0WK2HxEgAAgMKTjWnl/lfS85IOMrMmM7sw06+ZC7sO+nO5+vXs122xEhYv\nAQAAKDwZL8lw969m+jXyQddBf8s/Wq71W9d32segPwAAgMJDSUZAIg3661qzTA0zAABA4WHQX0Ai\nDfrrihpmAACAwkNgDkikkoyuvc7UMAMAABQeSjICEqkko2vNMjXMAAAAhYfAHJBESjIAAABQeAjM\nAYlUksGgPwAAgMJHDXNAIpVkdO1lZtAfAABA4aGHOSCRSjJYuAQAAKDw0cMckFfXvdppm4VLAAAA\nigM9zAH5cMuHnba7hmUAAAAUJgJzQNra27rtY5AfAABA4SMwB6RVrd32nbHfGSq38h3bi5sWq2FN\nQzabBQAAgDQRmAPS2tY5MA/qPUi1e9bq8CGH7zzGW/XQ2w9lu2kAAABIA4E5AA1rGtS4tnHHdg/r\noX/Z718kSRVlFZ2OZeAfAABAYSEwB+BPb/9JbdpZw3xs9bGq3bNWklRm/IgBAAAKGWkuAMyIAQAA\nULwIzBnG8tgAAACFjcCcYV2Xw2Z5bAAAgMJCYM4wlscGAAAobATmDOs6KwazZAAAABQWAjMAAAAQ\nA4EZAAAAiIHAHICN2zbG3AYAAEDhIjAH4OPmjztvb/s4ypEAAAAoNATmAPTp2afT9oBeA3LUEgAA\nAAStR64bUAw+2fZJrpuAFJ1838lavWV1WufoV9FPz5zzTEAtAgAA+YbAnKaGNQ1atWlVp33b27dH\nPZ765uwZe9dYbffofxdB2diyUaN/MzruceUqV8MFDRlvDwAACBaBOU13vHpHt31n7X/Wjq+7LoX9\n0pqX1LCmQbV71ma8baVi3G/Hqbm9OdfNiKtNbVGDdQ/10MsXvJzlFgEAgEQQmNPUdeW+fj37afJB\nk3dsn7HfGbrvH/ft2Ha57nj1Dt048castbGYfOGeL2jdtuJb/KVVrRHDtMl01xfv4gNWkUv2uj5y\nyJH61Um/ymCLAAC7ykpgNrNTJN0oqVzSbe4+Oxuvmw2bWzbHfLx2z1oN2W2I3t/y/o59Kz9ZmeFW\nFY9slVXkK5frvEfP67a/p/XUsvOX5aBFkKQb6m/QHX/vfncpW557/7mEyoCSNWL3EfrjWX8M/LwA\nUOgyHpjNrFzSzZJOlNQk6UUz+5O7v5bp186G5tbOpQAtbS3djhnad2inwMwsGtHlqrxi9MDRuvv0\nu5N6zree+Jaee/+5DLUotu2+PWJgYgBieg7/3eHa3Bb7Q3AxW/HJipSCOCVFwTn67qO1sYWxLvH0\nKe+jF772Qq6bUfSyfT2eNvw0zT42P/tUs9HDPF7SW+6+QpLM7B5JX5KUV4H5xPtO1AdbPkj7PO1q\n77avX69+MbdLWRCzVMSSyZKGZG6J1/6mVm1qC7wNXUUbgFhZVqkXz3sx46+fz7L1d1CKopUUJaOQ\n7ppwLeXe5rbNGbnLgtxa+M+FkpSXoTkbgXlvSe/ust0kaUIWXjdhJ993ciBhORpWAtwpk7eyvz7q\n6/pe3fcycu50xZodIxu/fJvbm6P+cin02Tty2dOP4ES7awKgtDzzXn7eJc1GYLYI+7zbQWbTJE2T\npGHDhmW6TZ0E2cN5/LDju+3ruvJfqa0EOOY3Y9Sq1kDPmUoJRb6KFlYz8XOLJNbsHbvKZi91ocx8\nErR4g/m4XQ+g2B2999G5bkJE2QjMTZL22WW7WlK3hOru8yTNk6S6urpugTqThu42NLDQHOk2Qtea\n5WKvYc7EL/UrDr+i0+wjpSBSTeh9b9ynq1+4Ogetid1LXaqyXeqSqfr0Lz3wJa34ZEVGzg0AiSr1\nGuYXJR1gZsMlvSdpiqRzsvC6CXt88uNp19KmM+glWplCoYxYz8RUb6UYkBMx+aDJEX8ulCUEK5/f\ntDMhnfcZ6nkzg6kDI8v1DDWlqtTeEyMx98x35prZqZLmKDSt3K/d/Sexjq+rq/P6+vqMtytbTl5w\nslZv3hnGh/YZqsfPflxSYv/4Gy9ozGj7kpWJ2+XFVGKRT3LZI52PCr1euxgV6jXKtQQUBzNb5u51\ncY/LRmBOVrEH5n49++mZr4ZurSZ6iztX0zZlqpaUWRvyQzH1DjKlHgAgWYkGZlb6y4KRe4zsFJg3\nbt+o+964T7977XcJnyPatE1BTMV0zsPnqHF9ZnuxWbEuPyXSQ5bLW6CU5gAA8gE9zFnQsKah22pt\nI/qN0IqNxT3Ihho8AACQz+hhziO1e9aqT48+2ty6cwWxVRtXRTz2t1/8rS77y2UZXcwjU6hDBgAA\nxYjAnCVde/Ij1Y1WVVSpds9aPT45NCAw3+tLuV0OAABKAYE5S8wird/S2S9P+GWn7Y760nwIzvm8\nih4AAEAmEZizJF6teM+ynlEHxEUamJWJqZgG9Rqkp6Y8Feg5AQAACh2BOUv6V/bXls1boj4+c/zM\npM4XbQELAAAABKss1w0oFd8c/c2YjxN+AQAA8hOBOUtiBeIjhxyZxZYAAAAgGQTmLBo9sPvCI2Uq\nY65iAACAPEZgzqK7T7+7U2juU95Hr1zwSg5bBAAAgHgY9JdlLOwBAABQWPJyaWwzWysp8lJ4mTVM\n0js5eF3kP64NxML1gWi4NhAN10Z+2NfdB8c7KC8Dc66Y2dpEfmgoPVwbiIXrA9FwbSAaro3CQg1z\nZxty3QDkLa4NxML1gWi4NhAN10YBITB3tjHXDUDe4tpALFwfiIZrA9FwbRQQAnNn83LdAOQtrg3E\nwvWBaLg2EA3XRgGhhhkAAACIgR5mAAAAIAYCMwAAABBDyQVmM2OxFgAAACSsZAKzmfUws+skXW9m\nJ+S6PcgvZna+mX3ezPqFt0vm3wZiM7NJZlZrZuXhbct1m5A/eO9ANLx3FJeSGPQXvkhvltRP0iOS\npkp6UNJt7r4th01DDoWvi89IultSu6S3JFVJ+nd3X2dm5qXwDwTdhK+NYZIWSPpE0npJb0i63t03\ncG3AzD4j6R5JbeK9A2G8dxSvUvkkXCWpVtJ0d/+9pOskHShpck5bhZwxs/Lwm1aVpPfc/XhJ/yZp\nnaRf5bRxyCkz2z18bewt6cXwtfFjha6Vn+S0ccg5MxtqZoMUuh6aeO9ABzPrG37vGCppCe8dxaUk\nArO7fyJppUI9y5L0rKSXJR0R7iVAiQiX5lwr6Voz+7ykgxTqIZK7t0r6rqQjzezz7u7cXi0tZvZv\nkhab2WclVUsaEn7obUk3SDrazMaFrw1ur5YQMysLv3e8IOkQhTphJPHeUep2+b3ygJl9TdKXJO0e\nfpj3jiJRSv+gH5BUa2ZD3P1TSY2StmvnL0QUuXBAXiZpgEK3UP9LUoukL5jZeEkK9w5cLWlWeLs9\nJ41FVu3yC6xKUrOkaZL+IKnOzMa4e6u7vyPpToV6E8Vt1ZJznqSRkg5z96clLVQoBPHeUcLMbIBC\nZX39Jc2RdKakJZJOMLNa3juKRykF5mcUqiWaKknuvkzSOEm9c9gmZFe7pOvc/dvufqukVyUNl3SF\npLnSjgE7D0haa2b75qylyKpdegT30s7xDidJulzSbClUxiOpXtKW8C9JlIjwB6oDJP3C3T82syMk\nVUi6TaESP947SldfSTXufrG7L5S0VdJ7CpVgXC3x3lEsSiYwu/v7Cg30+6KZTTazGoV6klpz2S5k\n1TJJ8ztGLCtUmjPM3e+UVG5ml4R7haoltbn7qhy1E1lmZmXhv/t1kjZLekLS1xTqKTrUzM5x9zZJ\nu0nazd0/zl1rkW3hHsFBkr5sZpdIuknSLQrddq81s/PDh/LeUWLc/V2FgvCdZvZ/ko5U6IN2i6Sj\nzGwK7x3FoWQCsyS5+3OSfirpi5Iek/Sguy/NbauQLe6+xd23hd+8JOlESWvDX39d0sFm9rCk/5X0\nksQ0QKVil9vnoyU9rtD7w6EK3Wr9paSvmtn88NdLJK6NEnSzpLGSRrn7WIXuTL2j0AfxQyX9SaHr\nhfeO0jNZ0nOSVrv7fgp9oOor6WlJZ4XfO+aK946CVhLTynVlZhUKdRrQu1yCwj3MrlAN4iXu/paZ\n7a9Q7+Ihkv7p7u/lso3IDTO7XKE61VpJGxXqJTrd3bea2RmSXg73KKHEmFmlQqHnMHf/XHjfNIXK\n+n4h6QuS3uC9ozSZ2VRJh7r798Lb1yn0YeqPkk4Q7x0Fr6R6mDu4ewthuaS1K1R/uE6h2+0PKzT1\nT7u7P8MvvJJWJmlPhebTPVahX3j/Lknu/id+4ZUud2+WNFOh8q1JZnawpCmSWjzkSd47StpbkqrN\n7HAz21PSeEll4TubvHcUgZLsYQbM7HCFbqE9J+kOd789x01CHjCz3u6+Nfy1SdrT3T/McbOQR8zs\naEkTJZ0u6dbwAGKUuPAdiG9L+heFPnT/wt3n5bZVCBKBGSXJzKoVmibqBlZ7RFdm1oO7UIglvPhR\nW/wjUUrMbLhCC9q05N19G3kAAAGPSURBVLotCBaBGQAAAIihJGuYAQAAgEQRmAEAAIAYCMwAAABA\nDARmAAAAIAYCMwDkKTPrb2YXh78eamYLct0mAChFzJIBAHnKzGokPezuh+S4KQBQ0nrkugEAgKhm\nS9rPzBokvSnpYHc/JLwM75mSyhVazv16ST0Vmlt8m6RT3f0jM9tP0s2SBkvaIukid389+98GABQ2\nSjIAIH/NlPS2u9dK+kGXxw6RdI5CS/D+RNIWdx8j6XlJ54ePmSfpEncfK+n7kn6ZlVYDQJGhhxkA\nCtNT7r5J0iYz2yjpofD+RkmHmllfSUdKui+0yrckqVf2mwkAhY/ADACFadcl3dt32W5X6L29TNKG\ncO80ACANlGQAQP7aJKkqlSe6+yeS/mlmkyXJQg4LsnEAUCoIzACQp9x9vaRnzexVST9L4RTnSrrQ\nzF6R9HdJXwqyfQBQKphWDgAAAIiBHmYAAAAgBgIzAAAAEAOBGQAAAIiBwAwAAADEQGAGAAAAYiAw\nAwAAADEQmAEAAIAYCMwAAABADP8/vW7Rdb5GTREAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "results.plot(y=['v_north', 'v_east', 'v_down'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": 299, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\plotting\\_core.py:1716: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n", + " series.name = label\n" + ] + }, + { + "data": { + "image/png": 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QB2GsqiF3f0TSIynnbuzxfZukGWH0FTunfk5qulfy7sSxd0u73uxxQXLEecwU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\nn5Hp4dXD024qAxzAiDMAACg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uYukpXt9qyj+AkkWpBgCgNF25V6gjR6HgQUWgYFGqAQAob/F6P+ejh3VXe+zS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\nXoJFTvX4RTZIUpukmZJ+J6nJzI509w5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M/vG5zO2vzksvWlPI9AWlq6dIsQnYWT4h6adRFwEAAIAIDF1uPdcDkzGfP7us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\n/52S7sxzrFXSsTn2d0o6tZh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5aXQ5+Tibtp0f9t9JAysR6XVp4/i07cnJ9Cm3/jLjpMPeiYkAAADIHwn2AK1LGl1OPs6k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\njpL0L5IulfSSpE+bWSPvHZWFBDu95xW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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "results.plot(y=['elevator', 'aileron', 'rudder', 'thrust'], **kwargs);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Propagating only one time step" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "dt = 0.05 # seconds\n", + "sim = Simulation(aircraft, system, environment, controls, dt)" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "time: 100%|█████████████████████████████████████████████████████████▉| 0.49999999999999994/0.5 [00:05<00:00, 11.52s/it]\n" + ] + }, + { + "data": { + "text/html": [ + "
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FxFyFzMachMxMyMzTASaaileron...thrustuvv_downv_eastv_northwx_earthy_earthz_earth
time
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" + ], + "text/plain": [ + " Fx Fy Fz Mach Mx My \\\n", + "time \n", + "0.05 -2860.288296 -0.000007 -23948.338630 0.133444 3.670972e-06 416.026942 \n", + "0.10 -2841.450134 -0.000007 -23790.055374 0.133135 2.754411e-06 382.934882 \n", + "0.15 -2814.079427 -0.000007 -23634.534640 0.132827 2.070495e-06 344.981012 \n", + "0.20 -2834.053374 -0.000006 -23475.855214 0.132523 1.564206e-06 331.492749 \n", + "0.25 -2844.314793 -0.000006 -23317.511918 0.132216 1.181851e-06 311.810632 \n", + "0.30 -2847.104415 -0.000006 -23160.410509 0.131908 8.962216e-07 288.008616 \n", + "0.35 -2867.759612 -0.000005 -23001.499461 0.131599 6.829096e-07 273.089782 \n", + "0.40 -2883.231719 -0.000005 -22843.131464 0.131287 5.237487e-07 255.164441 \n", + "0.45 -2892.153236 -0.000005 -22685.668716 0.130975 4.056468e-07 234.048222 \n", + "0.50 -2914.835086 -0.000004 -22525.832830 0.130659 3.167348e-07 219.601445 \n", + "0.55 -2921.787769 -0.000004 -22367.332766 0.130340 2.513504e-07 196.935789 \n", + "\n", + " Mz TAS a aileron ... thrust \\\n", + "time ... \n", + "0.05 -0.000001 44.895162 336.434581 2.959742e-10 ... 0.670198 \n", + "0.10 -0.000001 44.791157 336.434574 2.959742e-10 ... 0.670198 \n", + "0.15 -0.000001 44.687646 336.434555 2.959742e-10 ... 0.670198 \n", + "0.20 -0.000001 44.585409 336.434527 2.959742e-10 ... 0.670198 \n", + "0.25 -0.000001 44.482035 336.434473 2.959742e-10 ... 0.670198 \n", + "0.30 -0.000001 44.378277 336.434397 2.959742e-10 ... 0.670198 \n", + "0.35 -0.000001 44.274258 336.434294 2.959742e-10 ... 0.670198 \n", + "0.40 -0.000001 44.169584 336.434162 2.959742e-10 ... 0.670198 \n", + "0.45 -0.000001 44.064366 336.434000 2.959742e-10 ... 0.670198 \n", + "0.50 -0.000001 43.958162 336.433802 2.959742e-10 ... 0.670198 \n", + "0.55 -0.000001 43.850903 336.433567 2.959742e-10 ... 0.670198 \n", + "\n", + " u v v_down v_east v_north w \\\n", + "time \n", + "0.05 44.877493 1.089215e-07 -0.021778 21.523885 39.399206 -1.259451 \n", + "0.10 44.773564 1.085156e-07 -0.059100 21.474006 39.307904 -1.255270 \n", + "0.15 44.670646 1.080774e-07 -0.101132 21.424344 39.216999 -1.232525 \n", + "0.20 44.567449 1.076118e-07 -0.219729 21.375124 39.126902 -1.265389 \n", + "0.25 44.463623 1.071279e-07 -0.339570 21.325202 39.035520 -1.279696 \n", + "0.30 44.359858 1.066288e-07 -0.462223 21.274925 38.943489 -1.278443 \n", + "0.35 44.255295 1.061187e-07 -0.620164 21.224128 38.850505 -1.295661 \n", + "0.40 44.150414 1.056017e-07 -0.781931 21.172708 38.756382 -1.301203 \n", + "0.45 44.045377 1.050805e-07 -0.944579 21.120728 38.661234 -1.293510 \n", + "0.50 43.938927 1.045592e-07 -1.134443 21.067646 38.564068 -1.300252 \n", + "0.55 43.832154 1.040402e-07 -1.311274 21.013841 38.465578 -1.282176 \n", + "\n", + " x_earth y_earth z_earth \n", + "time \n", + "0.05 1.972256 1.077449 -999.999987 \n", + "0.10 3.939933 2.152395 -1000.001805 \n", + "0.15 5.903055 3.224853 -1000.006526 \n", + "0.20 7.861673 4.294852 -1000.013745 \n", + "0.25 9.815738 5.362362 -1000.027650 \n", + "0.30 11.765219 6.427369 -1000.047414 \n", + "0.35 13.710083 7.489853 -1000.073815 \n", + "0.40 15.650273 8.549783 -1000.107951 \n", + "0.45 17.585742 9.607135 -1000.149658 \n", + "0.50 19.516402 10.661859 -1000.200635 \n", + "0.55 21.442166 11.713909 -1000.261205 \n", + "\n", + "[11 rows x 35 columns]" + ] + }, + "execution_count": 76, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results = sim.propagate(sim.time+dt)\n", + "results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that `results` will include the previous timesteps as well as the last one. To get just the last one one can use pandas `loc` or `iloc`:" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Fx -2.921788e+03\n", + "Fy -3.761191e-06\n", + "Fz -2.236733e+04\n", + "Mach 1.303405e-01\n", + "Mx 2.513504e-07\n", + "My 1.969358e+02\n", + "Mz -1.203167e-06\n", + "TAS 4.385090e+01\n", + "a 3.364336e+02\n", + "aileron 2.959742e-10\n", + "alpha -2.924362e-02\n", + "beta 2.372590e-09\n", + "elevator 1.108958e-02\n", + "height 1.000261e+03\n", + "p 6.386588e-10\n", + "phi 2.537379e-10\n", + "pressure 8.987343e+04\n", + "psi 5.000000e-01\n", + "q 9.152033e-02\n", + "q_inf 1.068779e+03\n", + "r 1.349505e-10\n", + "rho 1.111631e+00\n", + "rudder -1.269086e-09\n", + "temperature 2.816493e+02\n", + "theta 6.638492e-04\n", + "thrust 6.701981e-01\n", + "u 4.383215e+01\n", + "v 1.040402e-07\n", + "v_down -1.311274e+00\n", + "v_east 2.101384e+01\n", + "v_north 3.846558e+01\n", + "w -1.282176e+00\n", + "x_earth 2.144217e+01\n", + "y_earth 1.171391e+01\n", + "z_earth -1.000261e+03\n", + "Name: 0.55, dtype: float64" + ] + }, + "execution_count": 77, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results.iloc[-1] # last time step" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Fx -2.921788e+03\n", + "Fy -3.761191e-06\n", + "Fz -2.236733e+04\n", + "Mach 1.303405e-01\n", + "Mx 2.513504e-07\n", + "My 1.969358e+02\n", + "Mz -1.203167e-06\n", + "TAS 4.385090e+01\n", + "a 3.364336e+02\n", + "aileron 2.959742e-10\n", + "alpha -2.924362e-02\n", + "beta 2.372590e-09\n", + "elevator 1.108958e-02\n", + "height 1.000261e+03\n", + "p 6.386588e-10\n", + "phi 2.537379e-10\n", + "pressure 8.987343e+04\n", + "psi 5.000000e-01\n", + "q 9.152033e-02\n", + "q_inf 1.068779e+03\n", + "r 1.349505e-10\n", + "rho 1.111631e+00\n", + "rudder -1.269086e-09\n", + "temperature 2.816493e+02\n", + "theta 6.638492e-04\n", + "thrust 6.701981e-01\n", + "u 4.383215e+01\n", + "v 1.040402e-07\n", + "v_down -1.311274e+00\n", + "v_east 2.101384e+01\n", + "v_north 3.846558e+01\n", + "w -1.282176e+00\n", + "x_earth 2.144217e+01\n", + "y_earth 1.171391e+01\n", + "z_earth -1.000261e+03\n", + "Name: 0.55, dtype: float64" + ] + }, + "execution_count": 78, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results.loc[sim.time] # results for current simulation time" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Test\n" + ] + }, + { + "cell_type": "code", + "execution_count": 984, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "a1 = Cessna172()\n", + "a2 = SimplifiedCessna172()\n", + "e1 = copy.deepcopy(environment)\n", + "e2 = copy.deepcopy(environment)" + ] + }, + { + "cell_type": "code", + "execution_count": 985, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(Aircraft State \n", + " x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", + " theta: 0.076 rad, phi: 0.000 rad, psi: 0.500 rad \n", + " u: 44.87 m/s, v: -0.00 m/s, w: 3.40 m/s \n", + " P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", + " u_dot: 0.00 m/s², v_dot: -0.00 m/s², w_dot: 0.00 m/s² \n", + " P_dot: -0.00 rad/s², Q_dot: 0.00 rad/s², R_dot: -0.00 rad/s² ,\n", + " {'delta_aileron': -1.2190588362567532e-17,\n", + " 'delta_elevator': -0.048951124635254917,\n", + " 'delta_rudder': 7.1787477633953699e-17,\n", + " 'delta_t': 0.57799667845449421})" + ] + }, + "execution_count": 985, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ts1, tc1 = steady_state_trim(\n", + " a1,\n", + " e1,\n", + " pos,\n", + " psi,\n", + " TAS,\n", + " controls0\n", + ")\n", + "e1.update(ts1)\n", + "ss1 = EulerFlatEarth(t0=0, full_state=ts1)\n", + "ts1, tc1" + ] + }, + { + "cell_type": "code", + "execution_count": 986, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "({'delta_aileron': -3.9966019045688599e-19,\n", + " 'delta_elevator': -0.07729883009616384,\n", + " 'delta_rudder': 2.7133156470881973e-18,\n", + " 'delta_t': 0.57166075967430052},\n", + " Aircraft State \n", + " x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", + " theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", + " u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", + " P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", + " u_dot: 0.00 m/s², v_dot: -0.00 m/s², w_dot: 0.00 m/s² \n", + " P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² )" + ] + }, + "execution_count": 986, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ts2, tc2 = steady_state_trim(\n", + " a2,\n", + " e2,\n", + " pos,\n", + " psi,\n", + " TAS,\n", + " controls0\n", + ") \n", + "e2.update(ts2)\n", + "ss2 = EulerFlatEarth(t0=0, full_state=ts2)\n", + "tc2, ts2" + ] + }, + { + "cell_type": "code", + "execution_count": 971, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "c1 = {\n", + " 'delta_elevator': Constant(tc1['delta_elevator']),\n", + " 'delta_aileron': Constant(tc1['delta_aileron']),\n", + " 'delta_rudder': Constant(tc1['delta_rudder']),\n", + " 'delta_t': Constant(tc1['delta_t'])\n", + "}\n", + "c2 = {\n", + " 'delta_elevator': Constant(tc2['delta_elevator']),\n", + " 'delta_aileron': Constant(tc2['delta_aileron']),\n", + " 'delta_rudder': Constant(tc2['delta_rudder']),\n", + " 'delta_t': Constant(tc2['delta_t'])\n", + "}\n", + "s1 = Simulation(a1, ss1, e1, c1)\n", + "s2 = Simulation(a2, ss2, e2, c2)\n", + " # Doublet(t_init=3, T=1, A=0.1, offset=0)," + ] + }, + { + "cell_type": "code", + "execution_count": 711, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "s1 = Simulation(aircraft, ss1, e1, c1)" + ] + }, + { + "cell_type": "code", + "execution_count": 712, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n", + "\n", + "time: 0%| | 0/5 [00:00]" + ] + }, + "execution_count": 713, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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NbjjG6Azi039W3erpS1DMbLO7F/U2Ll53In30e21fx8HdWfbdJ/hMUQF/v+bUQSpMRGR4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\nc/fHI6xJBsfXgF+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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(r1.alpha*180/np.pi)\n", + "plt.plot(r2.alpha*180/np.pi,'.')\n", + "plt.plot(results.alpha*180/np.pi,'.')" + ] + }, + { + "cell_type": "code", + "execution_count": 972, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\plotting\\_core.py:1716: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n", + " series.name = label\n" + ] + }, + { + "data": { + "image/png": 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NgT6DYPB4OLAe6o6e6hKjshdJgIKziIhIuM5ofQlNteENofDWltHeRK5hx8uw\n5UV61kJSXc2BkVNDIVuBWpooOIuIiKRCZ5cwtLSQFGhEPWlMqG/52VdB9Ra1RMwwCs4iIiKZpD2t\nD/e8Q9tHsw1p2Xmls3n144Hs0GJA/Yd2z77j8V7oZXgNu9rRiYiIZJL2tj6MN5odayJhrOXaY+3r\nSaeVQDta9mKDsOetxPZ991E48wuhkG1M8r/m2srQ9ZyWD4PGwcGN8HElEAids08BFJbARxvgeAW4\nbqjVZOMJKC8NtXc0BoacA6ePDC1C9P6zTTXsDhSeD0MmtnxtGVrektIRZ2PMlcCvgQCw0Fp7b0v7\na8RZREREkibWqLzqyDvAwLApMGgCFH4aKjYm3vs8zQJ32pVqGGMCwDbgcqAcWAt8w1r7QbznKDiL\niIhIp2utjhzUEjGZvLIXJyv0cb+hMPy8UFcW0zUj2elYqnEBsMNa+yGAMeZx4BogbnAWERER6XSJ\nlLn0lL7jJgDW0qUj7LHKXjY8durj9Y/BnOfTblQaUhuchwP7wj4vB6am8PwiIiIi7dOWGvLOaH3Y\n0X297fGWiI+uXW/pfJ1d3hKsD01UzPDgbGJsa1YnYoy5BbgFYOTIkZ19TSIiIiLJ1Z6JmqnWkesr\nmdN6F5eOjMgHckLdPdJQKoNzOTAi7PNC4ED0TtbaB4EHIVTjnJpLExEREZGEdeTFQUsj8mnerSOV\nkwOzCE0O/AKwn9DkwG9aa99v4TlVwJ6UXOApI4G9KT6npJ7uc2bQfc4Mus+ZQfc5M3TVfR5lrR3U\n2k6pbkd3FfAfhNrRPWytvTuB5zwMXA1UWmvPScI1LAOmASuttVeHbX8IKAEmAs8Cc6y1xzt6PklP\nxpiqRP6BSPem+5wZdJ8zg+5zZkj3++yk8mTW2r9Ya8daa8ckEpqbPAJcmcTL+CUwO8b2f7LWTgZ2\nEXql850knlPSz5GuvgBJCd3nzKD7nBl0nzNDWt/nlAbn9rDWvgkcCt9mjBljjFlmjFlnjFlhjBnX\nhuO9CtTG2H6s6cOjQG8ycj3RjHK0qy9AUkL3OTPoPmcG3efMkNb3ubsuuf0g8G1r7XZjzFTgv4HL\nOnpQY8wiYCyhYP3PHT2epLUHu/oCJCV0nzOD7nNm0H3ODGl9n1Na49xexpgi4Hlr7TnGmL5AFbA1\nbJde1trxxpjrgLtiHGK/tXZ62PEuBW4Lr3EOeywA/Cew1lq7KHlfhYiIiIh0Z91xxNkBjlhrp0Q/\nYK19Gni6Iwe31gaNMX8CfggoOIuIiIgI0A1qnKM11SLvMsbMAjAhkztyzKZjnOV9DMwAtnT4YkVE\nRESkx0j7Ug1jzGLgUqAAqABkK5MJAAAgAElEQVR+CrwGPAAMBbKBx621sUo0Yh1vBTAO6AvUADcB\nrwArgP6EVjjcANwaNmFQRERERDJc2gdnEREREZF00O1KNUREREREuoKCs4iIiIhIAtK6q0ZBQYEt\nKirq6ssQERERkR5s3bp11Yks9Z3WwbmoqIjS0tKuvoxurayyjNKKUkqGlDBlcLMOfiIiIiIZzxiz\nJ5H90jo4S8eUVZYx/+X51Afr6RXoxYIrFjBl8BSFaREREZF2UHBOU7HCbVsDb2lFKfXBeiyW+mA9\npRWlbD+8nbtX341rXbKcLC4Zfgn5vfOZOWamQrSIiIhICxScu5AXhPNy8jhaf9QPxGWVZcxdNpdG\n24hjHH489ccUDyjmppduot6tJ2AC/Gjqj5h19qwWj39a1mlYmtoNGsjLyePfVv2bv63BbeC1fa8B\n8Mz2Z/hs4WfJ753P+IHjI65HRERERBScO01ro8NllWXMfWkujW6jvy03kMuCKxZQWlFKow1td63L\nv636NyYWTKTerQcgaIPcvfpuAI7WHyUvJ48th7ZgsX7ozcvJ45elv/SPbTA8+v6jp4J0lEbb6Ido\nT5bJ4s6pd/oBvaWvqayyjKU7l2KxEaPXKgsRERHpGRoaGigvL6eurq6rL6XdcnNzKSwsJDs7u13P\nV3DuBPFqi8Mt270sIjQDnAyepLSilLMHnB2x3WLZVL0pYlvQBvn56p/jWjfmNTg4uIQeMxiCNsie\n2j0RjxsT2h5Po23k7lV3837N+0zMn8i9a+6lwW0gYAJ+oPYC81Pbn/KP9fT2p7mu+DrGDxzPfWvv\noyHYQE4gJ+b3QURERLqH8vJy+vXrR1FREcaYrr6cNrPWUlNTQ3l5OaNHj27XMRScO0FpRSkngycB\n/Npi17qsPbiWqUOnMmXwFNZXrG/2PIOhZEgJqz5aBYBjHKy1cUeJ44VmwA/N3nGiA/LXxn6NGWNm\ncP/a+9lYvTHucYIEeWr7Uzy9/Wn/OhptI3etuotntj/DpppNza4vaIM8se0JDCaiLKS0olTBWURE\npJuqq6vrtqEZwBhDfn4+VVVV7T6GFkDpBCVDSjCEfqgCToBDJw5x47Ib+W3Zb7nppZuYu2wuHxz6\noNnzBvQawNKdS3lgwwOh55oAnx/xeQImELGfd+xEGAzfmvAtcpwcf1uOk8OMMTOYMngKt59/O7mB\nXBwcAgS4bMRlzJ04FyfqRyNWeN9YszFuqI9+jjGhFwUiIiLSfXXX0Ozp6PVrxLkTfPTxR35ovHDo\nhfzv5v/1H6t3QyPQHgeHacOmkRvI5bV9r/HnbX/2H3Oty6RBk7h4+MXcs/oeXOs2Gz12cLBYHBw+\nN+JzjOo/ikfffzSiTKN/r/48NP2hmDXIUwZP8euqw+uQjzcc54ltT7Tp63ZwOG/weayvWt9sNHzi\nwIkALNy4sMV65+gJk179tmtdrjnrGo1Yi4iIZDBjDDfccAN/+MMfAGhsbGTo0KFMnTqV559/vtPP\nr+CcZGWVZdy54s5Tn1eVxR2VNRhyAjncOvlW/rr3r80eD5iAHzKLBxT7gfL+tffT4DaQ7WRz+/m3\nN+uAMaLfCD9o5wRy/Mfihc5Yj80cM5OlO5dSH6zHYDCOwVqLweBa1w/mEbXUxnBx4cV8+cwvc/eq\nuwlyKuAfrT/KnGVzsNaSE8jhtpLbKD9ezsh+I/3rB5j/8ny/zCXakp1LeGj6QwrPIiIiGapPnz5s\n2rSJEydO0Lt3b1555RWGDx+esvMrOCfZok2L/I4YAMfqj8XcL0CA68ZeFzH6+78f/K8/mmwwfOWs\nr0SMDHsfeyE63sjtrLNntbpPa6JHooGIj73R6/EDx0cE+fCg7+2z7dA2NlRv8I9dH6wPBfuwUfEs\nJ4vhfYfHDc1wqk46/FoUokVERDLLl770JV544QW+9rWvsXjxYr7xjW+wYsUKAK666ioOHDgAwK5d\nu/jNb37DjTfemLRzKzh3UFllGUt2LuFk8CQTBk6IaOkWMAGCNkhB7wLOLTiXlftX0uiGejOHt3mD\nUFD90dQfRYwUzxgzI+Y5Wxo9bss+rYk+RryPY4V077lllWXM2zEv8sAmcmKjxdLgNrD72O4Wr8cx\nDnk5ecxZNgfXunE7loiIiEh66Iy2tNdffz133XUXV199Ne+99x7z5s3zg/Nf/vIXANatW8fcuXP5\nyle+kpRzehSc2+DdindZsX8Fnyv83KlQ+NI8GtwGIFRK4DEYzsk/hw3VG6g5UcPbB97mjgvuaHFh\nkWSMFHeFlkJ6aUUpQTeq5V38+YS+SfmT2FgT6vYRIIDjOEwdOpU3y9/0R+VPBk+ydOdSLSMuIiKS\nYvetuY8th7a0uM/x+uNsPbwVS6jU8+wBZ9M3p2/c/ccNHMe/XPAvrZ773HPPZffu3SxevJirrrqq\n2ePV1dXMnj2bP//5z+Tl5bX+xbSBgnOCyirLuOnlm2h0G/n9+7/noekPUVpR6ofmaNlONsUDinmv\n+j1/RPVo/VHmT5rf4nmSMVKcTkqGlJATyKHBbcAxDg1uQ0SJRvHpxWw7si3iOTlODuPyx51qdWeg\nILeADZUbqG2o9fezWJ7Z8QzjBo7ze1pnmSxmT5hN/179FaJFRES6UG1DrT/Py2KpbahtMTi3xcyZ\nM7nttttYvnw5NTU1/vZgMMj111/P//k//4dzzjknKecKp+CcoNKKUn/Bknq3ngc2PMDFwy+Oua9X\nnzxjzAye//D5iPrfTBNeK9070Jt7197rP5btZDN58GS2H9nu/8OaVDCJ28+/HQjVUXsLrlSeqIy5\nWEuD28Aft/zRL/1otI0sen8RAL0CvVh4xUKFZxERkSRLZGS4rLKMm1++2c9B915yb9L+Js+bN4+8\nvDwmTZrE8uXL/e133HEH5557Ltdff31SzhNNwTlB0aH37QNv886Bd/zH+uf0Z+X+lQRtkGwn2++T\nHKvVW6bxRtEXblzoL4oS/uLCC8helxDv++R97w4cP8BT256Ke/ydR3bG3H4yeJIHNjzArZNvjbvs\n+aqPVjFt6LSMvTciIiKdpTNzUGFhId/73veabf/Vr37FxIkTmTIldK677rqLmTNnJu28xtoECk67\nSElJiS0tLW19x05WVlnG6/te5+FND1PYt5Dy4+URj+c4OTw0/SFA3R5aEv3K05vY11p9sve8+mA9\nWU4W15x1DTUnaiImYuY4oXKQ6NZ/BhMxiTC8T/Tdq+8maIP+yDTo/omIiMSzefNmxo8f39WX0WGx\nvg5jzDprbaulARpxbkVZZRlzls3xywTOG3weH338UUTZgNcmbf6k+QpcLYj3yrO1uu5YzyurLOPt\nA29TF6wDQuUzXheTcBZLXbCOn771U/rn9Oe9mvf8yYlerfXJ4EkWbVrEG+VvqFuHiIiIxJXSJbeN\nMVcaY7YaY3YYY+5I5bnb68VdL0aEsRd3vci3JnyLAKeWwc7U+uX2mDJ4SrteYEQ/zwvT04ZO8/ex\n1pJlsgiYADlOTsRS5R8e+5Cy6jJ/8RYvNHuWly8naIP+RM7w1R1FREREIIUjzsaYAPBfwOVAObDW\nGLPEWvtBqq4hES98+ALv7H+H2oZa8nvn827FuxGPu9alf6/+PPKlR2IuYS2pM2XwFP5hyj9QVlkW\ncyXFJTuXJLxseHhfacc4HDh+gLLKMoCIJcBVxiEiIpK5UlmqcQGww1r7IYAx5nHgGiBtgnNZZRl3\nrIg/EO4tkd3aEtaSOq1NPHhux3PUu/X+5+FLhMfT6Dby5LYneW7HczTaxohQnRvIjVmbDaqPFhGR\nns9aizGmqy+j3To6ty+VwXk4sC/s83JgagrP36rSilK/60M0B4dpw6bF7dAgXSfei5gpg6fw0PSH\nWLpzKdUnqsnvnc/pvU5nwcYFAH7P543VGyNKM7z7Hx64PfXBekorStl2aBv3rAmt8pjlZPmLvOQE\nclQfLSIiPVJubi41NTXk5+d3y/BsraWmpobc3Nx2HyOVwTnWd7hZQjXG3ALcAjBy5MjOvqYIJUNK\nyHaymwUmB4ecQI5CczcUHaoXvLfA/9hi6d+rPxeccUHCNc3GGPbX7ufX23/tbwtfBKfBbWDpzqUa\nfRYRkR6nsLCQ8vJyqqqquvpS2i03N5fCwsJ2Pz+VwbkcGBH2eSFwIHona+2DwIMQakeXmksLiTVC\nOX7geNW29iDnn3E+uYHcZovSPLzpYeqD9bi4mKbXeBZLn+w+fNzw8akDWHhy+5Nxj2+t5ekdT+O6\nboujz1oiXEREupvs7GxGjx7d1ZfRpVLWx9kYkwVsA74A7AfWAt+01r4f7znp0sdZepZYoTW8v/PR\n+qPsr90fEZDjlfB4zso7ix1Hd0Rsc3D47qe+y/xJ85vVQ897aR5BNxgzXCtUi4iIpFba9XG21jYa\nY74DvAQEgIdbCs0inSVWTXSskg4vLDs4FPYrpLy2PGJiYYAAFouLy65ju5qdx2LJy8mjrLKMeS/N\no9FtpFegF18c9UW/vONk8CRLdy6NCPBe3/DwiYgiIiLS9VLax9la+xdr7Vhr7Rhr7d2pPLdIW5x/\nxvn0CvQK9YQO5DBn4hxyAjl+j+hZY2dx3djr/P2tDQXscBbLPavv4ccrf+yvangyeJJdR3dF7PPs\njmf91ndrD671+4bXB+t5YMMD/mMiIiLStbRyoEgMsdrcFQ8obrZ64dKdS/166W+M+wZ/+OAP/kIq\nAI22kT21e/zjWiybD22OKP0I2iClFaVMGTyForwif18Xl7cPvE1pRSkPXfGQRp5FRKRV0aWHKvtL\nLgVnkTiiyzdifR4dri8beRlLdy7l2R3P+qPM0Vzrkp+bT219LfVuPa51Wf3RakqGlFDXWNds/4Zg\ngx+sRURE4imrLGP+y/M5GTwJhObn9Ar0UtlfEik4i3RAvHA9Y8wMlu5cylPbn4pYst0zdsBYLh91\nOXetuguLZdVHqyitKGVywWRynBx/6W9PvCXdNZFQRKT7897B9Dp6tbYisbd/9OrFpRWl1AdPtdT1\n/pakYvAlU/4eKTiLdILoAG2x9M3uy6MfPIprXUorSinsF9lHstFtZF3lumbHslie3PYkizYtiviF\nGj3pcMEVC2h0GymrKuvxv7hERLqjWIG3rLKMucvm0mgb/f2e2/EcD02PXaIXPok8et9YgyzWWjZW\nbaSssiyhMF59ohrAb8m75dCWZts2H9pMxccVBG2QRreRBreB96rfS7gVa15OXszjbjm0pdmLgXSj\n4CzSicJHpBduXOgv+ePaUL/oHCcn5gqFHq8W+rmdz/nbntr+FD+e+mMO1x32R6Ub3Ab+vPXPLP1w\nqd6aExFJQ2WVZcx5cQ5BQoH36e1P86OpP2L1R6sjQjPgjxIDLNm5BMAPk+GTyCG0yu39a+9nUO9B\nnGg4gcUyedBkxg8cz+NbH8fF5bV9r7Fy/8oWw3h0eG+vumAdP337p3x6yKcpHlDM+1XvU3mikqMn\nj7Ll8BZc67Z6jJZeOHQ1BWeRFCkZUkJOIMefTDhjzAx/RPqDQx+wqXpTxP4ODsaYZqUernW5Z/U9\nzB4/29/mTTr0Pq4L1vGTlT/h/KHnx33lnilvq4mIpINndzzrh2YITQy/a9VdMfd1jENeTh43vnij\n3wb1qW1PcW3xtRyuO9xs/43VGyM+/6DmA8YOGBsxET26ZCP8b8DCjQuTEpo9Hx79kA+Pftju56eq\nvKQ9UrYASntoARTpaeKF1bLKMm5++Wbqg/U4xmH2hNn079WfvJw87l1zb8xR6fzcfGrqalo9Z8AE\nuK74uohVMKHlRVhERKRtwsswYpU4vL3/bfZ/vL/FY5yZdya19bUE3SCnZZ9G+fHyuPtOKZhCXbCO\nLYe3NHvMYJg1dhbP7ng24u/HhUMv5PJRl7Ny/0qW71uOi0u2kx0xp6a9HJyItQ46IsfJSfmIc6IL\noCg4i6SJlkL10p1L2XlkJ2VVZTEnG7ZFwASYkD/BH6HwfsH+5MKfxJ1wIiIizSfxefW+2w9tZ0P1\nhhZXmPU4ONim/3nCS+zeKH8jVNrXiiyTxZ1T74w5uOIFT4BFmxbx2r7XEv4az8w7k6L+RS3WOIdv\nC98eb6AnXMAE+NaEb/Fxw8dpVeOcdisHikjLYq1oGL29rLKM367/LasPro55DIPBwYl4OzBa0AYj\n3tazWJ7e/jT7j+/n7QNv+7/M07nGTEQk1ZJVB2yM4dLCS3mz/E1c65LlZHHNWdf4YXHVR6uaPwcD\nEBG2XetytP4oD01/qNmkvvDgOWnQJF7f93qrod7BISeQw79e9K/t/r1fPKC42QuL6ODd3QdlFJxF\nupEpg6fwnfO+w/qX1vuv6gMEwIRmTucEcrj9/NsjflEl8guz0Tby1oG3IraF15ipHlpEuoOW3rl7\nctuT5ARy2h3cVu5f2eHQ7OCQ7WQz95y5zD1nbsxrnTZ0GgveW+D/js9xcrjjgjs4Wn+UYyeP8YcP\n/oBrQ90rvOe29PWUDCkh28lucSTYwWHasGncOvnWDv2Ob+1aegKVaoh0Q9ElFUDcYPvDN37Ist3L\nACImipim/8WrScsyWVwy/BKO1R9jQ9UG/xd1rHpoBWsRiae13w/J+v3x+r7X+f7r38dai4PD50Z8\njouHX8yag2v834HQtvrZ8N+1u4/tZu3BtS3u7+Bw6YhLuXj4xTFLHBJdya+lsrn2fL/i1V+v3L+S\noA2S7WRn/FwX1TiLCACv7n2V77/+fXpn9eb6s6+PGK24aNhFEbVvAQIU5RWx8+hOAiYQs556UsEk\nbj//9ojykbkvzaXRbSQ3kJvxv3xF5JSyyjJueukmGtwGAibAnVPvZNbZs/zHn9j6BHevvhvXuhFt\nNMPDIcQfGFh9YDVlVWVMHTqVX5X+ig1VG1q9JoPhHz/1j8yfNL/ZtXo9hjdWb2Troa1sPrS52Tt2\nAQJMGTyFM08/MyKEdscyBA16nKIaZxEBQqMrACcaT7B4y2LunHpnRHeNtw+87XfzuHPqnYwbOI5v\n/uWbcSchbqzeyE0v3cQdF9zBmoNr2Fe7j0Y39PZlfbA+bVsIiUjqvbr3Vb9EoNE28vNVPwdO1cI+\nse0JP5jWBetYunMpgL9stNeW0ytFC39hvr5yPTe/cjMWy+/e+x1BN/GJ0yvLV3Lg+AE/+G4/vJ2y\nqrKEJvdh4OLCi5sF7+4oE0orkk3BWaSH23p4q1+i0eA2cLT+aMQv/AVXLIgYcVhX0Xz1wug2Q/Vu\nfcz+oxbLsZPHWLhxoUYwRLqhjoxAxholrvqkKmIfF5efr/q5H1Cjg+ozO57BYjkZPOnv7+0SvrDG\nzDEzWbJjSUSPYgiNBru4MUeJJxVMoqw6FI7XVa6LuVJra7wa5Vgr9ElmSElwNsbMAn4GjAcusNaq\n/kIkRUqGlNAr0MtfeCX6F370iMP6yvURj08qmMS1Z12bUJshi2XR+4swGLKdbC4ceiH1bj1D+wzl\n2uJrtRCLSBorqyxj3kvzaHQbE1591Pv32ze7L/evvZ+gG8QxDkEbxBKqNT4t6zTqGuv8F98t9fpt\ncBt4v/r9uI97C2s8u+NZik8vbr6DgVnFs6g+Uc0b5W/gWtcvETlaf5Sy6rLEvhlhwuuWE61Rlp4r\nVSPOm4DrgN+l6Hwi0mTK4CnNRpVbUjKkhNxArh+0vXrm4gHF3L/2/mYrVMVisdS79byx/w1/25IP\nl/Av5/8LtfW1nH/G+X4doxZiEUkPK/ev9EduTwZP+mUTsWqNAZbuXMpT258iaIMRE4/Dl1R2cRly\n2hBmT5jN3avujtkq08HBcRy/5OuDQx/424GYK6g2uA3+fuECJsCMMTNidgMqqyxrdbGP6B7D3bFu\nWTpXSicHGmOWA7clOuKsyYEiXaO1FQ69iT6F/QrbtayqN4LTN6cvS3YuASIXYknkWkQyWVv/XZRV\nlvn/1uJ1d7j9jdt5cfeL/ucBEwgt02GtH4wtlmwnGyDh1eayTBaLrlzEkp1LeGLbE80eD5gAXy3+\nKvtq9/HOR+/42z87/LOcN+S8FldQDRfvd0j09yFen2GF5MymyYEi0m4tLcYSPnoNRATpa866huoT\n1by+7/UWj+/i8tq+1/ym/hAapX5y+5OMGziOwacNZuuhrQzIHcC9a++lPlhPr0AvFl6xUH/UJOOV\nVZYx/+X51AfrY3aq8Kw+sJqX97zs/5uMXqku28n2F94AIlq2ARGjvOHPbevyzBZLaUUpM8fMZOnO\npdS79WSZLP8c2U42M8bMAGDtwbV+r+RVH63i5nNv9t/xWrpzKaUVpTFfrHuLd3jHiUeT4aSjkjbi\nbIz5K3BGjId+ZK19rmmf5bQy4myMuQW4BWDkyJGf3rNnT1KuT0Q6R6y3Q29++Wbqg/UYTOiPlCHm\npEMAxzgRb+16ExENhoAJRCw4MKlgEuMGjmu1d3VL1yeSSon8/LX1Z3TBewv4zfrf+J97Sy+HjyI/\ntvkx7l1zb0LXGDBNE+eq2l7/6/GCuMUSdEOlG8YJdcMI7xHcWpu5u965yx+VDpgA3znvOxGTmaPf\n9brmrGva1B9ZJJ607OOsUg2RzBAdBBa8t4D/XP+fibV6ChPdzcOTZbIwxtDoNpLlZPGVs74S8RZr\n+NuxK/aviKihhsQCd1u+PpFYwnsUh4/uhv+cLtm5hGd2PEPQDTYbPY73c3bfmvv4383/G3Euxzhg\nIcvJ4uLhF/P2gbepC9a1+ZoDJgBEjjaH1y/75wtrExe+ZDTEroluy0IdXjCOtyiH/v1JZ1BwFpG0\nET1KdPHwizn48UF/co9XshHrj7OLy+Deg6k8UdniObxFCfpk92Hl/pXNArdjHL5a/FWe2v4U1lq/\nawC07Y+7t6BDo9uoCY0SV1llGd968VvNfqaznWy+ctZXGD9wPPetvc9vu+ZxcPjxtB9TPKDY/zkL\nOAFmnDmDa4uvZV3FOn797q/b/CLUM6lgEmf0OYNX9rzS7DGD4Wtjv8b4geO5f+39EROEtxzawgeH\nPuD96vexWL8ueWjfoUkPsArG0hXSqsbZGHMt8J/AIOAFY0yZtXZ6Ks4tIl0vVmeP6JGl6FUM4VTb\nqpq6GrJMVkTZRrQgwRb7sjrGofqTar8spC5Yxw/f+CGVn1T6QSBWrWj0H/G1B9f6k5Qa3AYt+JKg\ndAtDyb6eN8vfZFP1Ji4adhFTBk/h1b2vxgy3DW4DT2x7Iu7KnC4ud6+6m4LTCvyfM9d1eXrH0yzZ\nuaTFfwOxnJl3JnuO7fEXELn9/NtZ/dHquMF5WN9hzDp7FsUDipt9f6L/zXrdK5JNdciSzlISnK21\nzwDPpOJcIpKeov8Yxppo+PaBt2lwGzCYiIDgWpdZY2ex//h+3jrwlr/dYDDGRNRIx9Mnq0+zSUUH\nPznof9xoG7ln9T0UDyj2g/3SnUv9t9G90BHeAivLydJCCAlIRdvBtgThJ7Y+wT2r7yFog3GXeW7L\n9d27+l4e2/IYAIs2LWLBFQtaXcUuPDRHL9oRJEjFJxXNnhMdmh0cv9NFLDlODv960b8Czd9VWbBx\nAY1u46luGU3B2vt5jhVe29raUqQnSmmpRlupVEMks3jBJS8nj1+s+YU/ez/HyeGh6Q9RWlHKr9/9\ntb+/wfD5EZ/njX1vRPSHzTJZjOw/sl2t8iYVTOKyEZfx6/W/jthuMP7CDp4bJ9zIadmnMaj3oBZb\nWiU6QeypbU+R5WQxIX9Cq5OdOnsEN5nH/+363/K790Jt/KMnfCXjPF6XiYZgQ8xlmZfvW87nR3we\nCPUefnLbkxGlPBcNu4gvjvwi9629z+/g4pUnWGyzuuTw631t72t87/Xv+cdycPjup77LX/f8lb3H\n9jIqb5Rf3gDN64W9FmrjBo7j7tV3t1pbbJr+5xiH2RNms3jLYv/FprfoCIR+jr0e7PG+Zx2pRRbp\nadKyxrmtFJxFMpc34hseXLz6Yu8tbC9QAxG9Wb1JSje/fDMngydbrAeNt0RvR2SZLK4tvta/jnih\nzvs6/2fD/0SMpMc6TvRz4o3gllWWsfbgWn+RmfDnJBqOvOM3uA1JaQP4Pxv+h/8q+y8AcgO5/vWu\nr1zPnGVz/NXdfjT1RzHbqkVfW/TPxcKNC/0XVN6LqYLeBVSfqGZ5+XJ/cp5rXVzb/F7HeuciPLSG\n/5zNXTYX17r+JLyNVRupqquKeN43x3+TxzY/5neagFNt16JLkrwex1MGT+GJrU9ELGWfZbJwjEOD\n2+BfS8AEuK74uoh/E96LzfC6ZNXei7RNWtU4i4i0Vby3ih+a/lCz4OQ9Fm3BFQtYunMpz+54lka3\nERcXB8cPPV7IjrcwQ3s12kae2PYES3YuYeaYmf4EsJPBkyzatIhJgyZRMqSE7Ye38/NVP4+7BLF3\nnKU7l0YEoVUfrfJH48PrrP+85c/8fPXPsdiIgOq94PCCcHTQjg7UpRWlp44fjF3H3VIQj36svLbc\nf+y+z94HwMKNC1m2a5kfVoM2yM9X/RyAWWfPinn8ssoy5iyb44/KPrfjOR6a/lBEuYzFNquV975P\n0cIX9YgeRAoP1/VuPUt3LuW07NP8col6tz7meSyWxzY/5n8ctMGISXQQKkmqD9bjGIc7p97pf31H\n649GtGO8rvg6ZoyZwQMbHuCdA+/41zSs77CIn3vv41h1ySKSXArOItKttGXikLfvjDEz/FG5eCUQ\nz+14rtnKZLFqSFurKw13MniSdw6cWgnNC3Wv73udbCfbD/OtqQ/W89v1v+U7532HKYOn0Durd8Qx\n83LyKKss4+7Vd/vXdTJ40g+8D218yP/a6t16f3usQA2w79i+U1+v45CXk8fCjQv94Pf4lsd5afdL\nBG3zFmqLtyzmvjX34VqXXoFePHjFgyzft5zTe53OkZNH+N2G37Hl8JaYdekuLvesvgeAX6z5BY1u\nY0TQL60ojShl8AJt35y+rX4Po108/GIuG3FZs/KIeJ7c/iTnDTov7uMj+41kb+3eiG0OTsxJdPHq\nhEuGlJATyGk2+e7WydRQgfUAABkCSURBVLfybsW7/vZ4dfWaVCfS+VSqISJCaDRz0aZFvFH+RkQH\ngi2HtvDsjmf9t9rDtzW6jX6t6ccNH8dd1SwRAQJMGzbNL9kYN2AcWw9vjQjoOU4OV595NXuO7WF9\n5Xo/dOcGcrli1BUs+XBJxDEvG3EZnxryKX5V+it/m8Hwk2k/YdbZs/jhGz/0V4tzcLi2+Fqe3v50\nxDknDJwQuo6mfr1BG2wWNL0WakP6DOEfXv2HiO1fGPWFmB0cWlLYt5Dy4+X+MaYNm8atk2+l6pMq\nfvDGDyL2DS+pCJgA1tq4L0a8ThYGw4LLFzB12NSIBTfCrzvLyYq5pPxpgdP4JPhJxLYcJ4c7LriD\ne1bf449IGwwXDruQWyff2qYw29Jy9xpNFuk8qnEWEWmHeCUCiW7zVk0EEhpNBvz63uIBxX7v316B\nXlw8/GJe3ftqq893jENR/6KEQ3uvQC+uPvNqntr+VMQ1jOo/KuIYsSayxRtpDxBgQO4Aquuq/W1Z\nJovx+ePZWL0x/rXj4BjHL2uIxWDICeTw2cLP8sqeV7hw6IVUn6hm+5Htza7hurHXMX7geFbuX+m/\nCDImNHGuqF8Ru2t3A6dqrQH/nnkvgvr36u+P6s5dNrfFFnDhk/C8bh2uddXjW6SbUXAWEekC4ZO1\n7l1zr18i4U30O/jxQVbsXxHxnK+P/To/ufAnLNy4kN+8+xu/r/Tloy73R4RbEt4TON5qi60eg0BE\nZ5JE9m9tUuXfjP0bNlRtYOvhrRhMxHUFTIBvTfhWREj97frfsvrg6lbPnRvI5ctnfjki+MOpjhbR\nHTuqPqnij1v+GHn9Yd09WhrNDW9dF/0iIrpePPycGhkW6V40OVBEpAtET9aK1RkkfHJfjpPDjDEz\ngFCNa69AL7+WtV9Ov7jn8coJskwWJ4InIh6LF4LjLboBNNs/Vvu98Me+OvarjBs4LubkxmlDp/Fu\nxbu8deAt9h/fz0XDLqLkjBLycvJitnjzfOe877Bu2bpWF/moD9YTMAFyA7l+1xRvVDq8/te7Fwve\nWxAxWu51u2ipZ7HHWwzEm2Tq1XVHL58dfU4R6Zk04iwikmKxWqqFPxbeX9crI/A6LQRMwC8nyMvJ\ni6irdXAiarOrT1Szcv/KiPrsJR8uoayyzD9f9HLnXqi85qxr/KWXvfN7vPZsUwZPaVYjnGWyuHPq\nnfzbqn/zj5nlZLFo+qKEAmV4uYN3zj5Zffi48eOIcyy6chFAq5M+ve9p+JLv8UJvazSaLNJzacRZ\nRCRNtTQqGf2Y14EhVjhcuHGh350ifBJdS6UDxQOKm9X0eotoxAqVxQOKeWDDA7x94G0gFKy/ctZX\n/MdnjpnJ0p1LI9qrHa0/GvE1Bd1gwkuTh4/wPrHtCSyWumAd2U42QTfYrIVbIsdM1op3Gk0WEQVn\nEZE01lJYi25fFquDQ2tLnU8ZPIXLRl4WN1TGaofmlZbEO15ZZRnZTrZf391SC7V4X3NpReS7jdee\nda3fC7k94VWhV0SSQaUaIiLdWKrKB9p6npbKURI93/yX59PgNpDjqEOFiHQuddUQEZFuTTXFIpIq\nPSI4G2OqgD0pPu1IYG+re0l3p/ucGXSfM4Puc2bQfc4MXXWfR1lrB7W2U1oH565gjKlK5Bsn3Zvu\nc2bQfc4Mus+ZQfc5M6T7fXa6+gJaY4x52BhTaYzZlKTjLTPGHDHGPB+1/TFjzFagf9M5s5NxPklb\nR7r6AiQldJ8zg+5zZtB9zgxpfZ/TPjgDjwBXJvF4vwRmx9j+GDAO2Aj0BuYn8ZySfo62vov0ALrP\nmUH3OTPoPmeGtL7PaR+crbVvAofCtxljxjSNHK8zxqwwxoxrw/FeBWpjbP+LDdWtPAisAQo7eOmS\n3h7s6guQlNB9zgy6z5lB9zkzpPV97hY1zsaYIuB5a+05TZ+/CnzbWrvdGDMV+IW19rI2HO9S4DZr\n7dUxHssGVgPfs9auSMLli4iIiEgP0O0WQDHG9AUuAp4wxnibezU9dh1wV4yn7bfWTk/wFP8NvKnQ\nLCIiIiLhul1wJlRecsRa26ypp7X2aeDp9h7YGPNTYBDwd+2/PBERERHpidK+xjmatfYYsMsYMwvA\nhEzu6HGNMfOB6cA3rLVuR48nIiIiIj1L2tc4G2MWA5cCBUAF8FPgNeABYCiQDTxurY1VohHreCsI\ndc/oC9QAN1lrXzLGNBJabMWbOPh0oscUERERkZ4v7YOziIiIiEg66HalGiIiIiIiXSGlwdkYc6Ux\nZqsxZocx5o5UnltEREREpCNSVqphjAkA24DLgXJgLaGJeB/Ee05BQYEtKipKyfWJiIiISGZat25d\ntbV2UGv7pbId3QXADmvthwDGmMeBa4C4wbmoqIjS0tL/v737D5K7ru84/nzvXnI/ckdIIooaY9OA\n/A5cEiISkpCk0GqL+KMOjhE1LWWsWmc6g6Uj4x/ayrQFkYoViz+gTuuUhDFQO9N2xoIgaISBQEET\nsEwIRkqHhF6S43JHcvvpH7uHlx93u3fZ3e/+eD5mGO+++93bT/zM3b3uve/P51On4RUNbd3K3rvv\n4dDu3XS87nV0nXkGwz/fxqHduwGOee3I6wCz33M5Pf39dR27JEmSpi4idlZyXz2D85uBX477fBfw\n9jq+fllDW7eyc/2HoXD8u9ENbNxIz4oV9K25mJFnfjFhyB4fyA3bkiRJjauewTmOce2oPpGIuBq4\nGmDBggW1HtNhhh5+pCqhGYCUGHrwQYYefLDipwzcdRc9F1xAzJxB5PKAIVuSJKlR1DM47wLeMu7z\n+cALR96UUroNuA1g2bJldd0rr2f5+TBzJrz6aj1f9tdGRxl66KGKbh3YtInZ738/FAqMDgwAhmxJ\nkqRaqufiwA6KiwPXAb+iuDjwQymln030nGXLlqVm63EefOBHDN53X/Uq19WQyzFn/XrSqyMc2r0H\nOPrfYcCWJEmVOnjwILt27WJ4eDjroUxJV1cX8+fPZ8aMGYddj4hHU0rLyj2/rgegRMS7gJuBPPDt\nlNIXJ7s/i+BcDWPhGyi7kHD89cH774dDh+o+3tdEMGvVSvrWrGV427H/WAAXPkqS1O527NhBX18f\n8+bNI+JY3biNJ6XEnj172L9/PwsXLjzssYYMzlPVrMF5usZXu8ccGbJH9+7lwNatxYp2VnMXQde5\n59J12mkTVuRHB/bSs/x8A7YkSS1o27ZtnH766U0TmseklNi+fTtnnHHGYdcrDc717HFWGT39/RUF\nzaGtWxl6+BHyJ86etI2kZiE7JYYff5zhxx+f/L5cjq7Fi+mYN8/+a0mSWkyzhWY4/jEbnJtQpQEb\nKgvZI88+y4HHHqt+X3ahUDZcD9x1Fz3LlhGdnUSp38j+a0mSVE4+n+ecc8557fO7776bWh+cZ3Bu\ncVOpYk/Ul13ThY+jowz99KdlbxvYuJGety+n9+KLeXXHDhc5SpLU5rq7u3m83LvfVWZwFlBZwJ5z\nxRUV7TqS6+vl5dvvgNHR6g0wJYa2/JShLZWF7FkrV9K3duJFjoZsSZJaz8qVK7nllls477zzAFix\nYgW33norixcvrsrXNzhrSiqtYPetW3fYQse67iSSEq888ACvPPBA2VsHNm5k1kUX0bd2DcPbnzZk\nS5JUI2Pto9XaPODAgQOvBeSFCxeyefNmrrrqKu644w5uvvlmnnnmGUZGRqoWmsFdNZSxcjuJ1Kz/\nejoi6FmxghPWrmX4aUO2JKl9bdu27bWdKV68/npGtm2f9P7RwUFGtm8vblYQQefpp5Pv7Z3w/s4z\nTufkz3520q/Z29vL4ODgYdeGhoZYvHgx27Zt43Of+xzz58/nU5/61IRjH+OuGmoKlVSwK+m/rkvI\nnsIx6sWe7Lcza9UqDj73HIf27HntMYO2JKndFPbt+/UOXylR2Ldv0uA8XT09PVxyySXcc889bNy4\nkWoXYA3OanhT3UWkYUL2li0MbdlS0e0DmzZxwnsuJ42OkvYPQmm7nMlOr3SvbElSIyhXGYbi7+fn\nN/wB6eBBYsYM3nTjDTX7/XXVVVdx2WWXsXLlSubOnVvVr21wVktpypANUCiw73ubp/68XI6uc8+l\nY+7cskfEg6c+SpKy0dPfz4Lbv13VHueJLF26lBNOOIENGzZU/WsbnNW2mjZkj1coMLx1a8W3D2zc\nSOdZZ9F16ql0n3vupLuOjF0zbEuSqmEqv3crcWR/85gXXniBQqHApZdeWrXXGmNwlipQrZANxwja\n9TxCPSVGnnqKkaeeYu/myircA5s2Mfu97yUdOkRh/36ImHCXFNtIJElZ+s53vsN1113HTTfdRC6X\nq/rXd1cNKWMTne4IE1eBa7JXdrXlcnSedRYd8+Yx4w1vmLRSb4VbkprLsXamaBbuqiE1sem+dVXJ\nXtk1PfWxnEKBkSefZGSKTxvYtIkTP/hBOHiQQy+/DEy8D7gVbklSPRmcpSY1lcBd6amP46+N7t1b\n3zaSMYUCA9/97tSfl8vRtXgxXae9ja4zz6y4em+FW5KmJ6VElHaBahbH22lRl1aNiLgBuAx4FXgW\n2JBSGij3PFs1pGxN1EYyWQW4KdpIxsvnmbVqFTGuF84dSiRpcjt27KCvr4958+Y1TXhOKbFnzx72\n79/PwoULD3us0laNegXnS4F7U0qHIuKvAVJK15Z7nsFZak5HngjZ0BXu6Yqge+kSOhedUnYRqBVu\nSa3m4MGD7Nq1i+Hh4ayHMiVdXV3Mnz+fGTNmHHa9oYLzYS8Y8V7g91NK68vda3CW2ku7VLh7L774\nsEtWuCUpW40cnL8P3JlS+scJHr8auBpgwYIFS3fu3FnP4UlqQuX6t2Hi8D14//1w6FAWw56aXI7u\nJUvoXLSobPXeyrYkTU3dg3NE/AA4+RgPXZdSuqd0z3XAMuB9qYIXtuIsqdaObCuBBtyhZDoimLVq\nFX1r1pQ96GbsumFbUrtquIpzRHwU+DiwLqU0VMlzDM6SGlHLVrjzeXpWrCDX0eFBN5LaSkPt4xwR\nvwNcC6yuNDRLUqM6nmNjG7rCPTrK0AMPTO05pRaS/OzZk/47DNmSWkG9dtX4b6AT2FO6tCWl9PFy\nz7PiLEnlK9xHHeP+2GON2UpS2mu7Y95cOl53kgsiJTWMhmvVmA6DsyRN3VjQBio66nxMw7WRRNDd\n30/nqacasiXVlMFZkjQlley/PXa94bYBjKB7ST+dpxiyJU2dwVmSVFOVHnTTTCEb3GFEakcGZ0lS\nw5jKaZINseVfPk/P8uVEZyeRz7uNn9TiDM6SpKZV6YLIRgnZsy66iOjoOGxsHrcuNQ+DsySpLTRN\nyM7lmLN+PenVEQ7t3nPY2Dz1UcqWwVmSpCNUcngNZLzDSAS9a9bQu3qVixylOjE4S5I0TZXuMAIZ\nhuwIupcupXPRIltDpONkcJYkqQ7KhezRvXs5sHVrsUWknr9z83l6LnwHuZkzgTjm2AzYUpHBWZKk\nBjG0dStDDz9C/sTZjXfqYwS9a9fSu2qlx6WrbRmcJUlqMpWc+pjJIsdcju4lS8jPnm3VWi3J4CxJ\nUouqZJFjXXuvcznmXHklaXj4qH2urVqrGRicJUlqY0f2XkPGrSG5HN39/XSecoqLGdVwDM6SJGlS\n5VpD6npcei7HnI9cSTow7BZ8qruGDM4RcQ1wA3BSSml3ufsNzpIkZWuyXUNGnn22vjuGuAWfaqTh\ngnNEvAX4JnA6sNTgLElS85toxxDIoGqdz9O7ejVEHDYG+6xVTqXBuaMegyn5MvBnwD11fE1JklRD\nPf39ZcNo37p1Ey5mrOo+16OjDN5778SP53J0959H/sQ57g6iaalLcI6IdwO/Sik9EeP+CpQkSa2v\nXLgut8911bbgKxQ48OhjEz48sGkTcz/6UQpDQ0dVzg3Vgiq2akTED4CTj/HQdcBngUtTSnsj4jlg\n2UStGhFxNXA1wIIFC5bu3LmzKuOTJEnNK/Mt+PJ5ei64gFxnJ0RYsW4xDdPjHBHnAP8JDJUuzQde\nAJanlF6c7Ln2OEuSpEpNtAVf3fqsI+hds4be1atcuNhkGiY4H/WCZSrO4xmcJUlSNWS+O8gRFesj\nxwBut5clg7MkSVKFJtsdBOp0EmMEvWvX0rtqpRXrOmvY4DwVBmdJktQIylasa30KYy7HnA9/mDQy\n4gExNWBwliRJqpPJTmGEOlWsczm6lyw56oAYK9blGZwlSZIaxEQLF6u63d5kbAOZlMFZkiSpSUxU\nsa7qATETyeeZddFFRMevj/dotxMXG/HkQEmSJB3DZIfE1PyAmNFRXrn//okfL5242HnKqUe1obRb\nxdqKsyRJUpOb6ICYei1cnLthA4XBwaNCfbNUrG3VkCRJUvYLF0uLFvOzZzfsTiAGZ0mSJJWV6YmL\nR5y2CNmEaYOzJEmSjstELSC1XLgYM2ey4B/uqGt4dnGgJEmSjstkixZh8oWL061Yp4MHGXr4kYZo\n4TiSwVmSJEnTUi5Y961bd8wTFyfbCSRmzKBn+fk1G/PxMDhLkiSpJiYK1nOuuOKYixahcRYMHktD\n9zhHxEvAzjq/7ALg+Tq/purPeW4PznN7cJ7bg/PcHrKa57emlE4qd1NDB+csRMRLlfwfp+bmPLcH\n57k9OM/twXluD40+z7msB9CABrIegOrCeW4PznN7cJ7bg/PcHhp6ng3OR9ub9QBUF85ze3Ce24Pz\n3B6c5/bQ0PNscD7abVkPQHXhPLcH57k9OM/twXluDw09z/Y4S5IkSRWw4ixJkiRVoC2Dc0S4f3WL\ni4jIegyqj4jIZz0G1V5EzMx6DKq9iDgh6zGo9iKiYXfNKKetgnNEdETEjcCXIuK3sh6PaiMickCM\n+1gtqPT9fD1wfURckvV4VBsRkS/N8y0R8Xv+odS6IuKTwP0RsbT0uQWQFlP6fv4C8OOIeGvW45mO\ntgkVpW/ArwBvBB4Gro2IT0ZEZ7YjUzVFxAZgF/D5rMei2omI1cCjwBzgF8AXI+LCbEelaisVOP4L\nOBG4F/gb4OxMB6WqGxeQ+4Ah4GqA5CKslhIRKyn+vO4DVqaU6n3AXVW0TXCmOFHnAR9PKf0TcCPw\nNuADmY5KVRMRvcDlwF8DvxsRp6SUCladW1IBuDGl9McppW8CPwHenfGYVH2/BD6ZUvpESulO4EmK\nP8vVQlJKqfRz+g3A1ylm6fVgK1aL2Qf0pZT+NKX0YkQsjIg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9XvyUh2qpkBI0pIqxz7+vlZWVfPWrX+Xss8/mc5/7HDfffDNz5sxhxYoVPPPM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\n97k06D6Xhry/zzkNxs65V4C9sdvM7MR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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "r2.plot(y=['beta', 'My', 'Mz', 'Fy'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "plt.plot" + ] + }, + { + "cell_type": "code", + "execution_count": 1111, + "metadata": {}, + "outputs": [ + { + "ename": "ValueError", + "evalue": "x and y must have same first dimension, but have shapes (12,) and (9, 12)", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma1\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0malpha_data\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ma1\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mCN_delta_aile_data\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'.'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 2\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma1\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0malpha_data\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ma2\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mCN_delta_aile_cl\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0ma2\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mCL\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0ma2\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0malpha_data\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\pyplot.py\u001b[0m in \u001b[0;36mplot\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m 3259\u001b[0m mplDeprecation)\n\u001b[0;32m 3260\u001b[0m \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 3261\u001b[1;33m \u001b[0mret\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 3262\u001b[0m \u001b[1;32mfinally\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3263\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_hold\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mwashold\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\__init__.py\u001b[0m in \u001b[0;36minner\u001b[1;34m(ax, *args, **kwargs)\u001b[0m\n\u001b[0;32m 1715\u001b[0m warnings.warn(msg % (label_namer, func.__name__),\n\u001b[0;32m 1716\u001b[0m RuntimeWarning, stacklevel=2)\n\u001b[1;32m-> 1717\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0max\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1718\u001b[0m \u001b[0mpre_doc\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0minner\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__doc__\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1719\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mpre_doc\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py\u001b[0m in \u001b[0;36mplot\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m 1370\u001b[0m \u001b[0mkwargs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcbook\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnormalize_kwargs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0m_alias_map\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1371\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1372\u001b[1;33m \u001b[1;32mfor\u001b[0m \u001b[0mline\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_lines\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1373\u001b[0m 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\u001b[1;32mfor\u001b[0m \u001b[0mseg\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_plot_args\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mthis\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 405\u001b[0m \u001b[1;32myield\u001b[0m \u001b[0mseg\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 406\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_base.py\u001b[0m in \u001b[0;36m_plot_args\u001b[1;34m(self, tup, kwargs)\u001b[0m\n\u001b[0;32m 382\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mindex_of\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtup\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 383\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 384\u001b[1;33m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_xy_from_xy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 385\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 386\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcommand\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'plot'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_base.py\u001b[0m in \u001b[0;36m_xy_from_xy\u001b[1;34m(self, x, y)\u001b[0m\n\u001b[0;32m 241\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 242\u001b[0m raise ValueError(\"x and y must have same first dimension, but \"\n\u001b[1;32m--> 243\u001b[1;33m \"have shapes {} and {}\".format(x.shape, y.shape))\n\u001b[0m\u001b[0;32m 244\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m2\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 245\u001b[0m raise ValueError(\"x and y can be no greater than 2-D, but have \"\n", + "\u001b[1;31mValueError\u001b[0m: x and y must have same first dimension, but have shapes (12,) and (9, 12)" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(a1.alpha_data, a1.CN_delta_aile_data, '.')\n", + "plt.plot(a1.alpha_data, a2.CN_delta_aile_cl*a2.CL + 0*a2.alpha_data)" + ] + }, + { + "cell_type": "code", + "execution_count": 1106, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-0.069523541636556885" + ] + }, + "execution_count": 1106, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.sum(a2.CL_data*a2.CN_p_data)/np.sum(a2.CL_data**2)" + ] + }, + { + "cell_type": "code", + "execution_count": 1119, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-0.00027157871300302394" + ] + }, + "execution_count": 1119, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.reshape(a1.CL_data**2, (1, 12)) * np.reshape(a1.delta_aile_data, (9, 1))\n", + "np.sum(a1.CN_delta_aile_data*x) / np.sum(x**2)" + ] + }, + { + "cell_type": "code", + "execution_count": 1120, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "LinregressResult(slope=-0.00027568577531501706, intercept=0.00072199122345927057, rvalue=-0.94235806962343571, pvalue=3.266896179580671e-52, stderr=9.5077855389690054e-06)" + ] + }, + "execution_count": 1120, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "linregress(x.flatten(), a1.CN_delta_aile_data.flatten())" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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IIerTMY3/s+HkVnTn3sCTnJMaPfPvK/RFRA5RVkYqM8eewZq+Ewk0ac7xb09g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\nrkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(aircraft.J_data,aircraft.Ct_data,'.')\n", + "plt.plot(aircraft.J_data,-0.1692121*aircraft.J_data**2 + 0.03545196*aircraft.J_data +0.10446359)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [], + "source": [ + "a,b,c = np.polyfit(aircraft.J_data,aircraft.Ct_data,2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/.ipynb_checkpoints/How it works-checkpoint.ipynb b/.ipynb_checkpoints/How it works-checkpoint.ipynb new file mode 100644 index 0000000..6160320 --- /dev/null +++ b/.ipynb_checkpoints/How it works-checkpoint.ipynb @@ -0,0 +1,938 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Python Flight Mechanics Engine " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Aircraft " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to perform a simulation, the first thing we need is an aircraft:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from pyfme.aircrafts import Cessna172" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "aircraft = Cessna172()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Aircraft will provide the simulator the forces, moments and inertial properties in order to perform the integration of the dynamic system equations:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Aircraft mass: 1043.2616 kg\n", + "Aircraft inertia tensor: \n", + " [[ 1285.3154166 0. 0. ]\n", + " [ 0. 1824.9309607 0. ]\n", + " [ 0. 0. 2666.89390765]] kg/m²\n" + ] + } + ], + "source": [ + "print(f\"Aircraft mass: {aircraft.mass} kg\")\n", + "print(f\"Aircraft inertia tensor: \\n {aircraft.inertia} kg/m²\")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "forces: [ 0. 0. 0.] N\n", + "moments: [ 0. 0. 0.] N·m\n" + ] + } + ], + "source": [ + "print(f\"forces: {aircraft.total_forces} N\")\n", + "print(f\"moments: {aircraft.total_moments} N·m\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the aircraft, in order to calculate its forces and moments it is necessary to set the controls values within the limits: " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0}\n" + ] + } + ], + "source": [ + "print(aircraft.controls)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'delta_elevator': (-0.4537856055185257, 0.48869219055841229), 'delta_aileron': (-0.26179938779914941, 0.3490658503988659), 'delta_rudder': (-0.27925268031909273, 0.27925268031909273), 'delta_t': (0, 1)}\n" + ] + } + ], + "source": [ + "print(aircraft.control_limits)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "but also to provide and environment (ie. atmosphere, winds, gravity) and the aircraft state, which will also determine the aerodynamic contribution." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Environment " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.environment.atmosphere import ISA1976\n", + "from pyfme.environment.wind import NoWind\n", + "from pyfme.environment.gravity import VerticalConstant" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "atmosphere = ISA1976()\n", + "gravity = VerticalConstant()\n", + "wind = NoWind()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The atmosphere, wind and gravity model make up the environment:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.environment import Environment" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "environment = Environment(atmosphere, gravity, wind)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The environment has an update method which given the state (ie. position, altitude...) updates the environment variables (ie. density, wind magnitude, gravity force...)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Help on method update in module pyfme.environment.environment:\n", + "\n", + "update(state) method of pyfme.environment.environment.Environment instance\n", + "\n" + ] + } + ], + "source": [ + "help(environment.update)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## State " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Even if the state can be set manually by giving the position, attitude, velocity, angular velocities... Most of the times, the user will want to trim the aircraft in a stationary condition. The aircraft controls to flight in that condition will be also provided by the trimmer." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.utils.trimmer import steady_state_trim" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Help on function steady_state_trim in module pyfme.utils.trimmer:\n", + "\n", + "steady_state_trim(aircraft, environment, pos, psi, TAS, controls, gamma=0, turn_rate=0, exclude=None, verbose=0)\n", + " Finds a combination of values of the state and control variables\n", + " that correspond to a steady-state flight condition.\n", + " \n", + " Steady-state aircraft flight is defined as a condition in which all\n", + " of the motion variables are constant or zero. That is, the linear and\n", + " angular velocity components are constant (or zero), thus all\n", + " acceleration components are zero.\n", + " \n", + " Parameters\n", + " ----------\n", + " aircraft : Aircraft\n", + " Aircraft to be trimmed.\n", + " environment : Environment\n", + " Environment where the aircraft is trimmed including atmosphere,\n", + " gravity and wind.\n", + " pos : Position\n", + " Initial position of the aircraft.\n", + " psi : float, opt\n", + " Initial yaw angle (rad).\n", + " TAS : float\n", + " True Air Speed (m/s).\n", + " controls : dict\n", + " Initial value guess for each control or fixed value if control is\n", + " included in exclude.\n", + " gamma : float, optional\n", + " Flight path angle (rad).\n", + " turn_rate : float, optional\n", + " Turn rate, d(psi)/dt (rad/s).\n", + " exclude : list, optional\n", + " List with controls not to be trimmed. If not given, every control\n", + " is considered in the trim process.\n", + " verbose : {0, 1, 2}, optional\n", + " Level of least_squares verbosity:\n", + " * 0 (default) : work silently.\n", + " * 1 : display a termination report.\n", + " * 2 : display progress during iterations (not supported by 'lm'\n", + " method).\n", + " \n", + " Returns\n", + " -------\n", + " state : AircraftState\n", + " Trimmed aircraft state.\n", + " trimmed_controls : dict\n", + " Trimmed aircraft controls\n", + " \n", + " Notes\n", + " -----\n", + " See section 3.4 in [1] for the algorithm description.\n", + " See section 2.5 in [1] for the definition of steady-state flight\n", + " condition.\n", + " \n", + " References\n", + " ----------\n", + " .. [1] Stevens, BL and Lewis, FL, \"Aircraft Control and Simulation\",\n", + " Wiley-lnterscience.\n", + "\n" + ] + } + ], + "source": [ + "help(steady_state_trim)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.models.state.position import EarthPosition" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "pos = EarthPosition(x=0, y=0, height=1000)\n", + "psi = 0.5 # rad\n", + "TAS = 45 # m/s\n", + "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "trimmed_state, trimmed_controls = steady_state_trim(\n", + " aircraft,\n", + " environment,\n", + " pos,\n", + " psi,\n", + " TAS,\n", + " controls0\n", + ") " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'delta_aileron': 5.6949494207348974e-18,\n", + " 'delta_elevator': -0.048951124635247888,\n", + " 'delta_rudder': -1.4494655727415656e-17,\n", + " 'delta_t': 0.57799667845248459}" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trimmed_controls" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "environment.update(trimmed_state)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, all the necessary elements in order to calculate forces and moments are available " + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Environment conditions for the current state:\n", + "environment.update(trimmed_state)\n", + "\n", + "# Forces and moments calculation:\n", + "forces, moments = aircraft.calculate_forces_and_moments(trimmed_state, environment, controls0)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([ 1.14823706e-11, -6.00938052e-18, -5.45696821e-12]),\n", + " array([ 1.34219095e-13, -1.43613996e-11, -2.41989038e-15]))" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "forces, moments" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The aircraft is trimmed indeed: the total forces and moments (aerodynamics + gravity + thrust) are zero" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simulation " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to simulate the dynamics of the aircraft under certain inputs in an environment, the user can set up a simulation using a dynamic system:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.models import EulerFlatEarth" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Constant Controls " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.utils.input_generator import Constant" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "controls = controls = {\n", + " 'delta_elevator': Constant(trimmed_controls['delta_elevator']),\n", + " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", + " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", + " 'delta_t': Constant(trimmed_controls['delta_t'])\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.simulator import Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "sim = Simulation(aircraft, system, environment, controls)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once the simulation is set, the propagation can be performed:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results = sim.propagate(10)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The results are returned in a DataFrame:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "kwargs = {'marker': '.',\n", + " 'subplots': True,\n", + " 'sharex': True,\n", + " 'figsize': (12, 6)}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['x_earth', 'y_earth', 'height'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['psi', 'theta', 'phi'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['v_north', 'v_east', 'v_down'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['p', 'q', 'r'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['alpha', 'beta', 'TAS'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['Fx', 'Fy', 'Fz'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['Mx', 'My', 'Mz'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['elevator', 'aileron', 'rudder', 'thrust'], **kwargs);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Doublet " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.utils.input_generator import Doublet" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "de0 = trimmed_controls['delta_elevator']" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "controls = controls = {\n", + " 'delta_elevator': Doublet(t_init=2, T=1, A=0.1, offset=de0),\n", + " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", + " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", + " 'delta_t': Constant(trimmed_controls['delta_t'])\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "sim = Simulation(aircraft, system, environment, controls)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once the simulation is set, the propagation can be performed:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results = sim.propagate(90)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['x_earth', 'y_earth', 'height'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['psi', 'theta', 'phi'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['v_north', 'v_east', 'v_down'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['p', 'q', 'r'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['alpha', 'beta', 'TAS'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['Fx', 'Fy', 'Fz'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['Mx', 'My', 'Mz'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['elevator', 'aileron', 'rudder', 'thrust'], **kwargs);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Propagating only one time step" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "dt = 0.05 # seconds\n", + "sim = Simulation(aircraft, system, environment, controls, dt)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results = sim.propagate(0.5)\n", + "results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can propagate for one time step even once the simulation has been propagated before:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results = sim.propagate(sim.time+dt)\n", + "results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that `results` will include the previous timesteps as well as the last one. To get just the last one one can use pandas `loc` or `iloc`:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.iloc[-1] # last time step" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.loc[sim.time] # results for current simulation time" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Eigenvalue problem - tests.ipynb b/Eigenvalue problem - tests.ipynb new file mode 100644 index 0000000..eec39b2 --- /dev/null +++ b/Eigenvalue problem - tests.ipynb @@ -0,0 +1,864 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Python Flight Mechanics Engine " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.aircrafts import LinearB747, SimplifiedCessna172\n", + "from pyfme.models import EulerFlatEarth\n", + "import numpy as np\n", + "nl = np.linalg\n", + "import matplotlib.pyplot as plt\n", + "from pyfme.environment.atmosphere import ISA1976\n", + "from pyfme.environment.wind import NoWind\n", + "from pyfme.environment.gravity import VerticalConstant\n", + "from pyfme.environment import Environment\n", + "from pyfme.utils.trimmer import steady_state_trim\n", + "from pyfme.models.state.position import EarthPosition\n", + "from pyfme.simulator import Simulation\n", + "from pyfme.models import EulerFlatEarth" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Test on Boeing" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "aircraft = LinearB747()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Aircraft mass: 288660.5504587156 kg\n", + "Aircraft inertia tensor: \n", + " [[ 24700000. 0. -2120000.]\n", + " [ 0. 44900000. 0.]\n", + " [ -2120000. 0. 67300000.]] kg/m²\n" + ] + } + ], + "source": [ + "print(f\"Aircraft mass: {aircraft.mass} kg\")\n", + "print(f\"Aircraft inertia tensor: \\n {aircraft.inertia} kg/m²\")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "state, environment = aircraft.trimmed_conditions()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system = EulerFlatEarth(t0=0, full_state=state)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "A_long, A_lat = system.linearized_model(state, aircraft, environment, None)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ -6.86619629e-03 1.39437135e-02 0.00000000e+00 -9.80665000e+00]\n", + " [ -9.04964592e-02 -3.14906754e-01 2.35892792e+02 -0.00000000e+00]\n", + " [ 3.89092422e-04 -3.36169904e-03 -4.28171388e-01 0.00000000e+00]\n", + " [ 0.00000000e+00 0.00000000e+00 1.00000000e+00 0.00000000e+00]]\n" + ] + } + ], + "source": [ + "print(f\"{A_long}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "d = aircraft.calculate_derivatives(None, None, None)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "val, vec = nl.eig(A_long)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-0.37168337+0.88692454j, -0.37168337-0.88692454j,\n", + " -0.00328880+0.0671904j , -0.00328880-0.0671904j ])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "val" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ -5.57748538e-02 0.00000000e+00 -2.35900000e+02 9.80665000e+00]\n", + " [ -1.27028796e-02 -4.35107741e-01 4.14335937e-01 0.00000000e+00]\n", + " [ 3.56656916e-03 -6.05604146e-03 -1.45800775e-01 0.00000000e+00]\n", + " [ 0.00000000e+00 1.00000000e+00 0.00000000e+00 0.00000000e+00]]\n" + ] + } + ], + "source": [ + "print(f\"{A_lat}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "val, vec = nl.eig(A_lat)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([-0.03309986+0.94696989j, -0.03309986-0.94696989j,\n", + " -0.56322438+0.j , -0.00725928+0.j ])" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "val" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Eigen values are the same as the ones in Etkin. So the matrix was copy-pasted right in EulerFlatEarth.linearize()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Simplified Cessna: compare response with eigenvalue analysis" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [], + "source": [ + "aircraft = SimplifiedCessna172()" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [], + "source": [ + "atmosphere = ISA1976()\n", + "gravity = VerticalConstant()\n", + "wind = NoWind()\n", + "environment = Environment(atmosphere, gravity, wind)" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [], + "source": [ + "pos = EarthPosition(x=0, y=0, height=1000)\n", + "psi = 0.5 # rad\n", + "TAS = 45 # m/s\n", + "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}\n", + "trimmed_state, trimmed_controls = steady_state_trim(\n", + " aircraft,\n", + " environment,\n", + " pos,\n", + " psi,\n", + " TAS,\n", + " controls0\n", + ")\n", + "environment.update(trimmed_state)" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'Lp': -7133.3285464529754,\n", + " 'Lq': -1.3596490723877686e-10,\n", + " 'Lr': 2845.5233747989769,\n", + " 'Lu': -1.5072258133617629e-13,\n", + " 'Lv': -93.803403491879237,\n", + " 'Lw': 6.4642542808689936e-11,\n", + " 'Lw_dot': 0.0,\n", + " 'Mp': -1.3635270481322531e-10,\n", + " 'Mq': -5632.7295473571794,\n", + " 'Mr': 2.5855995439045339e-10,\n", + " 'Mu': -2.0740884413894751e-10,\n", + " 'Mv': -8.5234948148304966e-12,\n", + " 'Mw': -707.13949139550539,\n", + " 'Mw_dot': 0.0,\n", + " 'Np': -283.31950651664334,\n", + " 'Nq': -2.0902086546512417e-11,\n", + " 'Nr': -895.8625397666973,\n", + " 'Nu': -1.600102250108547e-12,\n", + " 'Nv': 63.401932933487544,\n", + " 'Nw': 4.8437512785752048e-12,\n", + " 'Nw_dot': 0.0,\n", + " 'Xp': 8.5635844119039128e-12,\n", + " 'Xq': -107.98409108583664,\n", + " 'Xr': -4.3879010396940393e-11,\n", + " 'Xu': -81.920634161805893,\n", + " 'Xv': -1.0186591357214635e-10,\n", + " 'Xw': 117.92566393495383,\n", + " 'Xw_dot': 0.0,\n", + " 'Yp': -94.244627388807359,\n", + " 'Yq': -8.5635868519158715e-12,\n", + " 'Yr': 482.90054315893269,\n", + " 'Yu': -7.5184642244713184e-12,\n", + " 'Yv': -126.09881477888285,\n", + " 'Yw': 2.053118461568279e-11,\n", + " 'Yw_dot': 0.0,\n", + " 'Zp': 0.0,\n", + " 'Zq': -2203.4392987142378,\n", + " 'Zr': 0.0,\n", + " 'Zu': -448.14552058364376,\n", + " 'Zv': 9.0763684172927728e-12,\n", + " 'Zw': -2221.7928894687734,\n", + " 'Zw_dot': 0.0}" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "aircraft.calculate_derivatives(trimmed_state, environment=environment, controls=trimmed_controls)" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [], + "source": [ + "A_long, A_lat = system.linearized_model(trimmed_state, aircraft, environment, trimmed_controls)" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "longitudinal eigenvalues : [[-2.61286215+4.04181191j -2.61286215-4.04181191j -0.03450179+0.26321042j\n", + " -0.03450179-0.26321042j]]\n" + ] + } + ], + "source": [ + "long_val, long_vec=nl.eig(A_long)\n", + "long_val = np.expand_dims(long_val, axis = 0)\n", + "print(f\"longitudinal eigenvalues : {long_val}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ -1.20869794e-01 -9.03365248e-02 -4.43934827e+01 9.80665000e+00]\n", + " [ -7.29808437e-02 -5.54986617e+00 2.21387166e+00 0.00000000e+00]\n", + " [ 2.37736990e-02 -1.06235762e-01 -3.35919827e-01 0.00000000e+00]\n", + " [ 0.00000000e+00 1.00000000e+00 0.00000000e+00 0.00000000e+00]]\n" + ] + } + ], + "source": [ + "print(f\"{A_lat}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "lat eigenvalues : [[-5.54552962+0.j -0.24937803+1.12210093j -0.24937803-1.12210093j\n", + " 0.03762989+0.j ]]\n" + ] + } + ], + "source": [ + "lat_val, lat_vec=nl.eig(A_lat)\n", + "lat_val = np.expand_dims(lat_val, axis = 0)\n", + "print(f\"lat eigenvalues : {lat_val}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Longitudinal checks" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Aircraft State \n", + "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", + "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", + "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", + "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", + "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", + "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " + ] + }, + "execution_count": 57, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trimmed_state" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def linear_stab_2_body(long_state=np.zeros(4), lat_state=np.zeros(4), u0=0, theta0=0,alpha0=0, beta0=0):\n", + " # velocities\n", + " v = wind2body(np.array([long_state[0] + u0, lat_state[0], long_state[1]]), alpha=alpha0, beta=beta0)\n", + " # Roll rates\n", + " r = wind2body(np.array([lat_state[1], long_state[2], lat_state[2]]), alpha=alpha0, beta=beta0)\n", + " long_stateB = np.copy(long_state)\n", + " lat_stateB = np.copy(lat_state)\n", + " long_stateB[0] = v[0]\n", + " long_stateB[1] = v[2]\n", + " long_stateB[2] = r[1]\n", + " long_stateB[3] += theta0\n", + " lat_stateB[0] = v[1]\n", + " lat_stateB[1] = r[0]\n", + " lat_stateB[2] = r[2]\n", + " return long_stateB.real, lat_stateB.real" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": {}, + "outputs": [], + "source": [ + "from pyfme.utils.coordinates import wind2body, body2wind, stab2body" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + "outputs": [], + "source": [ + "alpha = np.arctan2(trimmed_state.velocity.w, trimmed_state.velocity.u)\n", + "u = trimmed_state.velocity.u*1.0" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": {}, + "outputs": [], + "source": [ + "perturbation = (long_vec.T[0] + long_vec.T[1])/10" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Eigenvalue approach" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [], + "source": [ + "C = nl.lstsq(a=long_vec,b=perturbation.real)[0].real" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# stability axis\n", + "u, v, w = body2wind(trimmed_state.velocity.vel_body, alpha, 0)\n", + "theta0 = trimmed_state.attitude.theta*1.0" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 4.48563585e+01, -4.08894829e-12, 3.59264617e+00])" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trimmed_state.velocity._vel_body" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 4.48563585e+01, -4.08894829e-12, 3.59264617e+00])" + ] + }, + "execution_count": 65, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "wind2body(np.array([u,v,w]), alpha=alpha, beta=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": {}, + "outputs": [], + "source": [ + "t = np.linspace(0,3,100)\n", + "N = len(t)\n", + "X = np.zeros((N,4))\n", + "xx = []\n", + "for i in range(N):\n", + " x_stab = (long_vec*np.exp(long_val*t[i])).dot(C)\n", + " xx.append(x_stab[1])\n", + " X[i,:] = linear_stab_2_body(long_state=x_stab.real, alpha0=alpha, u0=u, theta0 = theta0)[0]" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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et25f9rY3zfvAUGjJKb/EVHD5qRTbZe/rYvQvu7x7of7sEvqLpN01+4R+Q3OGfOTEK6/9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\nd3XCAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(t,X[:,1],'.')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.utils.input_generator import Constant" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [], + "source": [ + "controls = {\n", + " 'delta_elevator': Constant(trimmed_controls['delta_elevator']),\n", + " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", + " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", + " 'delta_t': Constant(trimmed_controls['delta_t'])\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": {}, + "outputs": [], + "source": [ + "# Perturbate\n", + "trimmed_state.cancel_perturbation()\n", + "p = linear_stab_2_body(long_state=perturbation.real, alpha0=alpha)[0]\n", + "trimmed_state.perturbate(np.array([p[0],0,p[1]]), 'velocity')\n", + "trimmed_state.perturbate(np.array([0,p[2],0]), 'angular_vel')\n", + "trimmed_state.perturbate(np.array([0,p[3],0]), 'attitude')" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Aircraft State \n", + "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", + "theta: 0.080 rad, phi: 0.004 rad, psi: 0.500 rad \n", + "u: 44.84 m/s, v: -0.00 m/s, w: 3.79 m/s \n", + "P: 0.00 rad/s, Q: -0.00 rad/s, R: 0.00 rad/s \n", + "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", + "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " + ] + }, + "execution_count": 79, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trimmed_state" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0.00438011+0.j, 0.19901295+0.j, -0.00220572+0.j, 0.00353290+0.j])" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "perturbation" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "environment.update(trimmed_state)\n", + "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "sim = Simulation(aircraft, system, environment, controls)" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "time: 100%|████████████████████████████████████████████████████████████▉| 9.999999999999831/10 [00:06<00:00, 1.49it/s]\n" + ] + } + ], + "source": [ + "r = sim.propagate(10)" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Aircraft State \n", + "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", + "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", + "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", + "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", + "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", + "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " + ] + }, + "execution_count": 75, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trimmed_state.cancel_perturbation()" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(t,X[:,3],'.')\n", + "plt.plot(r.theta)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Aircraft State \n", + "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", + "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", + "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", + "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", + "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", + "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " + ] + }, + "execution_count": 77, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trimmed_state" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/How it works (modif).ipynb b/How it works (modif).ipynb new file mode 100644 index 0000000..1a228b7 --- /dev/null +++ b/How it works (modif).ipynb @@ -0,0 +1,4991 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Python Flight Mechanics Engine " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Aircraft " + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import pyfme\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy import stats" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The autoreload extension is already loaded. To reload it, use:\n", + " %reload_ext autoreload\n" + ] + } + ], + "source": [ + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.aircrafts import SimplifiedCessna172, Cessna172" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "aircraft = SimplifiedCessna172()" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [ + { + "ename": "AttributeError", + "evalue": "'SimplifiedCessna172' object has no attribute 'full_state'", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mAttributeError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0maircraft\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfull_state\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[1;31mAttributeError\u001b[0m: 'SimplifiedCessna172' object has no attribute 'full_state'" + ] + } + ], + "source": [ + "aircraft.full_state" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Aircraft will provide the simulator the forces, moments and inertial properties in order to perform the integration of the dynamic system equations:" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Aircraft mass: 1043.2616 kg\n", + "Aircraft inertia tensor: \n", + " [[ 1285.3154166 0. 0. ]\n", + " [ 0. 1824.9309607 0. ]\n", + " [ 0. 0. 2666.89390765]] kg/m²\n" + ] + } + ], + "source": [ + "print(f\"Aircraft mass: {aircraft.mass} kg\")\n", + "print(f\"Aircraft inertia tensor: \\n {aircraft.inertia} kg/m²\")" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "forces: [ 0. 0. 0.] N\n", + "moments: [ 0. 0. 0.] N·m\n" + ] + } + ], + "source": [ + "print(f\"forces: {aircraft.total_forces} N\")\n", + "print(f\"moments: {aircraft.total_moments} N·m\")" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Stability Derivatives : \n", + "CL_0 = 0.148;\n", + "CM_0 = 0.012068670774609398;\n", + "CL_alpha = 5.44;\n", + "CL_q = 7.281999999999999;\n", + "CL_delta_elev = 0.005677366997294861;\n", + "CM_alpha2 = -0.0008829539354397849;\n", + "CM_alpha = -0.01230758597735665;\n", + "CM_q = -12.464;\n", + "CM_delta_elev = -0.014180595130748421;\n", + "CD_K1 = 0.04394233763124108;\n", + "CD_0 = 0.029537580994030695;\n", + "CL_MAX = 1.889;\n", + "CY_beta = -0.26799999999999996;\n", + "CY_p = -0.05993333333333333;\n", + "CY_r = 0.2143333333333333;\n", + "CY_delta_rud = -0.561;\n", + "Cl_beta = -0.022292500000000003;\n", + "Cl_p = -0.3025083333333333;\n", + "Cl_r_cl = 0.17341925931518656;\n", + "Cl_delta_rud = -0.0027193749999999996;\n", + "Cl_delta_aile = 0.0044410237288135595;\n", + "CN_beta = 0.0126;\n", + "CN_p_al = -0.007206294994140298;\n", + "CN_r_cl = -0.00957535593543321;\n", + "CN_r_0 = -0.027354917660317425;\n", + "CN_delta_rud = 0.016818749999999997;\n", + "CN_delta_aile_cl = -0.0004745447361550377;\n", + "Ct_J2 = -0.16921210379223448;\n", + "Ct_J = 0.03545196433877688;\n", + "C_0 = 0.10446359303931643;\n" + ] + } + ], + "source": [ + "print(\"Stability Derivatives : \")\n", + "for k,val in aircraft.__dict__.items():\n", + " if k.startswith('C') and \"data\" not in k and \"_\" in k:\n", + " print(f\"{k} = {val};\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the aircraft, in order to calculate its forces and moments it is necessary to set the controls values within the limits: " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(aircraft.controls)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(aircraft.control_limits)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "but also to provide and environment (ie. atmosphere, winds, gravity) and the aircraft state, which will also determine the aerodynamic contribution." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Environment " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.environment.atmosphere import ISA1976\n", + "from pyfme.environment.wind import NoWind\n", + "from pyfme.environment.gravity import VerticalConstant" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "atmosphere = ISA1976()\n", + "gravity = VerticalConstant()\n", + "wind = NoWind()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The atmosphere, wind and gravity model make up the environment:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.environment import Environment" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "environment = Environment(atmosphere, gravity, wind)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The environment has an update method which given the state (ie. position, altitude...) updates the environment variables (ie. density, wind magnitude, gravity force...)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "help(environment.update)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## State " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Even if the state can be set manually by giving the position, attitude, velocity, angular velocities... Most of the times, the user will want to trim the aircraft in a stationary condition. The aircraft controls to flight in that condition will be also provided by the trimmer." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.utils.trimmer import steady_state_trim" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "help(steady_state_trim)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.models.state.position import EarthPosition" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "pos = EarthPosition(x=0, y=0, height=1000)\n", + "psi = 0.5 # rad\n", + "TAS = 45 # m/s\n", + "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "trimmed_state, trimmed_controls = steady_state_trim(\n", + " aircraft,\n", + " environment,\n", + " pos,\n", + " psi,\n", + " TAS,\n", + " controls0\n", + ") " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "trimmed_state" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "trimmed_controls" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, all the necessary elements in order to calculate forces and moments are available " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Environment conditions for the current state:\n", + "environment.update(trimmed_state)\n", + "\n", + "# Forces and moments calculation:\n", + "forces, moments = aircraft.calculate_forces_and_moments(trimmed_state, environment, controls0)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(\"NDIM forces : \")\n", + "for k,val in aircraft.__dict__.items():\n", + " if k.startswith('C') and \"data\" not in k and \"_\" not in k:\n", + " print(f\"{k} : {val}\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "forces, moments" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The aircraft is trimmed indeed: the total forces and moments (aerodynamics + gravity + thrust) are zero" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simulation " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to simulate the dynamics of the aircraft under certain inputs in an environment, the user can set up a simulation using a dynamic system:" + ] + }, + { + "cell_type": "code", + "execution_count": 739, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.models import EulerFlatEarth" + ] + }, + { + "cell_type": "code", + "execution_count": 740, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Constant Controls " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values." + ] + }, + { + "cell_type": "code", + "execution_count": 741, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.utils.input_generator import Constant" + ] + }, + { + "cell_type": "code", + "execution_count": 742, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "controls = {\n", + " 'delta_elevator': Constant(trimmed_controls['delta_elevator']),\n", + " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", + " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", + " 'delta_t': Constant(trimmed_controls['delta_t'])\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 743, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.simulator import Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 744, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "sim = Simulation(aircraft, system, environment, controls)" + ] + }, + { + "cell_type": "code", + "execution_count": 745, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system = EulerFlatEarth(t0=0, full_state=trimmed_state)\n", + "sim = Simulation(aircraft, system, environment, controls)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once the simulation is set, the propagation can be performed:" + ] + }, + { + "cell_type": "code", + "execution_count": 767, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n", + "\n", + "time: 10.0it [00:00, ?it/s]\n", + "\n" + ] + } + ], + "source": [ + "results = sim.propagate(5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The results are returned in a DataFrame:" + ] + }, + { + "cell_type": "code", + "execution_count": 747, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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FxFyFzMachMxMyMzTASaaileron...thrustuvv_downv_eastv_northwx_earthy_earthz_earth
time
0.011.546141e-111.688011e-160.000000e+000.133756-3.667941e-13-1.355845e-11-1.585097e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.511938e-154.440892e-1621.57414939.4912153.3964640.3949120.215741-1000.0
0.021.546141e-115.250914e-170.000000e+000.133756-3.506913e-13-1.314636e-11-1.347614e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.512042e-154.440892e-1621.57414939.4912153.3964640.7898240.431483-1000.0
0.031.546141e-11-3.441253e-160.000000e+000.133756-3.352723e-13-1.274679e-11-1.121474e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.512218e-154.440892e-1621.57414939.4912153.3964641.1847360.647224-1000.0
0.041.546141e-11-1.008065e-150.000000e+000.133756-3.205078e-13-1.235936e-11-9.062203e-1545.0336.434581-9.644866e-18...0.57799744.87164-3.512470e-154.440892e-1621.57414939.4912153.3964641.5796490.862966-1000.0
0.051.546141e-11-1.926832e-150.000000e+000.133756-3.063696e-13-1.198371e-11-7.014180e-1545.0336.434581-9.644866e-18...0.57799744.87164-3.512798e-154.440892e-1621.57414939.4912153.3964641.9745611.078707-1000.0
0.061.546141e-11-3.088483e-150.000000e+000.133756-2.928307e-13-1.161948e-11-5.066498e-1545.0336.434581-9.644866e-18...0.57799744.87164-3.513206e-154.440892e-1621.57414939.4912153.3964642.3694731.294449-1000.0
0.071.534772e-11-4.481585e-151.818989e-120.133756-2.798654e-13-1.126632e-11-3.215162e-1545.0336.434581-9.644866e-18...0.57799744.87164-3.513695e-154.440892e-1621.57414939.4912153.3964642.7643851.510190-1000.0
0.081.534772e-11-6.095197e-151.818989e-120.133756-2.674490e-13-1.092389e-11-1.456347e-1545.0336.434581-9.644866e-18...0.57799744.87164-3.514266e-154.440892e-1621.57414939.4912153.3964643.1592971.725932-1000.0
0.091.534772e-11-7.918846e-151.818989e-120.133756-2.555579e-13-1.059187e-112.136113e-1645.0336.434581-9.644866e-18...0.57799744.87164-3.514923e-150.000000e+0021.57414939.4912153.3964643.5542091.941673-1000.0
0.101.523404e-11-9.948167e-153.637979e-120.133756-2.441994e-13-9.889790e-121.798616e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.515665e-15-4.440892e-1621.57414939.4912153.3964643.9491222.157415-1000.0
0.111.489298e-11-1.213353e-145.456968e-120.133756-2.331439e-13-9.209049e-122.315148e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.516503e-15-8.881784e-1621.57414939.4912153.3964644.3440342.373156-1000.0
0.121.512035e-11-1.448774e-145.456968e-120.133756-2.225089e-13-8.548998e-122.316617e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.517460e-15-8.881784e-1621.57414939.4912153.3964644.7389462.588898-1000.0
0.131.523404e-11-1.701269e-145.456968e-120.133756-2.123358e-13-8.289160e-122.445525e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.518540e-15-4.440892e-1621.57414939.4912153.3964645.1338582.804639-1000.0
0.141.523404e-11-1.969178e-147.275958e-120.133756-2.025612e-13-7.664615e-123.206469e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.519743e-15-4.440892e-1621.57414939.4912153.3964645.5287703.020381-1000.0
0.151.568878e-11-2.252049e-141.273293e-110.133756-1.931933e-13-7.059053e-122.645450e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.521077e-150.000000e+0021.57414939.4912153.3964645.9236823.236122-1000.0
0.161.580247e-11-2.549911e-141.273293e-110.133756-1.842518e-13-6.844501e-122.752624e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.522536e-150.000000e+0021.57414939.4912153.3964646.3185943.451864-1000.0
0.171.557510e-11-2.861302e-141.637090e-110.133756-1.756801e-13-6.263865e-122.954086e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.524120e-150.000000e+0021.57414939.4912153.3964646.7135073.667605-1000.0
0.181.557510e-11-3.185448e-141.818989e-110.133756-1.674601e-13-5.700878e-123.081479e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.525830e-154.440892e-1621.57414939.4912153.3964647.1084193.883347-1000.0
0.191.557510e-11-3.522797e-141.818989e-110.133756-1.596367e-13-4.782397e-121.923424e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.527666e-154.440892e-1621.57414939.4912153.3964647.5033314.099088-1000.0
0.201.568878e-11-3.873125e-141.818989e-110.133756-1.522040e-13-4.637041e-122.008599e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.529612e-158.881784e-1621.57414939.4912153.3964647.8982434.314830-1000.0
0.211.568878e-11-4.234649e-141.818989e-110.133756-1.450822e-13-4.496103e-122.088193e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.531666e-158.881784e-1621.57414939.4912153.3964648.2931554.530571-1000.0
0.221.546141e-11-4.605667e-142.182787e-110.133756-1.382001e-13-3.986845e-123.475211e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.533831e-158.881784e-1621.57414939.4912153.3964648.6880674.746313-1000.0
0.231.568878e-11-4.985191e-142.182787e-110.133756-1.315377e-13-3.865669e-123.540318e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.536124e-151.332268e-1521.57414939.4912153.3964649.0829804.962054-1000.0
0.241.568878e-11-5.373557e-142.182787e-110.133756-1.251340e-13-3.375572e-124.004200e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.538548e-151.332268e-1521.57414939.4912153.3964649.4778925.177796-1000.0
0.251.568878e-11-5.770391e-142.364686e-110.133756-1.189899e-13-2.900371e-123.721343e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.541109e-151.776357e-1521.57414939.4912153.3964649.8728045.393537-1000.0
0.261.557510e-11-6.175787e-142.546585e-110.133756-1.131234e-13-2.439613e-123.636619e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.543804e-151.776357e-1521.57414939.4912153.39646410.2677165.609279-1000.0
0.271.580247e-11-6.588990e-142.546585e-110.133756-1.075064e-13-2.365464e-123.682321e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.546629e-151.776357e-1521.57414939.4912153.39646410.6626285.825020-1000.0
0.281.568878e-11-7.008588e-142.728484e-110.133756-1.020786e-13-1.920964e-124.699768e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.549585e-152.220446e-1521.57414939.4912153.39646411.0575406.040762-1000.0
0.291.557510e-11-7.434394e-142.910383e-110.133756-9.685431e-14-1.489974e-124.060594e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.552685e-152.220446e-1521.57414939.4912153.39646411.4524526.256503-1000.0
0.301.568878e-11-7.867110e-142.910383e-110.133756-9.187934e-14-1.444688e-124.092412e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.555922e-152.664535e-1521.57414939.4912153.39646411.8473656.472245-1000.0
..................................................................
9.711.479066e-10-5.311047e-124.729372e-110.133756-4.807148e-151.651500e-25-3.956346e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.664932e-155.875300e-1321.57414939.4912153.396464383.459700209.484989-1000.0
9.721.480203e-10-5.318273e-124.729372e-110.133756-4.794496e-151.597792e-25-3.952250e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.666790e-155.884182e-1321.57414939.4912153.396464383.854613209.700731-1000.0
9.731.482476e-10-5.325504e-124.729372e-110.133756-4.781638e-151.544085e-25-3.948197e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.668652e-155.888623e-1321.57414939.4912153.396464384.249525209.916472-1000.0
9.741.483613e-10-5.332739e-124.729372e-110.133756-4.768578e-151.503805e-25-3.944187e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.670518e-155.897505e-1321.57414939.4912153.396464384.644437210.132214-1000.0
9.751.484750e-10-5.339978e-124.729372e-110.133756-4.755319e-151.463524e-25-3.940220e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.672389e-155.901946e-1321.57414939.4912153.396464385.039349210.347955-1000.0
9.761.485887e-10-5.347222e-124.729372e-110.133756-4.741864e-151.409817e-25-3.936298e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.674264e-155.906386e-1321.57414939.4912153.396464385.434261210.563697-1000.0
9.771.488161e-10-5.354470e-124.729372e-110.133756-4.728216e-151.369536e-25-3.932421e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.676144e-155.915268e-1321.57414939.4912153.396464385.829173210.779438-1000.0
9.781.489298e-10-5.361722e-124.729372e-110.133756-4.714378e-151.315829e-25-3.928590e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.678028e-155.919709e-1321.57414939.4912153.396464386.224085210.995180-1000.0
9.791.490434e-10-5.368978e-124.729372e-110.133756-4.700354e-151.275549e-25-3.924805e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.679916e-155.928591e-1321.57414939.4912153.396464386.618998211.210921-1000.0
9.801.491571e-10-5.376239e-124.729372e-110.133756-4.686147e-151.248695e-25-3.921066e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.681810e-155.933032e-1321.57414939.4912153.396464387.013910211.426663-1000.0
9.811.493845e-10-5.383504e-124.729372e-110.133756-4.671759e-151.208414e-25-3.917374e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.683708e-155.937473e-1321.57414939.4912153.396464387.408822211.642404-1000.0
9.821.494982e-10-5.390773e-124.729372e-110.133756-4.657195e-151.181561e-25-3.913730e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.685612e-155.946355e-1321.57414939.4912153.396464387.803734211.858146-1000.0
9.831.496119e-10-5.398046e-124.729372e-110.133756-4.642458e-151.154707e-25-3.910134e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.687520e-155.950795e-1321.57414939.4912153.396464388.198646212.073887-1000.0
9.841.497256e-10-5.405323e-124.911271e-110.133756-4.627550e-151.114427e-25-3.906587e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.689434e-155.964118e-1321.57414939.4912153.396464388.593558212.289628-1000.0
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9.911.506351e-10-5.456378e-124.911271e-110.133756-4.518707e-158.861705e-26-3.883162e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.702982e-155.999645e-1321.57414939.4912153.396464391.357943213.799819-1000.0
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9.951.510898e-10-5.485638e-124.911271e-110.133756-4.453270e-157.921828e-26-3.870920e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.710851e-156.026291e-1321.57414939.4912153.396464392.937592214.662785-1000.0
9.961.514309e-10-5.492963e-124.911271e-110.133756-4.436576e-157.653291e-26-3.867993e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.712834e-156.030731e-1321.57414939.4912153.396464393.332504214.878526-1000.0
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10.001.519993e-10-5.522300e-124.911271e-110.133756-4.368557e-156.847682e-26-3.856835e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.720829e-156.057377e-1321.57414939.4912153.396464394.912153215.741492-1000.0
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1000 rows × 35 columns

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45.0 336.434581 -9.644866e-18 ... \n", + "0.05 -1.198371e-11 -7.014180e-15 45.0 336.434581 -9.644866e-18 ... \n", + "0.06 -1.161948e-11 -5.066498e-15 45.0 336.434581 -9.644866e-18 ... \n", + "0.07 -1.126632e-11 -3.215162e-15 45.0 336.434581 -9.644866e-18 ... \n", + "0.08 -1.092389e-11 -1.456347e-15 45.0 336.434581 -9.644866e-18 ... \n", + "0.09 -1.059187e-11 2.136113e-16 45.0 336.434581 -9.644866e-18 ... \n", + "0.10 -9.889790e-12 1.798616e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.11 -9.209049e-12 2.315148e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.12 -8.548998e-12 2.316617e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.13 -8.289160e-12 2.445525e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.14 -7.664615e-12 3.206469e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.15 -7.059053e-12 2.645450e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.16 -6.844501e-12 2.752624e-14 45.0 336.434581 -9.644866e-18 ... \n", + "0.17 -6.263865e-12 2.954086e-14 45.0 336.434581 -9.644866e-18 ... 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-3.906587e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.85 1.074146e-25 -3.903089e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.86 1.047292e-25 -3.899641e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.87 1.007012e-25 -3.896243e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.88 9.801583e-26 -3.892896e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.89 9.533047e-26 -3.889600e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.90 9.130242e-26 -3.886355e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.91 8.861705e-26 -3.883162e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.92 8.458901e-26 -3.880022e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.93 8.324632e-26 -3.876934e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.94 8.056096e-26 -3.873900e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.95 7.921828e-26 -3.870920e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.96 7.653291e-26 -3.867993e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.97 7.519023e-26 -3.865121e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.98 7.250486e-26 -3.862304e-14 45.0 336.434581 -9.644866e-18 ... \n", + "9.99 7.116218e-26 -3.859542e-14 45.0 336.434581 -9.644866e-18 ... \n", + "10.00 6.847682e-26 -3.856835e-14 45.0 336.434581 -9.644866e-18 ... \n", + "\n", + " thrust u v v_down v_east v_north \\\n", + "time \n", + "0.01 0.577997 44.87164 -3.511938e-15 4.440892e-16 21.574149 39.491215 \n", + "0.02 0.577997 44.87164 -3.512042e-15 4.440892e-16 21.574149 39.491215 \n", + "0.03 0.577997 44.87164 -3.512218e-15 4.440892e-16 21.574149 39.491215 \n", + "0.04 0.577997 44.87164 -3.512470e-15 4.440892e-16 21.574149 39.491215 \n", + "0.05 0.577997 44.87164 -3.512798e-15 4.440892e-16 21.574149 39.491215 \n", + "0.06 0.577997 44.87164 -3.513206e-15 4.440892e-16 21.574149 39.491215 \n", + "0.07 0.577997 44.87164 -3.513695e-15 4.440892e-16 21.574149 39.491215 \n", + "0.08 0.577997 44.87164 -3.514266e-15 4.440892e-16 21.574149 39.491215 \n", + "0.09 0.577997 44.87164 -3.514923e-15 0.000000e+00 21.574149 39.491215 \n", + "0.10 0.577997 44.87164 -3.515665e-15 -4.440892e-16 21.574149 39.491215 \n", + "0.11 0.577997 44.87164 -3.516503e-15 -8.881784e-16 21.574149 39.491215 \n", + "0.12 0.577997 44.87164 -3.517460e-15 -8.881784e-16 21.574149 39.491215 \n", + "0.13 0.577997 44.87164 -3.518540e-15 -4.440892e-16 21.574149 39.491215 \n", + "0.14 0.577997 44.87164 -3.519743e-15 -4.440892e-16 21.574149 39.491215 \n", + "0.15 0.577997 44.87164 -3.521077e-15 0.000000e+00 21.574149 39.491215 \n", + "0.16 0.577997 44.87164 -3.522536e-15 0.000000e+00 21.574149 39.491215 \n", + "0.17 0.577997 44.87164 -3.524120e-15 0.000000e+00 21.574149 39.491215 \n", + "0.18 0.577997 44.87164 -3.525830e-15 4.440892e-16 21.574149 39.491215 \n", + "0.19 0.577997 44.87164 -3.527666e-15 4.440892e-16 21.574149 39.491215 \n", + "0.20 0.577997 44.87164 -3.529612e-15 8.881784e-16 21.574149 39.491215 \n", + "0.21 0.577997 44.87164 -3.531666e-15 8.881784e-16 21.574149 39.491215 \n", + "0.22 0.577997 44.87164 -3.533831e-15 8.881784e-16 21.574149 39.491215 \n", + "0.23 0.577997 44.87164 -3.536124e-15 1.332268e-15 21.574149 39.491215 \n", + "0.24 0.577997 44.87164 -3.538548e-15 1.332268e-15 21.574149 39.491215 \n", + "0.25 0.577997 44.87164 -3.541109e-15 1.776357e-15 21.574149 39.491215 \n", + "0.26 0.577997 44.87164 -3.543804e-15 1.776357e-15 21.574149 39.491215 \n", + "0.27 0.577997 44.87164 -3.546629e-15 1.776357e-15 21.574149 39.491215 \n", + "0.28 0.577997 44.87164 -3.549585e-15 2.220446e-15 21.574149 39.491215 \n", + "0.29 0.577997 44.87164 -3.552685e-15 2.220446e-15 21.574149 39.491215 \n", + "0.30 0.577997 44.87164 -3.555922e-15 2.664535e-15 21.574149 39.491215 \n", + "... ... ... ... ... ... ... \n", + "9.71 0.577997 44.87164 -6.664932e-15 5.875300e-13 21.574149 39.491215 \n", + "9.72 0.577997 44.87164 -6.666790e-15 5.884182e-13 21.574149 39.491215 \n", + "9.73 0.577997 44.87164 -6.668652e-15 5.888623e-13 21.574149 39.491215 \n", + "9.74 0.577997 44.87164 -6.670518e-15 5.897505e-13 21.574149 39.491215 \n", + "9.75 0.577997 44.87164 -6.672389e-15 5.901946e-13 21.574149 39.491215 \n", + "9.76 0.577997 44.87164 -6.674264e-15 5.906386e-13 21.574149 39.491215 \n", + "9.77 0.577997 44.87164 -6.676144e-15 5.915268e-13 21.574149 39.491215 \n", + "9.78 0.577997 44.87164 -6.678028e-15 5.919709e-13 21.574149 39.491215 \n", + "9.79 0.577997 44.87164 -6.679916e-15 5.928591e-13 21.574149 39.491215 \n", + "9.80 0.577997 44.87164 -6.681810e-15 5.933032e-13 21.574149 39.491215 \n", + "9.81 0.577997 44.87164 -6.683708e-15 5.937473e-13 21.574149 39.491215 \n", + "9.82 0.577997 44.87164 -6.685612e-15 5.946355e-13 21.574149 39.491215 \n", + "9.83 0.577997 44.87164 -6.687520e-15 5.950795e-13 21.574149 39.491215 \n", + "9.84 0.577997 44.87164 -6.689434e-15 5.964118e-13 21.574149 39.491215 \n", + "9.85 0.577997 44.87164 -6.691353e-15 5.968559e-13 21.574149 39.491215 \n", + "9.86 0.577997 44.87164 -6.693277e-15 5.968559e-13 21.574149 39.491215 \n", + "9.87 0.577997 44.87164 -6.695207e-15 5.973000e-13 21.574149 39.491215 \n", + "9.88 0.577997 44.87164 -6.697142e-15 5.981882e-13 21.574149 39.491215 \n", + "9.89 0.577997 44.87164 -6.699083e-15 5.986323e-13 21.574149 39.491215 \n", + "9.90 0.577997 44.87164 -6.701029e-15 5.995204e-13 21.574149 39.491215 \n", + "9.91 0.577997 44.87164 -6.702982e-15 5.999645e-13 21.574149 39.491215 \n", + "9.92 0.577997 44.87164 -6.704940e-15 6.004086e-13 21.574149 39.491215 \n", + "9.93 0.577997 44.87164 -6.706904e-15 6.012968e-13 21.574149 39.491215 \n", + "9.94 0.577997 44.87164 -6.708875e-15 6.017409e-13 21.574149 39.491215 \n", + "9.95 0.577997 44.87164 -6.710851e-15 6.026291e-13 21.574149 39.491215 \n", + "9.96 0.577997 44.87164 -6.712834e-15 6.030731e-13 21.574149 39.491215 \n", + "9.97 0.577997 44.87164 -6.714823e-15 6.035172e-13 21.574149 39.491215 \n", + "9.98 0.577997 44.87164 -6.716819e-15 6.044054e-13 21.574149 39.491215 \n", + "9.99 0.577997 44.87164 -6.718821e-15 6.048495e-13 21.574149 39.491215 \n", + "10.00 0.577997 44.87164 -6.720829e-15 6.057377e-13 21.574149 39.491215 \n", + "\n", + " w x_earth y_earth z_earth \n", + "time \n", + "0.01 3.396464 0.394912 0.215741 -1000.0 \n", + "0.02 3.396464 0.789824 0.431483 -1000.0 \n", + "0.03 3.396464 1.184736 0.647224 -1000.0 \n", + "0.04 3.396464 1.579649 0.862966 -1000.0 \n", + "0.05 3.396464 1.974561 1.078707 -1000.0 \n", + "0.06 3.396464 2.369473 1.294449 -1000.0 \n", + "0.07 3.396464 2.764385 1.510190 -1000.0 \n", + "0.08 3.396464 3.159297 1.725932 -1000.0 \n", + "0.09 3.396464 3.554209 1.941673 -1000.0 \n", + "0.10 3.396464 3.949122 2.157415 -1000.0 \n", + "0.11 3.396464 4.344034 2.373156 -1000.0 \n", + "0.12 3.396464 4.738946 2.588898 -1000.0 \n", + "0.13 3.396464 5.133858 2.804639 -1000.0 \n", + "0.14 3.396464 5.528770 3.020381 -1000.0 \n", + "0.15 3.396464 5.923682 3.236122 -1000.0 \n", + "0.16 3.396464 6.318594 3.451864 -1000.0 \n", + "0.17 3.396464 6.713507 3.667605 -1000.0 \n", + "0.18 3.396464 7.108419 3.883347 -1000.0 \n", + "0.19 3.396464 7.503331 4.099088 -1000.0 \n", + "0.20 3.396464 7.898243 4.314830 -1000.0 \n", + "0.21 3.396464 8.293155 4.530571 -1000.0 \n", + "0.22 3.396464 8.688067 4.746313 -1000.0 \n", + "0.23 3.396464 9.082980 4.962054 -1000.0 \n", + "0.24 3.396464 9.477892 5.177796 -1000.0 \n", + "0.25 3.396464 9.872804 5.393537 -1000.0 \n", + "0.26 3.396464 10.267716 5.609279 -1000.0 \n", + "0.27 3.396464 10.662628 5.825020 -1000.0 \n", + "0.28 3.396464 11.057540 6.040762 -1000.0 \n", + "0.29 3.396464 11.452452 6.256503 -1000.0 \n", + "0.30 3.396464 11.847365 6.472245 -1000.0 \n", + "... ... ... ... ... \n", + "9.71 3.396464 383.459700 209.484989 -1000.0 \n", + "9.72 3.396464 383.854613 209.700731 -1000.0 \n", + "9.73 3.396464 384.249525 209.916472 -1000.0 \n", + "9.74 3.396464 384.644437 210.132214 -1000.0 \n", + "9.75 3.396464 385.039349 210.347955 -1000.0 \n", + "9.76 3.396464 385.434261 210.563697 -1000.0 \n", + "9.77 3.396464 385.829173 210.779438 -1000.0 \n", + "9.78 3.396464 386.224085 210.995180 -1000.0 \n", + "9.79 3.396464 386.618998 211.210921 -1000.0 \n", + "9.80 3.396464 387.013910 211.426663 -1000.0 \n", + "9.81 3.396464 387.408822 211.642404 -1000.0 \n", + "9.82 3.396464 387.803734 211.858146 -1000.0 \n", + "9.83 3.396464 388.198646 212.073887 -1000.0 \n", + "9.84 3.396464 388.593558 212.289628 -1000.0 \n", + "9.85 3.396464 388.988471 212.505370 -1000.0 \n", + "9.86 3.396464 389.383383 212.721111 -1000.0 \n", + "9.87 3.396464 389.778295 212.936853 -1000.0 \n", + "9.88 3.396464 390.173207 213.152594 -1000.0 \n", + "9.89 3.396464 390.568119 213.368336 -1000.0 \n", + "9.90 3.396464 390.963031 213.584077 -1000.0 \n", + "9.91 3.396464 391.357943 213.799819 -1000.0 \n", + "9.92 3.396464 391.752856 214.015560 -1000.0 \n", + "9.93 3.396464 392.147768 214.231302 -1000.0 \n", + "9.94 3.396464 392.542680 214.447043 -1000.0 \n", + "9.95 3.396464 392.937592 214.662785 -1000.0 \n", + "9.96 3.396464 393.332504 214.878526 -1000.0 \n", + "9.97 3.396464 393.727416 215.094268 -1000.0 \n", + "9.98 3.396464 394.122329 215.310009 -1000.0 \n", + "9.99 3.396464 394.517241 215.525751 -1000.0 \n", + "10.00 3.396464 394.912153 215.741492 -1000.0 \n", + "\n", + "[1000 rows x 35 columns]" + ] + }, + "execution_count": 747, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 749, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "kwargs = {'marker': '.',\n", + " 'subplots': True,\n", + " 'sharex': True,\n", + " 'figsize': (12, 6)}" + ] + }, + { + "cell_type": "code", + "execution_count": 750, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\plotting\\_core.py:1716: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n", + " series.name = label\n" + ] + }, + { + "data": { + "image/png": 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Y4VlSecsZjmfB7i3QsbEwddh3LEmTrpAbBmOYY2m/QREtQAvAwoULJ7smSRpd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\nRK5CYII=\n", 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GZkmSJptKgXpaR2OWGodCu0f3ApcaV1swMEuSNJVUWmp8sB92DTQmUO9zYGEh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\nFTfdkZnnVjvGwCyplVQL1I2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1M4OqVcnDsCRJyt2ZoXdXLx3dI7QhK0LYde2ussAwLElSEeQKu9PqptH+Sjtb\ne7e+enABOjOMtJTBzgxSHsJwRNQCrcCGlNL7Jl6SJEmVpxzbkLmFsDS6fMwMfwJYBxyah2tJklS2\ncu2qlnML4QK0IauN2j337hvoY8aUGS5lkCZgQmE4IhqB/wD8LfDJvFQkSVIJ5fqw2oidGYq0nMHO\nDFLhTHRm+CvAXwINuQ6IiEuASwCampomeDtJkiYm13KG7T3b2dG3Y+/lDLvlMfS6dlcqL+MOwxHx\nPmBzSml1RLwt13EppRXACoCWlha3UpMkFVSumd2+gT56+nvY8PKG/U+yDZmUWROZGX4LcGZEvBeo\nBw6NiJtSSufmpzRJkkaWsw1Zfy8dPYVvQzbSrmq2IZMq07jDcErp08CnAYZmhq80CEuS8iFnG7JJ\n09i8czPbere9erCdGSRNgH2GJUlFVw5tyMDlDJLyFIZTSvcB9+XjWpKk6pCrDVl3f/f+XRmgKG3I\n6mrq/LCapL04MyxJGpeRwm7fQB+TYhLtr7SzpXfL3ifYhkxSGTIMS5JyKseeu87sSsonw7AkZViu\ntbt9A31s79lOR3fhOzO4bldSKRmGJanK5erMUEMNbS+37X+CbcgkZYhhWJIq3O61u+u3r6eupm5P\n4JxeN532ne1s6Rm2drcASxmGh93dH1KzDZmkSmEYlqQKMHzt7vDAmbMzQ57t25nBsCupWhiGJakM\n5GpDRoLeXTl2Vcuz4Wt3dwduOzNIqnaGYUkqkn3X7u4OnHZmkKTSMQxLUp7kakO2vWc7O/p2FGVX\ntX23EDbsStKBGYYlaYzKoQ3ZEYccwbS6aXt9UM7ODJI0foZhSRomV2eG2ppaXuh6Yf8TitCGzF3V\nJKlwDMOSMifXcoaOVzro7Oks+P13r921DZkklZ5hWFLVGb6cYUvPlr1meHt39RZ8OcNIbcjAXdUk\nqRwZhiVVpIPeVS3PbEMmSdXBMCypLO27dnfPkoKeLrr6ugremcE2ZJKUDYZhSSWRqzODu6pJkorJ\nMCypYHLtqtbT3zPyB9UKMMN75LQj7cwgScpp3GE4Io4G/hfwWmAAWJFS+mq+CpNUGXJ1ZnBXNUlS\nJZjIzHA/cEVK6bGIaABWR8RPU0q/yVNtkspAruUM23u209XbxY7+HfuflOfQ29TQxKSaSXt1hbAz\ngyQpH8YdhlNKLwIvDj3uioh1wFGAYViqMLk2msjZmSHPYXd4ZwZ3VZMkFVNe1gxHRDOwCFg1wtcu\nAS4BaGpqysftJB2kXGF3et102ne2s6VnS0HvP9KuaoZdSVI5mHAYjojpwPeAy1NK2/f9ekppBbAC\noKWlJU30fpJGlmvt7raebWybp0gkAAAKhklEQVR6ZVPB79/U0ET/QP+e+9qZQZJUCSYUhiOijsEg\nfHNK6fb8lCQpl5E2mkgp0berj46ewu6qBiMvZ3DtriSpkk2km0QA1wPrUkpfyl9JUjblakMGUD+p\nns6dnWzr3fbqCXZmkCRpwiYyM/wW4DxgbUSsGXrtr1JKP5p4WVJ1Gmkpw/TJ0+l4paMobcjA5QyS\nJA03kW4SDwGRx1qkipdr3W4x25Dtu6ta30AfM6bM8MNqkiSNwB3opIMwvOfulp4te3Vm6O3vLcq6\nXRh5OYO7qkmSdPAMw9I+Drrnbp6N1IbMtbuSJBWGYViZkyvs2oZMkqTsMQyrKuXqzNDT30NnT+fI\nJ+VxOcO+63ZtQyZJUnkyDKtijdRzFyAINry8Ye+DC7Bu98hpR+63lMF1u5IkVRbDsMrWQXVmKFIb\nMtftSpJUXQzDKpnhnRlefPlF4NUlBV29XXT1de1/Up5D70hh1zZkkiRlh2FYBZMr7PYN9NHb3zty\nZ4Y8h92ROjPMmTbHsCtJkgDDsCYoV2eG2qjlhR0v7H+CPXclSVIZMQxrVLlmeEvZhgzszCBJkibO\nMCwgd2eGnBtN5HmGd1b9LCbXTjbsSpKkojIMZ0Su5QzT66bT/ko7W3q3vHpwgZYy7A67fQN91NXU\n2ZlBkiSVnGG4SuwbdncHzq7eLrr7u/l9z+8LXoNtyCRJUqUxDFeQce2qlmf7zvDahkySJFUyw3CZ\n2Xftbt9AH5NqJtHxSsf+s7tF6szgDK8kSapWhuEic1c1SZKk8jGhMBwR7wa+CtQC304pfS4vVVWw\nnBtN7Opje892Ono69j+pALuqTaqZtNcH5dxoQpIkaX/jDsMRUQtcC/wx0Ab8MiJ+kFL6Tb6KKxe5\nZnOHf0gNIAg2vLxh/wu4q5okSVJZmsjM8CnAMymlZwEi4v8AfwqUVRh+7KXH+MFvf8BzW5/bs0HE\n8BC5b6hNKTGtbho7+nYwwAD9u/pH7sRQoCUMu+1euzu8tvpJ9Zx7wrnuqiZJkpQnEwnDRwHD99tt\nA06dWDn5tWbzGi76yUXsSrv2/sLLOR4X0RGHHEFt1ALuqiZJklQqEwnDMcJrab+DIi4BLgFoamqa\nwO0OXutLrQykgaLec7iRNpqoq63jrGPPcnZXkiSpDEwkDLcBRw973ghs3PeglNIKYAVAS0vLfmG5\nkFqOaKGupo7egd68XG/f2dx91wzbmUGSJKmyTCQM/xL4w4iYC2wAlgIfyUtVebLw8IVc/67rR+zu\ncKAPwu37dWdzJUmSqtO4w3BKqT8iPg78hMHWajeklH6dt8ryZOHhC52hlSRJ0ogipeKtXIiIduD5\not3wVU3A70pwXxWX45wNjnP1c4yzwXHOhlKO8zEppdmjHVTUMFwqEdE+lm+GKpvjnA2Oc/VzjLPB\ncc6GShjnmlIXUCRbS12AisJxzgbHufo5xtngOGdD2Y9zVsLwtlIXoKJwnLPBca5+jnE2OM7ZUPbj\nnJUwvKLUBagoHOdscJyrn2OcDY5zNpT9OGdizbAkSZI0kqzMDEuSJEn7MQxLkiQps6omDEfERHbT\nU4WIGNoPW1UtIg4tdQ0qvIiYExFzSl2HCicippW6BhVWRESpa5ioig/DETEpIq4BvhgR7yx1PSqM\noXH+O+DvIuKPS12PCici/hNwf0QsHnpe8T9otbeIqBn673kVsCAiJpe6JuXXsJ/Zd0TExRFxTKlr\nUsFM3f2gUn9eV3QYHvqmfw2YAzwKXBUR/ykippS2MuVTRLwVWA3MAJ4G/jYi3lzaqpRvw36INgCv\nAJcAJD/lW43OA+YBC1JKd6WUektdkPInImYA/wwcBnwZ+CBwfEmLUt5FxDsi4iHg2og4Fyr353Wl\nLy1oABYC70opdUVEB/BeYAlwU0krUz4NANeklL4LEBELgDOBX5S0KuVVSilFRA1wBPAt4PSIOCel\ndHNE1KaUdpW4ROXB0C89fwh8LaW0LSJagB7gKUNx1ZgONKeU/iNARCwpcT3Ks4h4DfA/gS8CncAn\nImJuSulvIqImpTRQ2goPTkWH4ZTS9ohYDywDvg78nMFZ4jdFxN0ppU0lLE/5sxp4dFggegRYVOKa\nlGe7f4AO/VL7MnAv8P6IeBDYTgXsYqTRDf3SMws4a+gX2/OB54COiPhCSum50laoiUopvRARr0TE\nd4BGoBmYGREnAv/s/5sr09BkBUNB90hgLXBHSmlXRLQBj0TEt1NKL0ZEVNIscUUvkxhyB7AwIuak\nlHYwODi9DIZiVYGU0isppZ5hM4PvAn5XypqUf8NmEhYAPwHuBN7A4C+5J1bqWjSN6FpgMTA/pXQy\n8JcMzi4tL2lVyqclDP7t3caU0rHAl4DXAmeVtCqNS0RcCLQBfzP00g7gTcAsgJTS08DNwDdKUuAE\nVUMYfojBH6LLAFJKq4GTGbagW9UhImqH/TX6j4dem28nkarzOPBN4D4GZ4SfBH5TSbMMGtXTwP8D\nTgFIKa0HnmfwZ7mqQEqpncGJqY6h5/cPfamnZEVpXCJiOvCnwOeB90TE8UP/zT4GfGXYof8daIyI\nP6y0n9cVH4ZTSi8C/5fBAVoSEc1AN9BfyrpUEANAHYM/XE+KiB8CV+IvPtWmBjgc+M8ppTMY/IH7\nF6UtSfmUUuoGPgXURsSHIuIE4M8Y/OVH1eMZBsPRaRFxOHAqsLPENekgDf2t+39OKX0VuItXZ4cv\nBd4REW8aev4yg5MZ3cWvcmKqZjvmiHgPg38t82bgGymlipyq14FFxGkM/tXbL4AbU0rXl7gk5VlE\nTE0p7Rx6HMDhKaWXSlyWCiAi/h3wduB9wD+mlP6xxCUpjyKiHvgY8H4Gf8H9WkppRWmr0kRExGuB\nHwCfTSn961ArzPcCK4GmocfvSSn9voRlHrSqCcMAEVHH4OcznBWuUhHRyGBbpi+llPzrtioWEZP8\nbzkb7BZS3SJiLtCWUuordS2auIj4KHBuSun0oefvAf49cBTwqZTSC6WsbzyqKgxLkiSpMIZ1/VkJ\nbGJw+eK3gbWVtk54uIpfMyxJkqTCGwrChzC47OXDwDMppX+r5CAMFd5nWJIkSUV1KYMfbP7jalmu\n6DIJSZIkjUkl7jA3GsOwJEmSMss1w5IkScosw7AkSZIyyzAsSZKkzDIMS1IJRMRhEXHp0OMjh/p2\nSpKKzA/QSVIJREQz8C8ppRNLXIokZZp9hiWpND4HvD4i1gBPAyeklE6MiGXAB4Ba4ETgi8BkBrch\n7wHem1L6fUS8HrgWmA28AlycUnqy+G9DkiqbyyQkqTQ+Bfw2pbQQ+K/7fO1E4CPAKcDfAq+klBYB\nDwPnDx2zArgspbQYuBL4ZlGqlqQq48ywJJWfe1NKXUBXRGwDfjj0+lrgpIiYDrwZuC0idp8zpfhl\nSlLlMwxLUvkZvsXpwLDnAwz+3K4Btg7NKkuSJsBlEpJUGl1Aw3hOTCltB56LiCUAMeiN+SxOkrLC\nMCxJJZBS6gR+HhFPAF8YxyX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511ZgK0BfX18Rl66RI4Nkv6yU/fPR22rcIEmSJFXarME5pfSSEu8xAKzOe9wL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\nAElFTkSuQmCC\n", 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TQwTniJgC/Az4XGZ+Z5D9zgDOANh3330PXrVq1VCfQaq/yl/Pb9kEG35XnePu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\nSQUYnCVJkqQCDM6SJElSAQZ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kCpr2YcAnKnddZ5pVh/IIxl8GPgR8FegyGEuSlJPx0Lz74WdmfJ1pVhOrajCO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\n6dnVw+W3Fx60e7T/Ud52+9s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000/X/v37PTs3wXkojVulPVv61wOF0jmf8a89AAAA2aZxq7T5m54OrrBixQo9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\n3KTbF92ecNSNuuY6ffbJz9L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8imOjh23ZQ/9bAXsALcCvI2JiZr4AjMvMpyLincCtEfEw8FIFfZY2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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "results.plot(y=['elevator', 'aileron', 'rudder', 'thrust'], **kwargs);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Doublet " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values." + ] + }, + { + "cell_type": "code", + "execution_count": 291, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.utils.input_generator import Doublet" + ] + }, + { + "cell_type": "code", + "execution_count": 292, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "de0 = trimmed_controls['delta_elevator']" + ] + }, + { + "cell_type": "code", + "execution_count": 293, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "controls = controls = {\n", + " 'delta_elevator': Doublet(t_init=2, T=1, A=0.1, offset=de0),\n", + " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", + " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", + " 'delta_t': Constant(trimmed_controls['delta_t'])\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 294, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "sim = Simulation(aircraft, system, environment, controls)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once the simulation is set, the propagation can be performed:" + ] + }, + { + "cell_type": "code", + "execution_count": 295, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n", + "time: 0%| | 0/90 [00:00" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "results.plot(y=['x_earth', 'y_earth', 'height'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": 297, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\plotting\\_core.py:1716: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n", + " series.name = label\n" + ] + }, + { + "data": { + "image/png": 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kSaqSMyDW265DzEUz988aW4ckSZJqzjBdb0e8b/D10wd93lKSJEltxDBdb4Zm\nSZKkUcsw3Qi7zxh+WZIkSW3JMN0If768GKCj8OefL292RZIkSaqBskbzUA0YoCVJkkadyBw4M3jr\niojVwCNNuPQM4NEmXFetz3tDw/H+0FC8NzQU743W8NrMLGvq7bYK080SEavL/QvV2OK9oeF4f2go\n3hsaivdG+7HPdHmeaXYBalneGxqO94eG4r2hoXhvtBnDdHnWNbsAtSzvDQ3H+0ND8d7QULw32oxh\nujyXN7sAtSzvDQ3H+0ND8d7QULw32ox9piVJkqQK2TItSZIkVajtwnREXBURT0bEvTU6379GxDMR\ncfOA9W+LiF9GxLKI+FlE7FeL60mSJGn0aLswDVwDnFDD8/09cOYg678KnJ6ZXcB1wF/W8JqSJEka\nBdouTGfmT4G1pesi4veKLcxLI+I/IuLAEZzv34HnBtsE7FZ8vTuwqtKaJUmSNDqNlunELwfOzcz/\nioijgEuBt1Z5zg8Bt0bEi8CzwJwqzydJkqRRpu3DdETsChwN3BARW1fvWNz2HmDhIIc9npnHb+fU\nfw68IzN/ERGfAr5AIWBLkiRJwCgI0xS6qjxT7NvcT2Z+F/juSE8YEVOBIzLzF8VV3wb+taoqJUmS\nNOq0XZ/pgTLzWeC3EXEKQBQcUeVpnwZ2j4jXF5ePBe6v8pySJEkaZdpu0paI+BbwB8AU4HfA54Af\nUxh9Y29gInB9Zg7WvWOw8/0HcCCwK7AG+GBm3hYRf0Shi8gWCuH6A5n5UG3fjSRJktpZ24VpSZIk\nqVW0fTcPSZIkqVna6gHEKVOmZGdnZ7PLkCRJ0ii2dOnSpzJzajn7NjVMR8QJwJeA8cAVmXnhcPt3\ndnbS09PTkNokSZI0NkXEI+Xu27QwHRHjgUsojJTRCyyJiMWZeV+zahrMaTefxvI1y7e739F7H81l\nx13WgIokSZLUKprZMj0bWLl1hIyIuB6YB7RMmC43SAP8/Imfc9iiwyq6zjtnvpML3zRso7wkSZJa\nUDPD9L7AYyXLvcBRA3eKiPnAfIAZM2Y0prKi+9Y2Jtff8ttbuOW3t9T0nB3jOlhy5pKanlOSJEn9\nNTNMxyDrthmnLzMvBy4H6O7ubug4fge/+uCyW6ZbTd+Wvopbyrd63W6v43t/9L0aVSRJkkaLjRs3\n0tvbS19fX7NLqUpHRwfTpk1j4sSJFZ+jmWG6F5hesjwNWNWkWgZ13YnXjairx2jz0LMPVR3IxzOe\nZWcvq1FFkiSpFfT29jJp0iQ6OzuJGKx9tPVlJmvWrKG3t5eZM2dWfJ5mhuklwP4RMRN4HDgVOK2J\n9QzquhOvG3b7Mdcdw7qN6xqh8seHAAARiklEQVRUTfvZzOaqA7l9yiVJai19fX1tHaQBIoLJkyez\nevXqqs7TtDCdmZsi4jzgNgpD412VmSuaVU+lfnbazyo+ds4357B+8/oaVjM6VdOnfAITuOfse2pc\nkSRJaucgvVUt3kNTx5nOzFuBW5tZQzPddcZdNT/nDQ/cwMK7Ftb8vO1qE5uqahk/f875nHLAKTWs\nSJIkjSaR2dBn+qrS3d2dTtpSf8ffcDyrXmip7uttZ5+d9+G2U25rdhmSJNXF/fffz0EHHdTsMga1\ndZK/KVOm9Fu/ePFi7rvvPhYsWNBv/WDvJSKWZmZ3Oddrq+nE1Ri1CoFdi7rYzOaanKvdrHphVUUt\n4o6gIklSfZx00kmcdNJJNT+vYVp1U+0oHmPx4c5KRlBxTHFJUjtY9uQyen7XQ/druunas6vq8z38\n8MOccMIJHHXUUdxzzz28/vWv59prrwXgK1/5Ct///vfZuHEjN9xwAwceeCDXXHMNPT09XHzxxVVf\nu5RhWi2rmoc7lz25jDN/cGYNq2ldlYwpvvvE3av6+5UkaavP3/15fr3218Pu8/yG53ng6QdIkiA4\nYI8D2HWHXYfc/8BXH8hfzP6L7V77gQce4Morr2Tu3Ll84AMf4NJLLwVgypQp/PKXv+TSSy/loosu\n4oorrhjZmxoBw7RGpa49u1h+duXjg8+6dhYbckMNK2ot6zauG1EAd1QUSVI1ntv4HFmcmy9Jntv4\n3LBhulzTp09n7ty5AJxxxhl8+ctfBuA973kPALNmzeK73/1u1dcZjmFaGsTSs5ZWdNy8m+bx0LMP\n1bia5hvpqCi7jN+lLqPVSJJaTzktyMueXMaH/+3DbNyykYnjJnLh719Yk64eA4e227q84447AjB+\n/Hg2bdpU9XWGY5iWaqjShwdH2wgq6zevH1H4fv8h7+cT3Z+oY0WSpGbq2rOLrx/39Zr2mQZ49NFH\nufPOO3njG9/It771LY455hjuuaex36QapqUWUMkIKl/o+QJXr7i6DtU03tUrri77vTgjpiS1p649\nu2oWorc66KCDWLRoER/5yEfYf//9+ehHP8pXvvKVml5jexxnWhpDPvJvH+HnT/y82WU0hP28Jal+\nWmGc6YcffpgTTzyRe++9t6rzOM60pLJddtxlI9q/nUdFGUk/78MmH8Z1J15X54okSaORYVrSkEY6\nKsqCny7glt/eUseK6mP5muVlBW9ntpSk1tHZ2Vl1q3QtGKYl1cyFb7pwRP2Zj/zGkfRt6atjRbVV\n7syWzmQpaSzIzG1G02g3tejubJiW1DQjmblxzjfnsH7z+jpWUzvlzGQZBNe+/dqaP4wjSY3Q0dHB\nmjVrmDx5ctsG6sxkzZo1dHR0VHUeH0CUNKose3IZZ/3grJcnB2h3tnJLakUbN26kt7eXvr72+XZx\nMB0dHUybNo2JEyf2Wz+SBxAN05LGrLdc/xaeeumpZpdRNaeHl6TaMkxLUg2Nhpktp+w4hZ+c+pNm\nlyFJbcEwLUlN0O4zWTohjiQVGKYlqYW9YdEb2MSmZpcxYruM34W7zrir2WVIUt05aYsktbByZmZs\nxVbu9ZvXDztKyTjGsejtixyhRNKYYsu0JLWpdpse3uEAJbULu3lIkgA47ebTWL6m/Fksm2kCE8pq\ntZekejNMS5LK1i4T4jgiiaRGMUxLkmpmwU8XcMtvb2l2GcOyC4mkWjJMS5IaqtVHKHEmSUkjYZiW\nJLWUWdfOYkNuaHYZg7L7iKSBDNOSpLax7MllnPmDM5tdxqCcql0amwzTkqRRo1VHJNln53247ZTb\nml2GpDowTEuSxoxW7EJy9N5Hc9lxlzW7DEkVMkxLkkTrzSTpWNpSe3A6cUmSYNhuGM2YQXITm4ac\nkt1uI1J7smVakqQBWmmqdluzpcZr+W4eEXEKcAFwEDA7M8tKyIZpSVKztdIDke+c+U4ufNOFzS5D\nGnXaIUwfBGwBLgM+aZiWJI0Gx1x3DOs2rmt2GRw2+TCuO/G6Zpchta2W7zOdmfcDREQzLi9JUl0M\nNSb1sieXcdYPziJpTAPW8jXLB+2b7UyQUu01tc90RNzOdlqmI2I+MB9gxowZsx555JEGVSdJUv3N\nu2keDz37UFNrMGRL/bVEN4+I+BGw1yCbPpOZ3yvuczt285AkaRutMDOk3UU0VrVEmC7r4oZpSZJG\nbM4357B+8/qmXf/9h7yfT3R/omnXl+rNMC1J0hj0luvfwlMvPdWUa+8QO7D0rKVNubZUay0fpiPi\nj4CvAFOBZ4BlmXn89o4zTEuSNHLNnAnS/thqRy0fpitlmJYkqXaa9fDjeMaz7OxlDb+uVC7DtCRJ\nqlizuovYiq1WYZiWJEk1d+Q3jqRvS19Dr9kxroMlZy5p6DWllp+0RZIktZ/BQu0ND9zAwrsW1u2a\nfVv6tpmAJgiuffu1dO3ZVbfrSuWyZVqSJNVcM/pjO2SfasVuHpIkqSV1LepiM5sbdr2j9z6ay467\nrGHX0+hgmJYkSW2j0UP3GbC1PYZpSZLU1r7Q8wWuXnF1w65nwFYpw7QkSRqV3rDoDWxiU0OuZR/s\nscswLUmSxow535zD+s3r634dJ5sZOxwaT5IkjRl3nXHXNuvqMfHMZjZvM0yf42DLMC1Jkkadn5z6\nk23W1SNgDzYOtjM5ji1285AkSWPWMdcdw7qN6+p6DSeZaT/2mZYkSapQI6ZNn7LjlEFbz9UaDNOS\nJEk1VO/JZoLgs3M+yykHnFK3a6h8hmlJkqQ6asQ42PvsvA+3nXJbXa+hwRmmJUmSGqzeMznuEDuw\n9KyldTu/XmGYliRJagH1nmTmnTPfyYVvurBu5x+rDNOSJEkt6LSbT2P5muV1O7/D8tWGYVqSJKlN\nzLp2FhtyQ13Ovcv4XQad1EbDcwZESZKkNjGwH/S8m+bx0LMP1eTc6zev7zepzAQmcM/Z99Tk3Cqw\nZVqSJKmFLXtyGWf+4My6nNsJZQZnNw9JkqRRbM4357B+8/q6nPv8OeeP+fGuDdOSJEljSC27hgz0\n/kPezye6P1GXc7cqw7QkSdIYtuCnC7jlt7fU5dxjIVwbpiVJkvSyZU8u46wfnEVS29w3WqdBN0xL\nkiRpWPWYUGYc41j09kVt/0CjYVqSJEkjUo/xrtt1CnTHmZYkSdKIDAy9R37jSPq29FV1zg25od84\n17tP3J2fnfazqs7ZagzTkiRJ2saSM5f0W65FuF63cV2/cD0apj+3m4ckSZJGrB7dQlplpBD7TEuS\nJKmhav1AYzP7W7d8n+mI+HvgXcAG4EHg/Zn5TDNqkSRJUvXuOfuel1/f8MANLLxrYVXn29rf+rDJ\nh3HdiddVW17djGvSdX8IHJqZhwO/AT7dpDokSZJUY6cccArLz17+8s/Rex9d8bmWr1nOaTefVsPq\naqspLdOZ+W8li3cBJzejDkmSJNXfZcdd1m/5+BuOZ9ULq8o+/r6199W6pJpphdE8PgB8e6iNETEf\nmA8wY8aMRtUkSZKkOrntlNv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5RI899ph23z1GqA8IPcyZ0LWHuUdP6bNnSo3zO+9f8VT22gQAAEpXjJ7gHd5d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\nAwAAADEQmAEAAIAYCMwAAABADP8/vW7Rdb5GTREAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "results.plot(y=['v_north', 'v_east', 'v_down'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": 299, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\plotting\\_core.py:1716: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n", + " series.name = label\n" + ] + }, + { + "data": { + "image/png": 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QB2GsqiF3f0TSIynnbuzxfZukGWH0FTunfk5qulfy7sSxd0u73uxxQXLEecwU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\nn5Hp4dXD024qAxzAiDMAACg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uYukpXt9qyj+AkkWpBgCgNF25V6gjR6HgQUWgYFGqAQAob/F6P+ejh3VXe+zS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\nXoJFTvX4RTZIUpukmZJ+J6nJzI509w5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M/vG5zO2vzksvWlPI9AWlq6dIsQnYWT4h6adRFwEAAIAIDF1uPdcDkzGfP7us\nDzma2S8kHZzj0OXufldwzuWSWiR9yPMUZ2YrJK2QpIULFy7ZtGlTiSoGAAAAEjyLiJmdL+liSae6\n++5Rfk+HpCgS9kJJmyN4XcQf9wYK4f5APtwbyId7Ix4Wufvc0ZwYm4BtZmdKWi3pne7eEXU9IzGz\njtH+JaO6cG+gEO4P5MO9gXy4N5InNtP0SbpWUr2kB82s3cy+H3VBI9gx8imoUtwbKIT7A/lwbyAf\n7o2Eic1Dju5+RNQ1jFFX1AUgtrg3UAj3B/Lh3kA+3BsJE6cR7KRZE3UBiC3uDRTC/YF8uDeQD/dG\nwsSmBxsAAACoBIxgAwAAACEiYAMAAAAhImADAAAAISJgAwAAACEiYAMAAAAhImADAAAAISJgAwAA\nACEiYAMAAAAhImADAAAAISJgAwAAACEiYAMAAAAhmhB1AcWaM2eONzY2Rl0GAAAAKlhbW9s2d587\nmnMTH7AbGxvV2toadRkAAACoYGa2abTn0iISkdWtq/W+n79Pq1tXR10KAAAAQkTAjsDq1tW65elb\ntLl7s255+hZ96oFPRV0SAAAAQkLAjsC6Desytn/7ym91x7N3RFQNAAAAwpT4HuwkmjJhirbv3Z6x\n79+e+TctP3p5RBUBAACEr7e3V6lUSj09PVGXMmp1dXVqaGjQxIkTx30NAnYELlp8ka589MqMfTv3\n7oyoGgAAgNJIpVKqr69XY2OjzCzqckbk7urs7FQqlVJTU9O4r0OLSASWH71ck2omZeybVDspz9kA\nAADJ1NPTo9mzZyciXEuSmWn27NlFj7gTsCNy4KQDM7YPOeCQiCoBAAAonaSE60Fh1EvAjoi7Z2xP\nnzw9okoAAAAQJnqwI9D+ars693ZGXQYAAEDFq62t1eLFi/dvr1u3TqVeBZyAHYG7/3R31CUAAABU\nhSlTpqi9vb2sr0mLSAQ27tgYdQkAAACx1P5qu25cf6PaXy1dKL7ooovU3Nys5uZmzZ07V1dccUWo\n12cEOwLZc2ADAABUum88/g398bU/Fjxn175denb7s3K5TKajZx6taZOm5T3/TbPepM8v/XzBa+7Z\ns0fNzc2SpKamJq1du1Y33nijJGnTpk0644wzdMEFF4ztDzMCAnYEZk6eOWzf7CmzI6gEAAAgPrp7\nu+VKTwThcnX3dhcM2KORr0Wkp6dHy5cv17XXXqtFixYV9RrZCNgRyDVjyDGzjomgEgAAgPIYaaRZ\nSreHfPKBT6p3oFcTayZq1Umr1DyvuST1XHzxxfrQhz6k0047LfRrE7Aj0DfQN2zfIy8/wlLpAACg\nqjXPa9YNp9+g1q2tajmopWTdHcc0AAAR60lEQVTh+rrrrlN3d7dWrlxZkusTsCOQ6k4N2/efqf9U\n+6vtJbuRAAAAkqB5XnPJ89A3v/lNTZw4cX9v9sUXX6yLL744tOsTsMvsjmfv0Madw2cRGfABtW5t\nJWADAACEaNeuXcP2vfDCCyV9zaKn6TOzBWb2KzN7xsyeNrNLg/1fMbOXzaw9+PXeId/zBTPbYGbP\nmtkZQ/afGezbYGalGbOP2M83/Dznfpdr+iRWcwQAAEi6MEaw+yT9vbv/zszqJbWZ2YPBsW+7+zeH\nnmxmb5Z0rqS3SJov6RdmdlRw+DpJyySlJD1hZne7+x9CqDE2JtdMzntspKlrAAAAEH9FB2x3f0XS\nK8HX3Wb2jKRDC3zLWZJuc/e9kl4wsw2SlgbHNrj7Rkkys9uCcysqYOeaQWTQ4LQ0AAAAlcLdZWZR\nlzFq7sXnsVBXcjSzRklvlfRYsOsSM/u9md1sZoOTPx8q6aUh35YK9uXbn+t1VphZq5m1dnR0hPgn\niBZT9QEAgEpSV1enzs7OUEJrObi7Ojs7VVdXV9R1QnvI0cymSbpT0mXuvtPMrpf0VUke/P4tSZ+Q\nlOtHGFfusJ/zv4a7r5G0RpJaWlqS8V9sFGgRAQAAlaShoUGpVEpJGhCtq6tTQ0NDUdcIJWCb2USl\nw/WP3f3nkuTuW4ccv0HSPcFmStKCId/eIGlL8HW+/VWBFhEAAFBJJk6cqKampqjLKLswZhExSTdJ\nesbdVw/Zf8iQ086W9FTw9d2SzjWzyWbWJOlISY9LekLSkWbWZGaTlH4Q8u5i60sSWkQAAACSL4wR\n7BMkfUzSejMbXOj9i5L+h5k1K93m8aKkT0mSuz9tZrcr/fBin6TPuHu/JJnZJZLul1Qr6WZ3fzqE\n+hKDFhEAAIDkC2MWkUeUu6/6vgLfc5Wkq3Lsv6/Q91U6WkQAAACSL9RZRFAcWkQAAACSj4BdZv0D\n/Tn3m0xd+7rKXA0AAADCRsAusz7vy7mfpdIBAAAqAwG7zF7b81reYzzkCAAAkHwE7DJqf7Vdz2x/\nJu9xHnIEAABIPgJ2Gd3y1C0Fj/OQIwAAQPIRsMvoxZ0vZmzXT6zf/zUPOQIAAFQGAnYZzZw8M3O7\n7o1tHnIEAACoDATsMpo+OTNA9w1kzijCQ44AAADJR8COER5yBAAASD4CdoTqJ9VnbPOQIwAAQPIR\nsCPUO9Cbsc1DjgAAAMlHwC6jrr2ZATq7B3vn3p3lLAcAAAAlMCHqAqrJ9r3bM7a793VnbP/rH/5V\npyw8Rc3zmjP2n7X2LG3cuXH/9gG1B+jRjz5aukIBAAAwboxgl9GBEw/M2J43dZ5qrXb/dr/3q3Vr\na8Y52eFakl7vf12Lf7i4dIUCAABg3AjYZZTdYz1t4jS9v+n9+7dzzYWdHa6HOv7fjg+3QAAAABQt\ndgHbzM40s2fNbIOZrYy6nrC0v9quF3a+kLFv38A+zaibsX87ezXH1a2rC17z9f7XtfLhivkrAgAA\nqAix6sE2s1pJ10laJikl6Qkzu9vd/xBtZZlWPrxS975wb9HXOfuIs7Wrd9f+7ewR7J8++9MRr3Hv\nC/dq1cmrhu1f3bpatzx9S9E1Ipkm2SS1ndeW81jzD5vVr/4yVwQAQHjmT52v+5ffH3UZecUqYEta\nKmmDu2+UJDO7TdJZkmITsMMK13W1dVp+9HJd9+R1+/dlj2D39PWM6lr0YyPbPt/HfQEAqFhbdm/R\nGXecEduQHbcWkUMlvTRkOxXsy2BmK8ys1cxaOzo6ylacJD3y8iOhXGdwir7ZU2bv35erB3sok4Xy\n2gAAAEm3ZfeWqEvIK24BO1eCHLZ+uLuvcfcWd2+ZO3duGcp6w4mHnhjKdSbWTJQkPb/9+Yz9f3zt\nj5LSPdsDGsg4Nqlmktafvz6U1wcAAEiy+VPnR11CXnEL2ClJC4ZsN0iK1Y8nq05epfc1va/o6wx4\nOjx71s8Pg9u3PDW8f3pwtJuQDQAAqhk92GPzhKQjzaxJ0suSzpX0kWhLGm7VyatyPlhYyDt+8g51\n976xsMyk2kmSpGNmHZNx3uD24Ej2UBctvmj/1+vPXz+qh9Xqaur0xMeeGFOtSK47nr1DVz565Yjn\n1apW7ee3l6EiAACqT6wCtrv3mdklku6XVCvpZnd/OuKyQvHhoz6cMavHh4/6sKTMubGHPuS4r39f\nxvcfMOEALT96ecY+AhKyLT96+bD7BAAAlFesArYkuft9ku6Luo6wfa7lc5KkhzY/pFMXnrp/e+hD\njYUecpwyYUrpiwQAAEDRYhewK9nnWj63P1gPym4FydUaAgAAgOSI20OOVSffQ469A71RlAMAAIAi\nEbAjlushx/ZX2zN6s6U3HooEAABAvBGwI5brIcdcU/S9adabylkWAAAAxomAHbFcDzm+uPPFYed9\n/NiPl7EqAAAAjBcBO2K5HnIcXOVx0ML6hWqe11zOsgAAADBOBOyI5XrIsXtfd8a+voG+cpYEAACA\nIhCwI5ZvJUcAAAAkEwE7YrkecqyfVJ9xTvY2AAAA4ouAHbFcDzlmz4HNnNgAAADJQcCO2Ggecsze\nBgAAQHwRsCOW6yHHjj0dGfsYwQYAAEgOAnbEsh9q3N27W6/1vJaxr/HAxjJWBAAAgGIQsCPWta9L\nJpOUfsixdWvrsHNYZAYAACA5CNgRazmoZX+P9YSaCZpcOznjOIvMAAAAJAsBO2LN85p19TuvliQd\nN/e4YYvKTKiZEEVZAAAAGKeiAraZXW1mfzSz35vZWjObEexvNLM9ZtYe/Pr+kO9ZYmbrzWyDmX3X\nzCzYP8vMHjSz54PfZxb3R0uOugl1kqTfbf2dtry+JeMYM4gAAAAkS7Ej2A9KOtbdj5P0nKQvDDn2\nJ3dvDn5dPGT/9ZJWSDoy+HVmsH+lpIfc/UhJDwXbVWF9x3pJw2cUkTRs2XQAAADEW1EB290fcPfB\nnoZHJTUUOt/MDpF0oLv/t7u7pB9J+mBw+CxJPwy+/uGQ/RVvVt2sqEsAAABASMLswf6EpH8fst1k\nZk+a2X+a2UnBvkMlpYackwr2SdJB7v6KJAW/z8v3Qma2wsxazay1o6Mj32mJkb3YzFAskw4AAJAs\nIz5BZ2a/kHRwjkOXu/tdwTmXS+qT9OPg2CuSFrp7p5ktkbTOzN4iBfPRZRreFzECd18jaY0ktbS0\njPn742bbnm15j7HIDAAAQLKMGLDd/bRCx83sfEnvl3Rq0PYhd98raW/wdZuZ/UnSUUqPWA9tI2mQ\nNPhU31YzO8TdXwlaSV4d6x+mEs2cXDXPegIAAFSEYmcROVPS5yX9tbvvHrJ/rpnVBl8fpvTDjBuD\n1o9uMzs+mD3kPEl3Bd92t6Tzg6/PH7K/qh0+4/CoSwAAAMAYFDvJ8rWSJkt6MJht79FgxpCTJV1p\nZn2S+iVd7O6D63//raRbJU1Rumd7sG97laTbzexCSZslLS+ytorwgcM/EHUJAAAAGIOiAra7H5Fn\n/52S7sxzrFXSsTn2d0o6tZh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5aXQ5+Tibtp0f9t9JAysR6XVp4/i07cnJ9Cm3/jLjpMPeiYkAAADIHwn2AK1LGl1OPs6k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\njpL0L5IulfSSpE+bWSPvHZWFBDu95xW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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "results.plot(y=['elevator', 'aileron', 'rudder', 'thrust'], **kwargs);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Propagating only one time step" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "dt = 0.05 # seconds\n", + "sim = Simulation(aircraft, system, environment, controls, dt)" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "time: 100%|█████████████████████████████████████████████████████████▉| 0.49999999999999994/0.5 [00:05<00:00, 11.52s/it]\n" + ] + }, + { + "data": { + "text/html": [ + "
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FxFyFzMachMxMyMzTASaaileron...thrustuvv_downv_eastv_northwx_earthy_earthz_earth
time
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" + ], + "text/plain": [ + " Fx Fy Fz Mach Mx My \\\n", + "time \n", + "0.05 -2860.288296 -0.000007 -23948.338630 0.133444 3.670972e-06 416.026942 \n", + "0.10 -2841.450134 -0.000007 -23790.055374 0.133135 2.754411e-06 382.934882 \n", + "0.15 -2814.079427 -0.000007 -23634.534640 0.132827 2.070495e-06 344.981012 \n", + "0.20 -2834.053374 -0.000006 -23475.855214 0.132523 1.564206e-06 331.492749 \n", + "0.25 -2844.314793 -0.000006 -23317.511918 0.132216 1.181851e-06 311.810632 \n", + "0.30 -2847.104415 -0.000006 -23160.410509 0.131908 8.962216e-07 288.008616 \n", + "0.35 -2867.759612 -0.000005 -23001.499461 0.131599 6.829096e-07 273.089782 \n", + "0.40 -2883.231719 -0.000005 -22843.131464 0.131287 5.237487e-07 255.164441 \n", + "0.45 -2892.153236 -0.000005 -22685.668716 0.130975 4.056468e-07 234.048222 \n", + "0.50 -2914.835086 -0.000004 -22525.832830 0.130659 3.167348e-07 219.601445 \n", + "0.55 -2921.787769 -0.000004 -22367.332766 0.130340 2.513504e-07 196.935789 \n", + "\n", + " Mz TAS a aileron ... thrust \\\n", + "time ... \n", + "0.05 -0.000001 44.895162 336.434581 2.959742e-10 ... 0.670198 \n", + "0.10 -0.000001 44.791157 336.434574 2.959742e-10 ... 0.670198 \n", + "0.15 -0.000001 44.687646 336.434555 2.959742e-10 ... 0.670198 \n", + "0.20 -0.000001 44.585409 336.434527 2.959742e-10 ... 0.670198 \n", + "0.25 -0.000001 44.482035 336.434473 2.959742e-10 ... 0.670198 \n", + "0.30 -0.000001 44.378277 336.434397 2.959742e-10 ... 0.670198 \n", + "0.35 -0.000001 44.274258 336.434294 2.959742e-10 ... 0.670198 \n", + "0.40 -0.000001 44.169584 336.434162 2.959742e-10 ... 0.670198 \n", + "0.45 -0.000001 44.064366 336.434000 2.959742e-10 ... 0.670198 \n", + "0.50 -0.000001 43.958162 336.433802 2.959742e-10 ... 0.670198 \n", + "0.55 -0.000001 43.850903 336.433567 2.959742e-10 ... 0.670198 \n", + "\n", + " u v v_down v_east v_north w \\\n", + "time \n", + "0.05 44.877493 1.089215e-07 -0.021778 21.523885 39.399206 -1.259451 \n", + "0.10 44.773564 1.085156e-07 -0.059100 21.474006 39.307904 -1.255270 \n", + "0.15 44.670646 1.080774e-07 -0.101132 21.424344 39.216999 -1.232525 \n", + "0.20 44.567449 1.076118e-07 -0.219729 21.375124 39.126902 -1.265389 \n", + "0.25 44.463623 1.071279e-07 -0.339570 21.325202 39.035520 -1.279696 \n", + "0.30 44.359858 1.066288e-07 -0.462223 21.274925 38.943489 -1.278443 \n", + "0.35 44.255295 1.061187e-07 -0.620164 21.224128 38.850505 -1.295661 \n", + "0.40 44.150414 1.056017e-07 -0.781931 21.172708 38.756382 -1.301203 \n", + "0.45 44.045377 1.050805e-07 -0.944579 21.120728 38.661234 -1.293510 \n", + "0.50 43.938927 1.045592e-07 -1.134443 21.067646 38.564068 -1.300252 \n", + "0.55 43.832154 1.040402e-07 -1.311274 21.013841 38.465578 -1.282176 \n", + "\n", + " x_earth y_earth z_earth \n", + "time \n", + "0.05 1.972256 1.077449 -999.999987 \n", + "0.10 3.939933 2.152395 -1000.001805 \n", + "0.15 5.903055 3.224853 -1000.006526 \n", + "0.20 7.861673 4.294852 -1000.013745 \n", + "0.25 9.815738 5.362362 -1000.027650 \n", + "0.30 11.765219 6.427369 -1000.047414 \n", + "0.35 13.710083 7.489853 -1000.073815 \n", + "0.40 15.650273 8.549783 -1000.107951 \n", + "0.45 17.585742 9.607135 -1000.149658 \n", + "0.50 19.516402 10.661859 -1000.200635 \n", + "0.55 21.442166 11.713909 -1000.261205 \n", + "\n", + "[11 rows x 35 columns]" + ] + }, + "execution_count": 76, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results = sim.propagate(sim.time+dt)\n", + "results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that `results` will include the previous timesteps as well as the last one. To get just the last one one can use pandas `loc` or `iloc`:" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Fx -2.921788e+03\n", + "Fy -3.761191e-06\n", + "Fz -2.236733e+04\n", + "Mach 1.303405e-01\n", + "Mx 2.513504e-07\n", + "My 1.969358e+02\n", + "Mz -1.203167e-06\n", + "TAS 4.385090e+01\n", + "a 3.364336e+02\n", + "aileron 2.959742e-10\n", + "alpha -2.924362e-02\n", + "beta 2.372590e-09\n", + "elevator 1.108958e-02\n", + "height 1.000261e+03\n", + "p 6.386588e-10\n", + "phi 2.537379e-10\n", + "pressure 8.987343e+04\n", + "psi 5.000000e-01\n", + "q 9.152033e-02\n", + "q_inf 1.068779e+03\n", + "r 1.349505e-10\n", + "rho 1.111631e+00\n", + "rudder -1.269086e-09\n", + "temperature 2.816493e+02\n", + "theta 6.638492e-04\n", + "thrust 6.701981e-01\n", + "u 4.383215e+01\n", + "v 1.040402e-07\n", + "v_down -1.311274e+00\n", + "v_east 2.101384e+01\n", + "v_north 3.846558e+01\n", + "w -1.282176e+00\n", + "x_earth 2.144217e+01\n", + "y_earth 1.171391e+01\n", + "z_earth -1.000261e+03\n", + "Name: 0.55, dtype: float64" + ] + }, + "execution_count": 77, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results.iloc[-1] # last time step" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Fx -2.921788e+03\n", + "Fy -3.761191e-06\n", + "Fz -2.236733e+04\n", + "Mach 1.303405e-01\n", + "Mx 2.513504e-07\n", + "My 1.969358e+02\n", + "Mz -1.203167e-06\n", + "TAS 4.385090e+01\n", + "a 3.364336e+02\n", + "aileron 2.959742e-10\n", + "alpha -2.924362e-02\n", + "beta 2.372590e-09\n", + "elevator 1.108958e-02\n", + "height 1.000261e+03\n", + "p 6.386588e-10\n", + "phi 2.537379e-10\n", + "pressure 8.987343e+04\n", + "psi 5.000000e-01\n", + "q 9.152033e-02\n", + "q_inf 1.068779e+03\n", + "r 1.349505e-10\n", + "rho 1.111631e+00\n", + "rudder -1.269086e-09\n", + "temperature 2.816493e+02\n", + "theta 6.638492e-04\n", + "thrust 6.701981e-01\n", + "u 4.383215e+01\n", + "v 1.040402e-07\n", + "v_down -1.311274e+00\n", + "v_east 2.101384e+01\n", + "v_north 3.846558e+01\n", + "w -1.282176e+00\n", + "x_earth 2.144217e+01\n", + "y_earth 1.171391e+01\n", + "z_earth -1.000261e+03\n", + "Name: 0.55, dtype: float64" + ] + }, + "execution_count": 78, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results.loc[sim.time] # results for current simulation time" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Test\n" + ] + }, + { + "cell_type": "code", + "execution_count": 984, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "a1 = Cessna172()\n", + "a2 = SimplifiedCessna172()\n", + "e1 = copy.deepcopy(environment)\n", + "e2 = copy.deepcopy(environment)" + ] + }, + { + "cell_type": "code", + "execution_count": 985, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(Aircraft State \n", + " x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", + " theta: 0.076 rad, phi: 0.000 rad, psi: 0.500 rad \n", + " u: 44.87 m/s, v: -0.00 m/s, w: 3.40 m/s \n", + " P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", + " u_dot: 0.00 m/s², v_dot: -0.00 m/s², w_dot: 0.00 m/s² \n", + " P_dot: -0.00 rad/s², Q_dot: 0.00 rad/s², R_dot: -0.00 rad/s² ,\n", + " {'delta_aileron': -1.2190588362567532e-17,\n", + " 'delta_elevator': -0.048951124635254917,\n", + " 'delta_rudder': 7.1787477633953699e-17,\n", + " 'delta_t': 0.57799667845449421})" + ] + }, + "execution_count": 985, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ts1, tc1 = steady_state_trim(\n", + " a1,\n", + " e1,\n", + " pos,\n", + " psi,\n", + " TAS,\n", + " controls0\n", + ")\n", + "e1.update(ts1)\n", + "ss1 = EulerFlatEarth(t0=0, full_state=ts1)\n", + "ts1, tc1" + ] + }, + { + "cell_type": "code", + "execution_count": 986, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "({'delta_aileron': -3.9966019045688599e-19,\n", + " 'delta_elevator': -0.07729883009616384,\n", + " 'delta_rudder': 2.7133156470881973e-18,\n", + " 'delta_t': 0.57166075967430052},\n", + " Aircraft State \n", + " x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", + " theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", + " u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", + " P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", + " u_dot: 0.00 m/s², v_dot: -0.00 m/s², w_dot: 0.00 m/s² \n", + " P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² )" + ] + }, + "execution_count": 986, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ts2, tc2 = steady_state_trim(\n", + " a2,\n", + " e2,\n", + " pos,\n", + " psi,\n", + " TAS,\n", + " controls0\n", + ") \n", + "e2.update(ts2)\n", + "ss2 = EulerFlatEarth(t0=0, full_state=ts2)\n", + "tc2, ts2" + ] + }, + { + "cell_type": "code", + "execution_count": 971, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "c1 = {\n", + " 'delta_elevator': Constant(tc1['delta_elevator']),\n", + " 'delta_aileron': Constant(tc1['delta_aileron']),\n", + " 'delta_rudder': Constant(tc1['delta_rudder']),\n", + " 'delta_t': Constant(tc1['delta_t'])\n", + "}\n", + "c2 = {\n", + " 'delta_elevator': Constant(tc2['delta_elevator']),\n", + " 'delta_aileron': Constant(tc2['delta_aileron']),\n", + " 'delta_rudder': Constant(tc2['delta_rudder']),\n", + " 'delta_t': Constant(tc2['delta_t'])\n", + "}\n", + "s1 = Simulation(a1, ss1, e1, c1)\n", + "s2 = Simulation(a2, ss2, e2, c2)\n", + " # Doublet(t_init=3, T=1, A=0.1, offset=0)," + ] + }, + { + "cell_type": "code", + "execution_count": 711, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "s1 = Simulation(aircraft, ss1, e1, c1)" + ] + }, + { + "cell_type": "code", + "execution_count": 712, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n", + "\n", + "time: 0%| | 0/5 [00:00]" + ] + }, + "execution_count": 713, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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NbjjG6Azi039W3erpS1DMbLO7F/U2Ll53In30e21fx8HdWfbdJ/hMUQF/v+bUQSpMRGR4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\nc/fHI6xJBsfXgF+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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(r1.alpha*180/np.pi)\n", + "plt.plot(r2.alpha*180/np.pi,'.')\n", + "plt.plot(results.alpha*180/np.pi,'.')" + ] + }, + { + "cell_type": "code", + "execution_count": 972, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\plotting\\_core.py:1716: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n", + " series.name = label\n" + ] + }, + { + "data": { + "image/png": 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NgT6DYPB4OLAe6o6e6hKjshdJgIKziIhIuM5ofQlNteENofDWltHeRK5hx8uw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\nP8vVQlJKqfRz+g3A1ylm6fVgK1aL2Qf0pZT+NKX0YkQsjIg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9XvyUh2qpkBI0pIqxz7+vlZWVfPWrX+Xss8/mc5/7HDfffDNz5sxhxYoVPPPM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\n97k06D6Xhry/zzkNxs65V4C9sdvM7MR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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "r2.plot(y=['beta', 'My', 'Mz', 'Fy'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "plt.plot" + ] + }, + { + "cell_type": "code", + "execution_count": 1111, + "metadata": {}, + "outputs": [ + { + "ename": "ValueError", + "evalue": "x and y must have same first dimension, but have shapes (12,) and (9, 12)", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma1\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0malpha_data\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ma1\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mCN_delta_aile_data\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'.'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 2\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma1\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0malpha_data\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ma2\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mCN_delta_aile_cl\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0ma2\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mCL\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0ma2\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0malpha_data\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\pyplot.py\u001b[0m in \u001b[0;36mplot\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m 3259\u001b[0m mplDeprecation)\n\u001b[0;32m 3260\u001b[0m \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 3261\u001b[1;33m \u001b[0mret\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 3262\u001b[0m \u001b[1;32mfinally\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3263\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_hold\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mwashold\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\__init__.py\u001b[0m in \u001b[0;36minner\u001b[1;34m(ax, *args, **kwargs)\u001b[0m\n\u001b[0;32m 1715\u001b[0m warnings.warn(msg % (label_namer, func.__name__),\n\u001b[0;32m 1716\u001b[0m RuntimeWarning, stacklevel=2)\n\u001b[1;32m-> 1717\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0max\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1718\u001b[0m \u001b[0mpre_doc\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0minner\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__doc__\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1719\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mpre_doc\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py\u001b[0m in \u001b[0;36mplot\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m 1370\u001b[0m \u001b[0mkwargs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcbook\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnormalize_kwargs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0m_alias_map\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1371\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1372\u001b[1;33m \u001b[1;32mfor\u001b[0m \u001b[0mline\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_lines\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1373\u001b[0m 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\u001b[1;32mfor\u001b[0m \u001b[0mseg\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_plot_args\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mthis\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 405\u001b[0m \u001b[1;32myield\u001b[0m \u001b[0mseg\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 406\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_base.py\u001b[0m in \u001b[0;36m_plot_args\u001b[1;34m(self, tup, kwargs)\u001b[0m\n\u001b[0;32m 382\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mindex_of\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtup\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 383\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 384\u001b[1;33m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_xy_from_xy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 385\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 386\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcommand\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'plot'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_base.py\u001b[0m in \u001b[0;36m_xy_from_xy\u001b[1;34m(self, x, y)\u001b[0m\n\u001b[0;32m 241\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 242\u001b[0m raise ValueError(\"x and y must have same first dimension, but \"\n\u001b[1;32m--> 243\u001b[1;33m \"have shapes {} and {}\".format(x.shape, y.shape))\n\u001b[0m\u001b[0;32m 244\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m2\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 245\u001b[0m raise ValueError(\"x and y can be no greater than 2-D, but have \"\n", + "\u001b[1;31mValueError\u001b[0m: x and y must have same first dimension, but have shapes (12,) and (9, 12)" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(a1.alpha_data, a1.CN_delta_aile_data, '.')\n", + "plt.plot(a1.alpha_data, a2.CN_delta_aile_cl*a2.CL + 0*a2.alpha_data)" + ] + }, + { + "cell_type": "code", + "execution_count": 1106, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-0.069523541636556885" + ] + }, + "execution_count": 1106, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.sum(a2.CL_data*a2.CN_p_data)/np.sum(a2.CL_data**2)" + ] + }, + { + "cell_type": "code", + "execution_count": 1119, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-0.00027157871300302394" + ] + }, + "execution_count": 1119, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.reshape(a1.CL_data**2, (1, 12)) * np.reshape(a1.delta_aile_data, (9, 1))\n", + "np.sum(a1.CN_delta_aile_data*x) / np.sum(x**2)" + ] + }, + { + "cell_type": "code", + "execution_count": 1120, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "LinregressResult(slope=-0.00027568577531501706, intercept=0.00072199122345927057, rvalue=-0.94235806962343571, pvalue=3.266896179580671e-52, stderr=9.5077855389690054e-06)" + ] + }, + "execution_count": 1120, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "linregress(x.flatten(), a1.CN_delta_aile_data.flatten())" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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IIerTMY3/s+HkVnTn3sCTnJMaPfPvK/RFRA5RVkYqM8eewZq+Ewk0ac7xb09g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\nrkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(aircraft.J_data,aircraft.Ct_data,'.')\n", + "plt.plot(aircraft.J_data,-0.1692121*aircraft.J_data**2 + 0.03545196*aircraft.J_data +0.10446359)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [], + "source": [ + "a,b,c = np.polyfit(aircraft.J_data,aircraft.Ct_data,2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/How it works.ipynb b/How it works.ipynb new file mode 100644 index 0000000..6160320 --- /dev/null +++ b/How it works.ipynb @@ -0,0 +1,938 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Python Flight Mechanics Engine " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Aircraft " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to perform a simulation, the first thing we need is an aircraft:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from pyfme.aircrafts import Cessna172" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "aircraft = Cessna172()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Aircraft will provide the simulator the forces, moments and inertial properties in order to perform the integration of the dynamic system equations:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Aircraft mass: 1043.2616 kg\n", + "Aircraft inertia tensor: \n", + " [[ 1285.3154166 0. 0. ]\n", + " [ 0. 1824.9309607 0. ]\n", + " [ 0. 0. 2666.89390765]] kg/m²\n" + ] + } + ], + "source": [ + "print(f\"Aircraft mass: {aircraft.mass} kg\")\n", + "print(f\"Aircraft inertia tensor: \\n {aircraft.inertia} kg/m²\")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "forces: [ 0. 0. 0.] N\n", + "moments: [ 0. 0. 0.] N·m\n" + ] + } + ], + "source": [ + "print(f\"forces: {aircraft.total_forces} N\")\n", + "print(f\"moments: {aircraft.total_moments} N·m\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the aircraft, in order to calculate its forces and moments it is necessary to set the controls values within the limits: " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0}\n" + ] + } + ], + "source": [ + "print(aircraft.controls)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'delta_elevator': (-0.4537856055185257, 0.48869219055841229), 'delta_aileron': (-0.26179938779914941, 0.3490658503988659), 'delta_rudder': (-0.27925268031909273, 0.27925268031909273), 'delta_t': (0, 1)}\n" + ] + } + ], + "source": [ + "print(aircraft.control_limits)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "but also to provide and environment (ie. atmosphere, winds, gravity) and the aircraft state, which will also determine the aerodynamic contribution." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Environment " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.environment.atmosphere import ISA1976\n", + "from pyfme.environment.wind import NoWind\n", + "from pyfme.environment.gravity import VerticalConstant" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "atmosphere = ISA1976()\n", + "gravity = VerticalConstant()\n", + "wind = NoWind()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The atmosphere, wind and gravity model make up the environment:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.environment import Environment" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "environment = Environment(atmosphere, gravity, wind)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The environment has an update method which given the state (ie. position, altitude...) updates the environment variables (ie. density, wind magnitude, gravity force...)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Help on method update in module pyfme.environment.environment:\n", + "\n", + "update(state) method of pyfme.environment.environment.Environment instance\n", + "\n" + ] + } + ], + "source": [ + "help(environment.update)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## State " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Even if the state can be set manually by giving the position, attitude, velocity, angular velocities... Most of the times, the user will want to trim the aircraft in a stationary condition. The aircraft controls to flight in that condition will be also provided by the trimmer." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.utils.trimmer import steady_state_trim" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Help on function steady_state_trim in module pyfme.utils.trimmer:\n", + "\n", + "steady_state_trim(aircraft, environment, pos, psi, TAS, controls, gamma=0, turn_rate=0, exclude=None, verbose=0)\n", + " Finds a combination of values of the state and control variables\n", + " that correspond to a steady-state flight condition.\n", + " \n", + " Steady-state aircraft flight is defined as a condition in which all\n", + " of the motion variables are constant or zero. That is, the linear and\n", + " angular velocity components are constant (or zero), thus all\n", + " acceleration components are zero.\n", + " \n", + " Parameters\n", + " ----------\n", + " aircraft : Aircraft\n", + " Aircraft to be trimmed.\n", + " environment : Environment\n", + " Environment where the aircraft is trimmed including atmosphere,\n", + " gravity and wind.\n", + " pos : Position\n", + " Initial position of the aircraft.\n", + " psi : float, opt\n", + " Initial yaw angle (rad).\n", + " TAS : float\n", + " True Air Speed (m/s).\n", + " controls : dict\n", + " Initial value guess for each control or fixed value if control is\n", + " included in exclude.\n", + " gamma : float, optional\n", + " Flight path angle (rad).\n", + " turn_rate : float, optional\n", + " Turn rate, d(psi)/dt (rad/s).\n", + " exclude : list, optional\n", + " List with controls not to be trimmed. If not given, every control\n", + " is considered in the trim process.\n", + " verbose : {0, 1, 2}, optional\n", + " Level of least_squares verbosity:\n", + " * 0 (default) : work silently.\n", + " * 1 : display a termination report.\n", + " * 2 : display progress during iterations (not supported by 'lm'\n", + " method).\n", + " \n", + " Returns\n", + " -------\n", + " state : AircraftState\n", + " Trimmed aircraft state.\n", + " trimmed_controls : dict\n", + " Trimmed aircraft controls\n", + " \n", + " Notes\n", + " -----\n", + " See section 3.4 in [1] for the algorithm description.\n", + " See section 2.5 in [1] for the definition of steady-state flight\n", + " condition.\n", + " \n", + " References\n", + " ----------\n", + " .. [1] Stevens, BL and Lewis, FL, \"Aircraft Control and Simulation\",\n", + " Wiley-lnterscience.\n", + "\n" + ] + } + ], + "source": [ + "help(steady_state_trim)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.models.state.position import EarthPosition" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "pos = EarthPosition(x=0, y=0, height=1000)\n", + "psi = 0.5 # rad\n", + "TAS = 45 # m/s\n", + "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "trimmed_state, trimmed_controls = steady_state_trim(\n", + " aircraft,\n", + " environment,\n", + " pos,\n", + " psi,\n", + " TAS,\n", + " controls0\n", + ") " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'delta_aileron': 5.6949494207348974e-18,\n", + " 'delta_elevator': -0.048951124635247888,\n", + " 'delta_rudder': -1.4494655727415656e-17,\n", + " 'delta_t': 0.57799667845248459}" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trimmed_controls" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "environment.update(trimmed_state)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, all the necessary elements in order to calculate forces and moments are available " + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Environment conditions for the current state:\n", + "environment.update(trimmed_state)\n", + "\n", + "# Forces and moments calculation:\n", + "forces, moments = aircraft.calculate_forces_and_moments(trimmed_state, environment, controls0)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([ 1.14823706e-11, -6.00938052e-18, -5.45696821e-12]),\n", + " array([ 1.34219095e-13, -1.43613996e-11, -2.41989038e-15]))" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "forces, moments" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The aircraft is trimmed indeed: the total forces and moments (aerodynamics + gravity + thrust) are zero" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simulation " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to simulate the dynamics of the aircraft under certain inputs in an environment, the user can set up a simulation using a dynamic system:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.models import EulerFlatEarth" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Constant Controls " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.utils.input_generator import Constant" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "controls = controls = {\n", + " 'delta_elevator': Constant(trimmed_controls['delta_elevator']),\n", + " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", + " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", + " 'delta_t': Constant(trimmed_controls['delta_t'])\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.simulator import Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "sim = Simulation(aircraft, system, environment, controls)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once the simulation is set, the propagation can be performed:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results = sim.propagate(10)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The results are returned in a DataFrame:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "kwargs = {'marker': '.',\n", + " 'subplots': True,\n", + " 'sharex': True,\n", + " 'figsize': (12, 6)}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['x_earth', 'y_earth', 'height'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['psi', 'theta', 'phi'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['v_north', 'v_east', 'v_down'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['p', 'q', 'r'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['alpha', 'beta', 'TAS'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['Fx', 'Fy', 'Fz'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['Mx', 'My', 'Mz'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['elevator', 'aileron', 'rudder', 'thrust'], **kwargs);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Doublet " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.utils.input_generator import Doublet" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "de0 = trimmed_controls['delta_elevator']" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "controls = controls = {\n", + " 'delta_elevator': Doublet(t_init=2, T=1, A=0.1, offset=de0),\n", + " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", + " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", + " 'delta_t': Constant(trimmed_controls['delta_t'])\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "sim = Simulation(aircraft, system, environment, controls)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once the simulation is set, the propagation can be performed:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results = sim.propagate(90)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['x_earth', 'y_earth', 'height'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['psi', 'theta', 'phi'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['v_north', 'v_east', 'v_down'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['p', 'q', 'r'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['alpha', 'beta', 'TAS'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['Fx', 'Fy', 'Fz'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['Mx', 'My', 'Mz'], **kwargs);" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.plot(y=['elevator', 'aileron', 'rudder', 'thrust'], **kwargs);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Propagating only one time step" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "dt = 0.05 # seconds\n", + "sim = Simulation(aircraft, system, environment, controls, dt)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results = sim.propagate(0.5)\n", + "results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can propagate for one time step even once the simulation has been propagated before:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results = sim.propagate(sim.time+dt)\n", + "results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that `results` will include the previous timesteps as well as the last one. To get just the last one one can use pandas `loc` or `iloc`:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.iloc[-1] # last time step" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "results.loc[sim.time] # results for current simulation time" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/src/pyfme/aircrafts/__init__.py b/src/pyfme/aircrafts/__init__.py index b6b8531..e8aa0ff 100644 --- a/src/pyfme/aircrafts/__init__.py +++ b/src/pyfme/aircrafts/__init__.py @@ -1,2 +1,3 @@ from .cessna_310 import Cessna310 -from .cessna_172 import Cessna172 +from .cessna_172 import Cessna172, SimplifiedCessna172 +from .boeing_linear import LinearB747 diff --git a/src/pyfme/aircrafts/boeing_linear.py b/src/pyfme/aircrafts/boeing_linear.py new file mode 100644 index 0000000..fcd62d3 --- /dev/null +++ b/src/pyfme/aircrafts/boeing_linear.py @@ -0,0 +1,87 @@ +# -*- coding: utf-8 -*- +""" +Python Flight Mechanics Engine (PyFME). +Copyright (c) AeroPython Development Team. +Distributed under the terms of the MIT License. +---------- +Cessna 172 +---------- + +References +---------- +[1] ETKIN, Dynamics of Flight, Stability and Control +---------- +""" + + +import numpy as np +import pdb + +from pyfme.aircrafts.aircraft import Aircraft +from pyfme.models.state import AircraftState, EarthPosition, EulerAttitude, BodyVelocity +from pyfme.environment.atmosphere import ISA1976 +from pyfme.environment.wind import NoWind +from pyfme.environment.gravity import VerticalConstant +from pyfme.environment.environment import Environment + +class LinearB747(Aircraft): + """ + Purely linear model of a Boeing 747 around a particular equilibrium condition + """ + + def __init__(self): + + # Mass & Inertia + self.mass = 2.83176e6/9.81 # kg + self.inertia = np.diag([.247e8, .449e8, .673e8]) # kg·m² + self.inertia[0, 2] = -.212e7 + self.inertia[2, 0] = -.212e7 + + # Geometry + self.Sw = 511 # m2 + self.chord = 8.324 # m + self.span = 59.64 # m + + # Aerodynamic Data# Values used for testing + self.stability_derivatives = { + 'Xu': -1.982e3, + 'Xw': 4.025e3, + 'Xq': 0, + 'Xw_dot': 0, + 'Zu': -2.595e4, + 'Zw': -9.030e4, + 'Zq': -4.524e5, + 'Zw_dot': 1.909e3, + 'Mu': 1.593e4, + 'Mw': -1.563e5, + 'Mq': -1.521e7, + 'Mw_dot': -1.702e4, + 'Yv': -1.610e4, + 'Yp': 0, + 'Yr': 0, + 'Lv': -3.062e5, + 'Lp': -1.076e7, + 'Lr': 9.925e6, + 'Nv': 2.131e5, + 'Np': -1.330e6, + 'Nr': -8.934e6 + } + + def calculate_derivatives(self, state, environment, controls): + return self.stability_derivatives + + def trimmed_conditions(self): + # state + att = EulerAttitude(0, 0, 0) # from Etkin + vel = BodyVelocity(235.9, 0, 0, att) # from Etkin + pos = EarthPosition(0, 0, -1000) # arbitrary + state = AircraftState(pos, att, vel) + + # environment + atmosphere = ISA1976() + gravity = VerticalConstant() + wind = NoWind() + environment = Environment(atmosphere, gravity, wind) + environment._rho = 0.3045 + + return state, environment \ No newline at end of file diff --git a/src/pyfme/aircrafts/cessna_172.py b/src/pyfme/aircrafts/cessna_172.py index 8414c41..31f8d12 100644 --- a/src/pyfme/aircrafts/cessna_172.py +++ b/src/pyfme/aircrafts/cessna_172.py @@ -74,11 +74,14 @@ deflection and the angle of attack via [2] """ import numpy as np +import pdb from scipy.interpolate import RectBivariateSpline +from scipy.stats import linregress from pyfme.aircrafts.aircraft import Aircraft from pyfme.models.constants import slugft2_2_kgm2, lbs2kg -from pyfme.utils.coordinates import wind2body +from pyfme.utils.coordinates import wind2body, body2wind +from copy import deepcopy as cp class Cessna172(Aircraft): @@ -142,7 +145,7 @@ def __init__(self): self.CN_r_data = np.array([-0.028, -0.027, -0.027, -0.0275, -0.0293, -0.0325, -0.037, -0.043, -0.05484, -0.058, -0.0592, -0.06015]) self.CN_delta_rud_data = (-1)*np.array([-0.211, -0.215, -0.218, -0.22, -0.224, -0.226, -0.228, -0.229, -0.23, -0.23, -0.23, -0.23]) self.CN_delta_aile_data = np.array([[-0.004321, -0.002238, -0.0002783, 0.001645, 0.003699, 0.005861, 0.008099, 0.01038, 0.01397, 0.01483, 0.01512, 0.01539], - [-0.003318, -0.001718, -0.0002137, 0.001263, 0.00284, 0.0045, 0.006218, 0.00797, 0.01072, 0.01138, 0.01161, 0.01181], + [-0.003318, -0.001718, -0.0002137, 0.001263, 0.00284, 0.0045, 0.006218, 0.00797, 0.01072, 0.01138, 0.01161, 0.01181], [-0.002016, -0.001044, -0.000123, 0.0007675, 0.00173, 0.002735, 0.0038, 0.004844, 0.00652, 0.00692, 0.00706, 0.0072], [-0.00101, -0.000522, -0.0000649, 0.000384, 0.000863, 0.00137, 0.0019, 0.00242, 0.00326, 0.00346, 0.00353, 0.0036], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], @@ -353,4 +356,212 @@ def calculate_forces_and_moments(self, state, environment, controls): self.total_forces = Ft + Fg + Fa self.total_moments = np.array([l, m, n]) + self.Fa_wind = Fa_wind + + # return state.velocity._vel_body, state.angular_vel._vel_ang_body return self.total_forces, self.total_moments + + + + def calculate_derivatives(self, state, environment, controls): + """ + Calculate dimensional derivatives of the forces at the vicinity of the state. + The output consists in 2 dictionaries, one for force one for moment + key: type of variables derivatives are taken for + val : 3x3 np array with X,Y,Z and L,M,N as columns, and the variable we differentiate against in lines + (u,v,w ; phi,theta,psi ; p,q,r ; x,y,z) + """ + names = {'velocity': ['u', 'v', 'w'], + 'angular_vel': ['p', 'q', 'r'], + 'acceleration': ['w_dot']} + Fnames = ['X', 'Y', 'Z'] + Mnames = ['L', 'M', 'N'] + + eps = 1e-3 + # F, M = self.calculate_forces_and_moments(state, environment, controls) + + # Rotation for stability derivatives in stability axis + V = np.sqrt(state.velocity.u**2 + state.velocity.v**2 + state.velocity.w**2) + alpha = np.arctan2(state.velocity.w, state.velocity.u) + beta = np.arcsin(state.velocity.v / V) + + + derivatives = {} + for keyword in names.keys(): + for i in range(len(names[keyword])): + eps_v0 = np.zeros(3) + + # plus perturb + eps_v0[i] = eps/2 + eps_vec = wind2body(eps_v0, alpha, beta) + state.perturbate(eps_vec, keyword) + forces_p, moments_p = self.calculate_forces_and_moments(state, environment, controls) + forces_p = body2wind(forces_p, alpha, beta) + moments_p = body2wind(moments_p, alpha, beta) + state.cancel_perturbation() + + # minus perturb + eps_v0[i] = - eps/2 + eps_vec = wind2body(eps_v0, alpha, beta) + state.perturbate(eps_vec, keyword) + forces_m, moments_m = self.calculate_forces_and_moments(state, environment, controls) + forces_m = body2wind(forces_m, alpha, beta) + moments_m = body2wind(moments_m, alpha, beta) + state.cancel_perturbation() + + k = names[keyword][i] + for j in range(3): + # print(Fnames[j] + k, forces[j]) + derivatives[Fnames[j] + k] = (forces_p[j] - forces_m[j]) / eps + derivatives[Mnames[j] + k] = (moments_p[j] - moments_m[j]) / eps + + return derivatives + + def build_linear_system(self, state, environment, controls): + """ + Building linear system as described in Etkin. For full linearized equations see page 113. The variables are + delta_u, w, q and delta_theta for the long. system,. and v,p,r and psi for the lateral one. + /!\ Important notice: Ixz is defined as done in Roskam + """ + ## TODO : Verify definitions for Izx + + +class SimplifiedCessna172(Cessna172): + def __init__(self): + super().__init__() + self.CL_0 = 0.148 + self.CM_0 = 0.0075 + self.CL_alpha = 5.440E+00 + self.CL_q = np.mean(self.CL_q_data) + self.CL_delta_elev = np.sum(self.delta_elev_data*self.CL_delta_elev_data)/np.sum(self.delta_elev_data**2) + + self.CM_alpha2, self.CM_alpha, self.CM_0 = np.polyfit(self.alpha_data, self.CM_data, 2) + self.CM_q = 2*np.mean(self.CM_q_data) + self.CM_delta_elev = np.sum(self.delta_elev_data*self.CM_delta_elev_data)/np.sum(self.delta_elev_data**2) + + + # pre-stall drag model + ICL_max = self.CL_data.argmax() + cl = self.CL_data[:ICL_max-2] + cd = self.CD_data[:ICL_max-2] + al = self.alpha_data[: ICL_max] + self.CD_K1, self.CD_0, r_value, p_value, std_err = linregress(cl ** 2, cd) + self.CL_MAX = self.CL_data[ICL_max] + + self.CY_beta = np.mean(self.CY_beta_data) + self.CY_p = np.mean(self.CY_p_data) + self.CY_r = np.mean(self.CY_r_data) + self.CY_delta_rud = np.mean(self.CY_delta_rud_data) + + # XXX: Tunned Cl_delta_rud + self.Cl_beta = 0.1*np.mean(self.Cl_beta_data) + self.Cl_p = np.mean(self.Cl_p_data) + self.Cl_r_cl = np.sum(self.CL_data*self.Cl_r_data)/np.sum(self.CL_data**2) + self.Cl_delta_rud = .075*np.mean(self.Cl_delta_rud_data) + self.Cl_delta_aile = np.sum(self.delta_aile_data*self.Cl_delta_aile_data)/np.sum(self.delta_aile_data**2) + + + # XXX: Tunned CN_delta_rud + self.CN_beta = np.mean(self.CN_beta_data) + self.CN_p_al = np.sum(self.alpha_data*self.CN_p_data)/np.sum(self.alpha_data**2) + self.CN_r_cl, self.CN_r_0, _, _,_ = linregress(self.CL_data**2,self.CN_r_data) + self.CN_delta_rud = 0.075*np.mean(self.CN_delta_rud_data) + x = np.reshape(self.CL_data, (1, 12)) * np.reshape(self.delta_aile_data, (9, 1)) + self.CN_delta_aile_cl = np.sum(self.CN_delta_aile_data*x) / np.sum(x**2) + + # simplistic thrust model + self.RPM_delta_t = 1800 + self.RPM_idle = 1000 + self.Ct_J2, self.Ct_J, self.Ct_0 = np.polyfit(self.J_data, self.Ct_data, 2) + + + + def _calculate_aero_lon_forces_moments_coeffs(self, state): + """ + Simplified dynamics for the Cessna 172: strictly linear dynamics. + Stability derivatives are considered constant, the value for small angles is kept. + + Parameters + ---------- + state + + Returns + ------- + + """ + + delta_elev = np.rad2deg(self.controls['delta_elevator']) # deg + alpha_DEG = np.rad2deg(self.alpha) # deg + alpha_RAD = self.alpha # rad + c = self.chord # m + V = self.TAS # m/s + p, q, r = (state.angular_vel.p, state.angular_vel.q, + state.angular_vel.r) # rad/s + + self.CL = ( + self.CL_0 + + self.CL_alpha*alpha_RAD + + self.CL_delta_elev*delta_elev + + self.CL_q * q * c/(2*V) + ) + # STALL + self.CL = self.CL if abs(self.CL) < self.CL_MAX else np.sign(self.CL)*self.CL_MAX + + self.CD = self.CD_0 + self.CD_K1*self.CL**2 + + self.CM = ( + self.CM_0 + + (self.CM_alpha2*alpha_DEG + self.CM_alpha)*alpha_DEG + + self.CM_delta_elev * delta_elev + + self.CM_q * q * c/(2*V) + ) + + def _calculate_aero_lat_forces_moments_coeffs(self, state): + delta_aile = np.rad2deg(self.controls['delta_aileron']) # deg + delta_rud_RAD = self.controls['delta_rudder'] # rad + alpha_DEG = np.rad2deg(self.alpha) # deg + b = self.span + V = self.TAS + p, q, r = state.angular_vel.p, state.angular_vel.q, state.angular_vel.r + + self.CY = ( + self.CY_beta * self.beta + + self.CY_delta_rud * delta_rud_RAD + + b/(2 * V) * (self.CY_p * p + self.CY_r * r) + ) + + self.Cl = ( + self.Cl_beta * self.beta + + self.Cl_delta_aile * delta_aile + + self.Cl_delta_rud * delta_rud_RAD + + b/(2 * V) * (self.Cl_p * p + self.Cl_r_cl * self.CL * r) + ) + + self.CN = ( + self.CN_beta * self.beta + + (self.CN_delta_aile_cl*self.CL*delta_aile) + + self.CN_delta_rud * delta_rud_RAD + + b/(2 * V) * (self.CN_p_al*alpha_DEG * p + (self.CN_r_cl*self.CL**2 + self.CN_r_0) * r) + ) + + def _calculate_thrust_forces_moments(self, environment): + delta_t = self.controls['delta_t'] + rho = environment.rho + V = self.TAS + prop_rad = self.propeller_radius + + # throttle controls the revolutions of the propeller linearly. + RPM = self.RPM_delta_t*delta_t + self.RPM_idle # rpm + omega_RAD = (RPM * 2 * np.pi) / 60.0 # rad/s + + # We calculate the relation between the thrust coefficient Ct and the + # advance ratio J using the program JavaProp + J = (np.pi * V) / (omega_RAD * prop_rad) # non-dimensional + Ct = self.Ct_J2*J + self.Ct_J*J + self.Ct_0 # non-dimensional + + T = (2/np.pi)**2 * rho * (omega_RAD * prop_rad)**2 * Ct # N + + # We will consider that the engine is aligned along the OX (body) axis + Ft = np.array([T, 0, 0]) + + return Ft \ No newline at end of file diff --git a/src/pyfme/models/euler_flat_earth.py b/src/pyfme/models/euler_flat_earth.py index f0d1623..a9a2e8c 100644 --- a/src/pyfme/models/euler_flat_earth.py +++ b/src/pyfme/models/euler_flat_earth.py @@ -21,6 +21,7 @@ AircraftState, EarthPosition, EulerAttitude, BodyVelocity, BodyAngularVelocity, BodyAcceleration, BodyAngularAcceleration ) +from pyfme.utils.coordinates import body2wind class EulerFlatEarth(AircraftDynamicSystem): @@ -82,8 +83,8 @@ def _adapt_full_state_to_dynamic_system(self, full_state): full_state.position.lat, full_state.position.lon) - att = EulerAttitude(full_state.attitude.theta, - full_state.attitude.phi, + att = EulerAttitude(full_state.attitude.phi, + full_state.attitude.theta, full_state.attitude.psi) vel = BodyVelocity(full_state.velocity.u, @@ -129,6 +130,51 @@ def _get_state_vector_from_full_state(self, full_state): ) return x0 + def linearized_model(self, state, aircraft, environment, controls): + """ + Outputs matrices A_long and A_lat that are the lateral and longitudinal state matrices for the linearized system. + As done in Etkin [2], these matrices are useful in stability axis. + + """ + + + # get derivatives + d = aircraft.calculate_derivatives(state, environment, controls) + + # get inertias + m = aircraft.mass + Ix = aircraft.inertia[0, 0] + Iy = aircraft.inertia[1, 1] + Iz = aircraft.inertia[2, 2] + Ixz = aircraft.inertia[0, 2] + Ixprime = (Ix*Iz - Ixz**2)/Iz + Izprime = (Ix*Iz - Ixz**2)/Ix + Ixzprime = Ixz/(Ix*Iz - Ixz**2) + + # recover state variables + u, v, w = state.velocity.vel_body + phi, theta, psi = state.attitude.euler_angles + g = environment.gravity_magnitude + + # Longitudinal matrix + # Todo : add alpha_dot derivatives + A1 = np.array([d['Xu'] / m, d['Xw'] / m, 0, -g*np.cos(theta)]) + A2 = np.array([d['Zu'], d['Zw'], d['Zq'] + m*u, -m*g*np.sin(theta)])/(m - d['Zw_dot']) + A3 = (np.array([d['Mu'], d['Mw'], d['Mq'], 0]) + A2*d['Mw_dot']) / Iy + A4 = np.array([0, 0, 1, 0]) + A_long = np.vstack((A1, A2, A3, A4)) + + # Lateral dynamics + A1 = np.array([d['Yv']/m, d['Yp']/m, d['Yr']/m - u, g*np.cos(theta)]) + A2 = np.array([d['Lv']/Ixprime + d['Nv']*Ixzprime, d['Lp']/Ixprime + d['Np']*Ixzprime, + d['Lr']/Ixprime + d['Nr']*Ixzprime, 0]) + A3 = np.array([d['Lv']*Ixzprime + d['Nv']/Izprime, d['Lp']*Ixzprime + d['Np']/Izprime, + d['Lr'] * Ixzprime + d['Nr'] / Izprime, 0]) + A4 = np.array([0, 1, np.tan(theta), 0]) + A_lat = np.vstack((A1, A2, A3, A4)) + + return A_long, A_lat + # TODO: numba jit def _system_equations(time, state_vector, mass, inertia, forces, moments): diff --git a/src/pyfme/models/state/acceleration.py b/src/pyfme/models/state/acceleration.py index 4488010..8b8b7cb 100644 --- a/src/pyfme/models/state/acceleration.py +++ b/src/pyfme/models/state/acceleration.py @@ -36,6 +36,7 @@ def __init__(self): self._accel_body = np.zeros(3) # m/s² # Local horizon (NED) self._accel_NED = np.zeros(3) # m/s² + self._accel_body_ref = None @abstractmethod def update(self, coords, attitude): @@ -92,6 +93,17 @@ def update(self, coords, attitude): attitude.phi, attitude.psi) + def perturbate(self, eps_vector, **kwargs): + assert self._accel_body_ref is None, "Cancel perturbation on velocity before perturbating again" + self._accel_body_ref = np.copy(self._accel_body) + self.update(self._accel_body + eps_vector, kwargs['attitude']) + + def cancel_perturbation(self, **kwargs): + if self._accel_body_ref is not None: + self.update(self._accel_body_ref, kwargs['attitude']) + self._accel_body_ref = None + + def __repr__(self): rv = (f"u_dot: {self.u_dot:.2f} m/s², v_dot: {self.v_dot:.2f} m/s², " f"w_dot: {self.u_dot:.2f} m/s²") diff --git a/src/pyfme/models/state/aircraft_state.py b/src/pyfme/models/state/aircraft_state.py index 737e685..90abec0 100644 --- a/src/pyfme/models/state/aircraft_state.py +++ b/src/pyfme/models/state/aircraft_state.py @@ -14,6 +14,7 @@ from .angular_velocity import BodyAngularVelocity from .acceleration import BodyAcceleration from .angular_acceleration import BodyAngularAcceleration +from pyfme.utils.coordinates import wind2body class AircraftState: @@ -35,6 +36,7 @@ def __init__(self, position, attitude, velocity, angular_vel=None, self.acceleration = acceleration self.angular_accel = angular_accel + @property def value(self): """Only for testing purposes""" @@ -53,3 +55,25 @@ def __repr__(self): f"{self.angular_accel} \n" ) return rv + + def perturbate(self, eps_vector, keyword): + """ + Perturbates the "keyword" part of the state (position, attitude, velocity, angular_vel) by eps_vec (size (3,)). + Each vector V becomes V + eps_vector, so eps is the change in each direction. + The perturbations can optionally be specified in the stability_axis. Note that it is common to linearize the + dynamics in stability axis + """ + # Get the "keyword" part of the state + attr = getattr(self, keyword) + + # Perturbate + attr.perturbate(eps_vector, attitude=self.attitude) + + def cancel_perturbation(self): + """ + Brings back to reference state. + """ + for keyword in ['position', 'attitude', 'velocity', 'angular_vel', 'acceleration']: + getattr(self, keyword).cancel_perturbation(attitude=self.attitude) + + return self diff --git a/src/pyfme/models/state/angular_velocity.py b/src/pyfme/models/state/angular_velocity.py index 8d7d349..0b681a4 100644 --- a/src/pyfme/models/state/angular_velocity.py +++ b/src/pyfme/models/state/angular_velocity.py @@ -32,6 +32,7 @@ def __init__(self): self._vel_ang_body = np.zeros(3) # rad/s # EULER ANGLE RATES (theta_dot, phi_dot, psi_dot) self._euler_ang_rate = np.zeros(3) # rad/s + self._vel_ang_body_ref = None @abstractmethod def update(self, coords, attitude): @@ -88,6 +89,16 @@ def update(self, coords, attitude): # rates self._euler_ang_rate = np.zeros(3) # rad/s + def perturbate(self, eps_vector, **kwargs): + assert self._vel_ang_body_ref is None, "Cancel perturbation on velocity before perturbating again" + self._vel_ang_body_ref = np.copy(self._vel_ang_body) + self.update(self._vel_ang_body + eps_vector, kwargs['attitude']) + + def cancel_perturbation(self, **kwargs): + if self._vel_ang_body_ref is not None: + self.update(self._vel_ang_body_ref, kwargs['attitude']) + self._vel_ang_body_ref = None + def __repr__(self): return (f"P: {self.p:.2f} rad/s, " f"Q: {self.q:.2f} rad/s, " diff --git a/src/pyfme/models/state/attitude.py b/src/pyfme/models/state/attitude.py index 395b2c9..f8baae2 100644 --- a/src/pyfme/models/state/attitude.py +++ b/src/pyfme/models/state/attitude.py @@ -37,6 +37,7 @@ def __init__(self): self._euler_angles = np.zeros(3) # rad # Quaternions (q0, q1, q2, q3) self._quaternions = np.zeros(4) + self._euler_angles_ref = None @abstractmethod def update(self, value): @@ -96,6 +97,16 @@ def update(self, value): # TODO: transform quaternions to Euler angles self._quaternions = np.zeros(4) + def perturbate(self, eps_vector, **kwargs): + assert self._euler_angles_ref is None, "Cancel perturbation on velocity before perturbating again" + self._euler_angles_ref = np.copy(self._euler_angles) + self.update(self._euler_angles + eps_vector) + + def cancel_perturbation(self, **kwargs): + if self._euler_angles_ref is not None: + self.update(self._euler_angles_ref) + self._euler_angles_ref = None + def __repr__(self): rv = (f"theta: {self.theta:.3f} rad, phi: {self.phi:.3f} rad, " f"psi: {self.psi:.3f} rad") diff --git a/src/pyfme/models/state/position.py b/src/pyfme/models/state/position.py index e40c985..814172a 100644 --- a/src/pyfme/models/state/position.py +++ b/src/pyfme/models/state/position.py @@ -46,6 +46,7 @@ def __init__(self, geodetic, geocentric, earth): self._geocentric_coordinates = np.asarray(geocentric, dtype=float) # m # Earth coordinates (x_earth, y_earth, z_earth) self._earth_coordinates = np.asarray(earth, dtype=float) # m + self._earth_coordinates_ref = None @abstractmethod def update(self, coords): @@ -133,6 +134,16 @@ def update(self, value): # Update Earth coordinates with value self._earth_coordinates[:] = value + def perturbate(self, eps_vector, **kwargs): + assert self._earth_coordinates_ref is None, "Cancel perturbation on position before perturbating again" + self._earth_coordinates_ref = np.copy(self._earth_coordinates) + self.update(self._earth_coordinates + eps_vector) + + def cancel_perturbation(self, **kwargs): + if self._earth_coordinates_ref is not None: + self.update(self._earth_coordinates_ref) + self._earth_coordinates_ref = None + def __repr__(self): rv = (f"x_e: {self.x_earth:.2f} m, y_e: {self.y_earth:.2f} m, " f"z_e: {self.z_earth:.2f} m") diff --git a/src/pyfme/models/state/velocity.py b/src/pyfme/models/state/velocity.py index ccbcc99..719e3f0 100644 --- a/src/pyfme/models/state/velocity.py +++ b/src/pyfme/models/state/velocity.py @@ -43,6 +43,8 @@ def __init__(self): self._vel_body = np.zeros(3) # m/s # Local horizon (NED) self._vel_NED = np.zeros(3) # m/s + # Reference in case of perturbation + self._vel_body_ref = None @abstractmethod def update(self, coords, attitude): @@ -100,6 +102,16 @@ def update(self, value, attitude): attitude.phi, attitude.psi) # m/s + def perturbate(self, eps_vector, **kwargs): + assert self._vel_body_ref is None, "Cancel perturbation on velocity before perturbating again" + self._vel_body_ref = np.copy(self._vel_body) + self.update(self._vel_body + eps_vector, kwargs['attitude']) + + def cancel_perturbation(self, **kwargs): + if self._vel_body_ref is not None: + self.update(self._vel_body_ref, kwargs['attitude']) + self._vel_body_ref = None + def __repr__(self): return f"u: {self.u:.2f} m/s, v: {self.v:.2f} m/s, w: {self.w:.2f} m/s" diff --git a/src/pyfme/utils/anemometry.py b/src/pyfme/utils/anemometry.py index fb5ca6e..6e79528 100644 --- a/src/pyfme/utils/anemometry.py +++ b/src/pyfme/utils/anemometry.py @@ -23,7 +23,7 @@ position error. """ -from math import asin, atan, sqrt +from math import asin, atan2, sqrt from pyfme.models.constants import RHO_0, P_0, SOUND_VEL_0, GAMMA_AIR @@ -78,7 +78,7 @@ def calculate_alpha_beta_TAS(u, v, w): TAS = sqrt(u ** 2 + v ** 2 + w ** 2) - alpha = atan(w / u) + alpha = atan2(w, u) beta = asin(v / TAS) return alpha, beta, TAS diff --git a/src/pyfme/utils/coordinates.py b/src/pyfme/utils/coordinates.py index 8f48750..ffee070 100644 --- a/src/pyfme/utils/coordinates.py +++ b/src/pyfme/utils/coordinates.py @@ -448,3 +448,27 @@ def wind2body(wind_coords, alpha, beta): body_coords = Lbw.dot(wind_coords) return body_coords + + +def body2stab(body_coords, alpha, beta): + return body2wind(body_coords, alpha, beta) + +def stab2body(body_coords, alpha, beta): + check_alpha_beta_range(alpha, beta) + + # Transformation matrix from body to wind + Lwb = np.array([ + [cos(alpha) * cos(beta), + sin(beta), + sin(alpha) * cos(beta)], + [- cos(alpha) * sin(beta), + cos(beta), + -sin(alpha) * sin(beta)], + [-sin(alpha), + 0, + cos(alpha)] + ]) + + wind_coords = np.linalg.lstsq(Lwb, body_coords)[0] + + return wind_coords From c94f59b118195f546406ccf79130ecf87727a7b3 Mon Sep 17 00:00:00 2001 From: jdebecdelievre Date: Mon, 4 Jun 2018 16:53:33 -0700 Subject: [PATCH 2/5] Added validation by comapring to the solution of an eigenvalue problem and of a matlab simulink project --- .gitignore | 4 + ...igenvalue problem - tests-checkpoint.ipynb | 1390 +++-- Eigenvalue problem - tests.ipynb | 864 --- How it works (modif).ipynb | 4991 ----------------- How it works.ipynb | 938 ---- src/pyfme/aircrafts/boeing_linear.py | 2 +- src/pyfme/aircrafts/cessna_172.py | 10 +- src/pyfme/environment/atmosphere.py | 6 + src/pyfme/models/euler_flat_earth.py | 287 +- src/pyfme/models/state/aircraft_state.py | 23 + src/pyfme/utils/coordinates.py | 24 - src/pyfme/utils/export.py | 18 + validation/PyFME vs Eigenvalue analysis.ipynb | 1515 +++++ validation/PyFME vs Simulink.ipynb | 440 ++ 14 files changed, 3298 insertions(+), 7214 deletions(-) delete mode 100644 Eigenvalue problem - tests.ipynb delete mode 100644 How it works (modif).ipynb delete mode 100644 How it works.ipynb create mode 100644 src/pyfme/utils/export.py create mode 100644 validation/PyFME vs Eigenvalue analysis.ipynb create mode 100644 validation/PyFME vs Simulink.ipynb diff --git a/.gitignore b/.gitignore index 2ce6417..5b03dce 100644 --- a/.gitignore +++ b/.gitignore @@ -10,5 +10,9 @@ build .spyder* examples/.ipynb_checkpoints +validation/.ipynb_checkpoints examples/examples-notebook/.ipynb_checkpoints/ +.ipynb_checkpoints + + diff --git a/.ipynb_checkpoints/Eigenvalue problem - tests-checkpoint.ipynb b/.ipynb_checkpoints/Eigenvalue problem - tests-checkpoint.ipynb index 3b5f60d..d86403e 100644 --- a/.ipynb_checkpoints/Eigenvalue problem - tests-checkpoint.ipynb +++ b/.ipynb_checkpoints/Eigenvalue problem - tests-checkpoint.ipynb @@ -9,10 +9,8 @@ }, { "cell_type": "code", - "execution_count": 55, - "metadata": { - "collapsed": true - }, + "execution_count": 299, + "metadata": {}, "outputs": [], "source": [ "from pyfme.aircrafts import LinearB747, SimplifiedCessna172\n", @@ -27,14 +25,24 @@ "from pyfme.utils.trimmer import steady_state_trim\n", "from pyfme.models.state.position import EarthPosition\n", "from pyfme.simulator import Simulation\n", - "from pyfme.models import EulerFlatEarth" + "from pyfme.models import EulerFlatEarth\n", + "from pyfme.models.euler_flat_earth import wind2body4attitude" ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 300, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The autoreload extension is already loaded. To reload it, use:\n", + " %reload_ext autoreload\n" + ] + } + ], "source": [ "%load_ext autoreload\n", "%autoreload 2" @@ -49,7 +57,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 301, "metadata": { "collapsed": true }, @@ -60,7 +68,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 302, "metadata": {}, "outputs": [ { @@ -82,7 +90,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 303, "metadata": { "collapsed": true }, @@ -93,7 +101,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 304, "metadata": { "collapsed": true }, @@ -104,16 +112,16 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 305, "metadata": {}, "outputs": [], "source": [ - "A_long, A_lat = system.linearized_model(state, aircraft, environment, None)" + "A_long, A_lat = system.linearized_model(state, aircraft, environment, method=\"from_forces\")" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 306, "metadata": {}, "outputs": [ { @@ -133,7 +141,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 307, "metadata": { "collapsed": true }, @@ -144,7 +152,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 308, "metadata": { "collapsed": true }, @@ -155,7 +163,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 309, "metadata": {}, "outputs": [ { @@ -165,7 +173,7 @@ " -0.00328880+0.0671904j , -0.00328880-0.0671904j ])" ] }, - "execution_count": 11, + "execution_count": 309, "metadata": {}, "output_type": "execute_result" } @@ -176,7 +184,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 310, "metadata": {}, "outputs": [ { @@ -184,8 +192,8 @@ "output_type": "stream", "text": [ "[[ -5.57748538e-02 0.00000000e+00 -2.35900000e+02 9.80665000e+00]\n", - " [ -1.27028796e-02 -4.35107741e-01 4.14335937e-01 0.00000000e+00]\n", - " [ 3.56656916e-03 -6.05604146e-03 -1.45800775e-01 0.00000000e+00]\n", + " [ -1.21578588e-02 -4.38509325e-01 3.91486496e-01 0.00000000e+00]\n", + " [ 2.78343743e-03 -3.35756281e-02 -1.20416770e-01 0.00000000e+00]\n", " [ 0.00000000e+00 1.00000000e+00 0.00000000e+00 0.00000000e+00]]\n" ] } @@ -196,7 +204,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 311, "metadata": { "collapsed": true }, @@ -207,17 +215,17 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 312, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([-0.03309986+0.94696989j, -0.03309986-0.94696989j,\n", - " -0.56322438+0.j , -0.00725928+0.j ])" + "array([ 0.01992122+0.88015949j, 0.01992122-0.88015949j,\n", + " -0.64722566+0.j , -0.00731773+0.j ])" ] }, - "execution_count": 14, + "execution_count": 312, "metadata": {}, "output_type": "execute_result" } @@ -242,10 +250,8 @@ }, { "cell_type": "code", - "execution_count": 463, - "metadata": { - "collapsed": true - }, + "execution_count": 313, + "metadata": {}, "outputs": [], "source": [ "aircraft = SimplifiedCessna172()" @@ -253,7 +259,7 @@ }, { "cell_type": "code", - "execution_count": 464, + "execution_count": 314, "metadata": {}, "outputs": [], "source": [ @@ -265,7 +271,7 @@ }, { "cell_type": "code", - "execution_count": 465, + "execution_count": 315, "metadata": {}, "outputs": [], "source": [ @@ -286,7 +292,33 @@ }, { "cell_type": "code", - "execution_count": 466, + "execution_count": 316, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Aircraft State \n", + "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", + "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", + "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", + "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", + "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", + "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " + ] + }, + "execution_count": 316, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trimmed_state" + ] + }, + { + "cell_type": "code", + "execution_count": 317, "metadata": { "collapsed": true }, @@ -297,24 +329,24 @@ }, { "cell_type": "code", - "execution_count": 467, + "execution_count": 318, "metadata": {}, "outputs": [], "source": [ - "A_long, A_lat = system.linearized_model(trimmed_state, aircraft, environment, trimmed_controls)" + "A_long, A_lat = system.linearized_model(trimmed_state, aircraft, environment, trimmed_controls, method=\"from_forces\",eps=1e-10)" ] }, { "cell_type": "code", - "execution_count": 468, + "execution_count": 319, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "longitudinal eigenvalues : [[-2.61877991+4.03883858j -2.61877991-4.03883858j -0.02858402+0.26539636j\n", - " -0.02858402-0.26539636j]]\n" + "longitudinal eigenvalues : [[-2.61284085+4.04869466j -2.61284085-4.04869466j -0.03452750+0.26286901j\n", + " -0.03452750-0.26286901j]]\n" ] } ], @@ -326,22 +358,55 @@ }, { "cell_type": "code", - "execution_count": 469, + "execution_count": 320, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def linear_stab_2_body(long_state=np.zeros(4), lat_state=np.zeros(4), u0=0, theta0=0,alpha0=0, beta0=0):\n", + " # velocities\n", + " v = wind2body(np.array([long_state[0] + u0, lat_state[0], long_state[1]]), alpha=alpha0, beta=beta0)\n", + " # Roll rates\n", + " r = wind2body(np.array([lat_state[1], long_state[2], lat_state[2]]), alpha=alpha0, beta=beta0)\n", + " # attitude\n", + " ang = wind2body4attitude(np.array([long_state[3], lat_state[3], 0]), alpha=alpha0, beta=beta0)\n", + " long_stateB = np.copy(long_state)\n", + " lat_stateB = np.copy(lat_state)\n", + " long_stateB[0] = v[0]\n", + " long_stateB[1] = v[2]\n", + " long_stateB[2] = r[1]\n", + " long_stateB[3] += theta0\n", + " lat_stateB[0] = v[1]\n", + " lat_stateB[1] = r[0]\n", + " lat_stateB[2] = r[2]\n", + " return long_stateB.real, lat_stateB.real" + ] + }, + { + "cell_type": "code", + "execution_count": 321, "metadata": {}, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "lat eigenvalues : [[-5.64040610+0.j -0.22741980+1.12082018j -0.22741980-1.12082018j\n", - " 0.02242997+0.j ]]\n" - ] + "data": { + "text/plain": [ + "Aircraft State \n", + "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", + "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", + "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", + "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", + "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", + "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " + ] + }, + "execution_count": 321, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "lat_val, lat_vec=nl.eig(A_lat)\n", - "lat_val = np.expand_dims(lat_val, axis = 0)\n", - "print(f\"lat eigenvalues : {lat_val}\")" + "trimmed_state" ] }, { @@ -353,10 +418,8 @@ }, { "cell_type": "code", - "execution_count": 490, - "metadata": { - "collapsed": true - }, + "execution_count": 322, + "metadata": {}, "outputs": [], "source": [ "from pyfme.utils.coordinates import wind2body, body2wind" @@ -364,7 +427,7 @@ }, { "cell_type": "code", - "execution_count": 491, + "execution_count": 323, "metadata": {}, "outputs": [], "source": [ @@ -374,11 +437,11 @@ }, { "cell_type": "code", - "execution_count": 492, + "execution_count": 324, "metadata": {}, "outputs": [], "source": [ - "perturbation = (long_vec.T[0] + long_vec.T[1])/10" + "perturbation = (long_vec.T[0] + long_vec.T[1])/1000" ] }, { @@ -390,7 +453,7 @@ }, { "cell_type": "code", - "execution_count": 493, + "execution_count": 325, "metadata": {}, "outputs": [], "source": [ @@ -399,101 +462,43 @@ }, { "cell_type": "code", - "execution_count": 494, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 0.00068044+0.j, 0.19898677+0.j, -0.00221646+0.j, 0.00352200+0.j])" - ] - }, - "execution_count": 494, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "perturbation" - ] - }, - { - "cell_type": "code", - "execution_count": 495, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 4.47131754e+01 +9.11776957e-18j,\n", - " -7.57841343e-13 +2.78656422e-19j, 3.58117832e+00 +7.30262577e-19j])" - ] - }, - "execution_count": 495, - "metadata": {}, - "output_type": "execute_result" - } - ], + "execution_count": 326, + "metadata": { + "collapsed": true + }, + "outputs": [], "source": [ - "x1" + "# stability axis\n", + "u, v, w = body2wind(trimmed_state.velocity.vel_body, alpha, 0)\n", + "theta0 = trimmed_state.attitude.theta*1.0" ] }, { "cell_type": "code", - "execution_count": 496, + "execution_count": 327, "metadata": {}, "outputs": [], "source": [ - "t = np.linspace(0,10,100)\n", + "t = np.linspace(0,3,100)\n", "N = len(t)\n", "X = np.zeros((N,4))\n", "xx = []\n", "for i in range(N):\n", " x_stab = (long_vec*np.exp(long_val*t[i])).dot(C)\n", " xx.append(x_stab[1])\n", - " x1 = wind2body(np.array([x_stab[0] + trimmed_state.velocity.u, x_stab[1], 0]), alpha=alpha, beta=0)\n", - " X[i,:2] = x1.real[2:]" - ] - }, - { - "cell_type": "code", - "execution_count": 497, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\numpy\\core\\numeric.py:531: ComplexWarning: Casting complex values to real discards the imaginary part\n", - " return array(a, dtype, copy=False, order=order)\n" - ] - }, - { - "data": { - "image/png": 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Moc0NesNe0lpVbOjv3r5xyRdZ59OJYSJJ6pRiQx+eeqF0Oea7eGvoS1qr/JbNc3R2mKg/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\nVQAAAABJRU5ErkJggg==\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(xx,'.')\n", - "plt.show()" + " X[i,:] = linear_stab_2_body(long_state=x_stab.real, alpha0=alpha, u0=u, theta0 = theta0)[0]" ] }, { "cell_type": "code", - "execution_count": 498, + "execution_count": 328, "metadata": {}, "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -501,7 +506,7 @@ } ], "source": [ - "plt.plot(t,X[:,1],'.')\n", + "plt.plot(t,X[:,0],'.')\n", "plt.show()" ] }, @@ -514,7 +519,7 @@ }, { "cell_type": "code", - "execution_count": 499, + "execution_count": 329, "metadata": { "collapsed": true }, @@ -525,7 +530,7 @@ }, { "cell_type": "code", - "execution_count": 500, + "execution_count": 330, "metadata": {}, "outputs": [], "source": [ @@ -539,21 +544,89 @@ }, { "cell_type": "code", - "execution_count": 501, + "execution_count": 331, "metadata": {}, "outputs": [], "source": [ "# Perturbate\n", "trimmed_state.cancel_perturbation()\n", - "p = perturbation.real\n", - "trimmed_state.perturbate(np.array([p[0],p[1],0]), 'velocity',reference_frame = 'stability_axis')\n", - "trimmed_state.perturbate(np.array([0,p[2],0]), 'angular_vel',reference_frame = 'stability_axis')\n", - "trimmed_state.perturbate(np.array([0,p[3],0]), 'attitude',reference_frame = 'stability_axis')" + "p = linear_stab_2_body(long_state=perturbation.real, alpha0=alpha)[0]\n", + "trimmed_state.perturbate(np.array([p[0],0,p[1]]), 'velocity')\n", + "trimmed_state.perturbate(np.array([0,p[2],0]), 'angular_vel')\n", + "trimmed_state.perturbate(np.array([p[3],0,0]), 'attitude') # /!\\ Convention theta, phi, psi" + ] + }, + { + "cell_type": "code", + "execution_count": 332, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Aircraft State \n", + "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", + "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", + "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", + "P: 0.00 rad/s, Q: -0.00 rad/s, R: 0.00 rad/s \n", + "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", + "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " + ] + }, + "execution_count": 332, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trimmed_state" + ] + }, + { + "cell_type": "code", + "execution_count": 333, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 4.35247324e-05+0.j, 1.99016773e-03+0.j, -2.19846816e-05+0.j,\n", + " 3.52384151e-05+0.j])" + ] + }, + "execution_count": 333, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "perturbation" + ] + }, + { + "cell_type": "code", + "execution_count": 334, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ -1.15502388e-04, 1.98728991e-03, -2.19846816e-05,\n", + " 3.52384151e-05])" + ] + }, + "execution_count": 334, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "p" ] }, { "cell_type": "code", - "execution_count": 502, + "execution_count": 335, "metadata": { "collapsed": true }, @@ -565,7 +638,7 @@ }, { "cell_type": "code", - "execution_count": 503, + "execution_count": 336, "metadata": { "collapsed": true }, @@ -576,184 +649,14 @@ }, { "cell_type": "code", - "execution_count": 484, + "execution_count": 337, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "\n", - "\n", - "time: 0%| | 0/10 [00:00" + "" ] }, "metadata": {}, @@ -804,14 +747,14 @@ } ], "source": [ - "plt.plot(t,X[:,1] - max(X[:,1]),'.')\n", - "plt.plot(r.w - max(r.w))\n", + "plt.plot(t,X[:,3],'.')\n", + "plt.plot(r.theta)\n", "plt.show()" ] }, { "cell_type": "code", - "execution_count": 487, + "execution_count": 176, "metadata": {}, "outputs": [ { @@ -826,7 +769,7 @@ "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " ] }, - "execution_count": 487, + "execution_count": 176, "metadata": {}, "output_type": "execute_result" } @@ -835,33 +778,794 @@ "trimmed_state" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Lateral Checks" + ] + }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" + "execution_count": 277, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ -1.20869794e-01 -9.03365248e-02 -4.45371242e+01 9.80665000e+00]\n", + " [ -7.47735120e-02 -5.52245304e+00 2.23529676e+00 0.00000000e+00]\n", + " [ 2.69453703e-02 1.21841526e-01 -4.29492904e-01 0.00000000e+00]\n", + " [ 0.00000000e+00 1.00000000e+00 0.00000000e+00 0.00000000e+00]]\n" + ] + } + ], + "source": [ + "print(f\"{A_lat}\")" + ] }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.3" + { + "cell_type": "code", + "execution_count": 278, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "lat eigenvalues : [[-5.58724126+0.j -0.26870849+1.12020645j -0.26870849-1.12020645j\n", + " 0.05184251+0.j ]]\n" + ] + } + ], + "source": [ + "lat_val, lat_vec=nl.eig(A_lat_0)\n", + "lat_val = np.expand_dims(lat_val, axis = 0)\n", + "print(f\"lat eigenvalues : {lat_val}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 279, + "metadata": {}, + "outputs": [], + "source": [ + "# # Normalize eigvec to have delta_psi=1\n", + "# delta_psi = lat_vec[2]/np.cos(theta0)\n", + "# lat_vec /= delta_psi\n", + "# print(f\"{lat_vec.T}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 280, + "metadata": {}, + "outputs": [], + "source": [ + "alpha = np.arctan2(trimmed_state.velocity.w, trimmed_state.velocity.u)\n", + "V = np.sqrt(trimmed_state.velocity.w**2 + trimmed_state.velocity.v**2 + trimmed_state.velocity.u**2)\n", + "beta = np.arcsin(trimmed_state.velocity.v/V)\n", + "u = trimmed_state.velocity.u*1.0" + ] + }, + { + "cell_type": "code", + "execution_count": 281, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-5.58724126+0.j , -0.26870849+1.12020645j,\n", + " -0.26870849-1.12020645j, 0.05184251+0.j ]])" + ] + }, + "execution_count": 281, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "lat_val" + ] + }, + { + "cell_type": "code", + "execution_count": 282, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# perturbation = (lat_vec.T[1] + lat_vec.T[2])/1000\n", + "perturbation = (lat_vec.T[3])/10000" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Eigenvalue approach" + ] + }, + { + "cell_type": "code", + "execution_count": 283, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "C = nl.lstsq(a=lat_vec,b=perturbation.real)[0].real" + ] + }, + { + "cell_type": "code", + "execution_count": 284, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# stability axis\n", + "u, v, w = body2wind(trimmed_state.velocity.vel_body, alpha, 0)\n", + "theta0 = trimmed_state.attitude.theta*1.0" + ] + }, + { + "cell_type": "code", + "execution_count": 285, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "t = np.linspace(0,10,100)\n", + "N = len(t)\n", + "X = np.zeros((N,4))\n", + "xx = []\n", + "for i in range(N):\n", + " x_stab = (lat_vec*np.exp(lat_val*t[i])).dot(C)\n", + " xx.append(x_stab[1])\n", + " X[i,:] = linear_stab_2_body(lat_state=x_stab.real, beta0=beta, alpha0=alpha, u0=u, theta0 = theta0)[1]" + ] + }, + { + "cell_type": "code", + "execution_count": 286, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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NR96Ykp4DLgWWpj4PpHHXpXAZsRX4fM5aFwE/jog3q3hfE8Kn0czMyqsmdKYB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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(t,X[:,3],'.')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 287, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.utils.input_generator import Constant" + ] + }, + { + "cell_type": "code", + "execution_count": 288, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "controls = {\n", + " 'delta_elevator': Constant(trimmed_controls['delta_elevator']),\n", + " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", + " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", + " 'delta_t': Constant(trimmed_controls['delta_t'])\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 289, + "metadata": {}, + "outputs": [], + "source": [ + "# Perturbate\n", + "trimmed_state.cancel_perturbation()\n", + "p = linear_stab_2_body(lat_state=perturbation.real, alpha0=alpha, beta0=beta)[1]\n", + "trimmed_state.perturbate(np.array([0,p[0],0]), 'velocity')\n", + "trimmed_state.perturbate(np.array([p[1],0,p[2]]), 'angular_vel')\n", + "trimmed_state.perturbate(np.array([0,p[3],0]), 'attitude') # /!\\ Convention theta, phi, psi" + ] + }, + { + "cell_type": "code", + "execution_count": 290, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Aircraft State \n", + "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", + "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", + "u: 44.86 m/s, v: 0.00 m/s, w: 3.59 m/s \n", + "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", + "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", + "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " + ] + }, + "execution_count": 290, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trimmed_state" + ] + }, + { + "cell_type": "code", + "execution_count": 291, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 9.60060356e-05, 5.13657549e-07, 5.67794858e-06,\n", + " 2.73923016e-05])" + ] + }, + "execution_count": 291, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "p" + ] + }, + { + "cell_type": "code", + "execution_count": 292, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "environment.update(trimmed_state)\n", + "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" + ] + }, + { + "cell_type": "code", + "execution_count": 293, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "sim = Simulation(aircraft, system, environment, controls)" + ] + }, + { + "cell_type": "code", + "execution_count": 294, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "time: 100%|████████████████████████████████████████████████████████████▉| 9.999999999999831/10 [00:06<00:00, 1.64it/s]\n" + ] + } + ], + "source": [ + "r = sim.propagate(10)" + ] + }, + { + "cell_type": "code", + "execution_count": 295, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Aircraft State \n", + "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", + "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", + "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", + "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", + "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", + "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " + ] + }, + "execution_count": 295, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trimmed_state.cancel_perturbation()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "plt.plot(r2.r)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 296, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(t,X[:,2],'.')\n", + "plt.plot(r.r)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 200, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Aircraft State \n", + "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", + "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", + "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", + "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", + "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", + "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " + ] + }, + "execution_count": 200, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trimmed_state" + ] + }, + { + "cell_type": "code", + "execution_count": 201, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[-5.54556785+0.j , -0.24930832+1.12369875j,\n", + " -0.24930832-1.12369875j, 0.03752870+0.j ]])" + ] + }, + "execution_count": 201, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "lat_val" + ] + }, + { + "cell_type": "code", + "execution_count": 202, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 0.43547942+0.j, 0.88576915+0.j, 0.01607544+0.j, -0.15972560+0.j])" + ] + }, + "execution_count": 202, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "lat_vec.T[0]" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.0" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trimmed_state.angular_vel." + ] + }, + { + "cell_type": "code", + "execution_count": 269, + "metadata": {}, + "outputs": [], + "source": [ + "A_long, A_lat = system.linearized_model(aircraft=aircraft, environment=environment, controls=trimmed_controls, state=trimmed_state, method='from_forces',eps=1e-5)" + ] + }, + { + "cell_type": "code", + "execution_count": 276, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "> c:\\users\\jean\\box sync\\recherche\\aeropython\\pyfme\\pyfme\\src\\pyfme\\models\\euler_flat_earth.py(240)linearized_model()\n", + "-> derivatives[keyword][i][\"acceleration\"] = (accel_p - accel_m)/eps\n", + "(Pdb) eps_vec\n", + "array([ -4.98403983e-06, 4.54327588e-19, -3.99182908e-07])\n", + "(Pdb) angle_der_p\n", + "array([ 2.90510260e-21, 5.03197145e-06, -1.27828591e-09])\n", + "(Pdb) angle_der_m\n", + "array([ -2.90510260e-21, -5.03197145e-06, 1.27828591e-09])\n", + "(Pdb) (angle_der_p - angle_der_m)/eps\n", + "array([ 5.81020520e-16, 1.00639429e+00, -2.55657183e-04])\n", + "(Pdb) body2wind4attitude(np.array([ 5.81020520e-16, 1.00639429e+00, -2.55657183e-04]), alpha,0)\n", + "array([ 5.81020520e-16, 1.00316143e+00, -8.06019209e-02])\n", + "(Pdb) body2wind(np.array([ 5.81020520e-16, 1.00639429e+00, -2.55657183e-04]), alpha,0)\n", + "array([ -2.04107955e-05, 1.00639429e+00, -2.54841116e-04])\n", + "(Pdb) body2wind(np.array([ 5.81020520e-16, -2.55657183e-04, 1.00639429e+00]), alpha,0)\n", + "array([ 8.03470798e-02, -2.55657183e-04, 1.00318184e+00])\n", + "(Pdb) body2wind(np.array([1.00639429e+00, 5.81020520e-16, -2.55657183e-04]), alpha,0)\n", + "array([ 1.00316143e+00, 5.81020520e-16, -8.06019209e-02])\n", + "(Pdb) body2wind4attitude(np.array([ 5.81020520e-16, 1.00639429e+00, -2.55657183e-04]), alpha,0)\n", + "array([ 5.81020520e-16, 1.00316143e+00, -8.06019209e-02])\n", + "(Pdb) body2wind4attitude(np.array([ 5.81020520e-16, 1.00316143e+00, -8.06019209e-02]), alpha,0)\n", + "array([ 5.81020520e-16, 9.93524322e-01, -1.60433616e-01])\n", + "(Pdb) q\n" + ] + }, + { + "ename": "BdbQuit", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mBdbQuit\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mA_long_0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mA_lat_0\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msystem\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlinearized_model\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0maircraft\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0maircraft\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0menvironment\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0menvironment\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcontrols\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mtrimmed_controls\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstate\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mtrimmed_state\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'direct'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0meps\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1e-5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[1;32mc:\\users\\jean\\box sync\\recherche\\aeropython\\pyfme\\pyfme\\src\\pyfme\\models\\euler_flat_earth.py\u001b[0m in \u001b[0;36mlinearized_model\u001b[1;34m(self, state, aircraft, environment, controls, method, eps)\u001b[0m\n\u001b[0;32m 238\u001b[0m \u001b[0mpdb\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mset_trace\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 240\u001b[1;33m \u001b[0mderivatives\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mkeyword\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m\"acceleration\"\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m 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\u001b[1;33m(\u001b[0m\u001b[0mangle_der_p\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mangle_der_m\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0meps\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\bdb.py\u001b[0m in \u001b[0;36mtrace_dispatch\u001b[1;34m(self, frame, event, arg)\u001b[0m\n\u001b[0;32m 46\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[1;31m# None\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 47\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mevent\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'line'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 48\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdispatch_line\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mframe\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 49\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mevent\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'call'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 50\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdispatch_call\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mframe\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0marg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\bdb.py\u001b[0m in \u001b[0;36mdispatch_line\u001b[1;34m(self, frame)\u001b[0m\n\u001b[0;32m 65\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstop_here\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mframe\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mbreak_here\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mframe\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 66\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0muser_line\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mframe\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mquitting\u001b[0m\u001b[1;33m:\u001b[0m \u001b[1;32mraise\u001b[0m \u001b[0mBdbQuit\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtrace_dispatch\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mBdbQuit\u001b[0m: " + ] + } + ], + "source": [ + "A_long_0, A_lat_0 = system.linearized_model(aircraft=aircraft, environment=environment, controls=trimmed_controls, state=trimmed_state, method='direct',eps=1e-5)" + ] + }, + { + "cell_type": "code", + "execution_count": 271, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ -1.20869794e-01, -9.03365248e-02, -4.45371242e+01,\n", + " 9.74414359e+00],\n", + " [ -7.47735120e-02, -5.52245304e+00, 2.23529676e+00,\n", + " 0.00000000e+00],\n", + " [ 2.69453703e-02, 1.21841526e-01, -4.29492904e-01,\n", + " 0.00000000e+00],\n", + " [ 0.00000000e+00, 1.00639429e+00, 7.98365815e-02,\n", + " 0.00000000e+00]])" + ] + }, + "execution_count": 271, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A_lat_0" + ] + }, + { + "cell_type": "code", + "execution_count": 272, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ -1.20869794e-01, -9.03365248e-02, -4.45371242e+01,\n", + " 9.80665000e+00],\n", + " [ -7.47735120e-02, -5.52245304e+00, 2.23529676e+00,\n", + " 0.00000000e+00],\n", + " [ 2.69453703e-02, 1.21841526e-01, -4.29492904e-01,\n", + " 0.00000000e+00],\n", + " [ 0.00000000e+00, 1.00000000e+00, 0.00000000e+00,\n", + " 0.00000000e+00]])" + ] + }, + "execution_count": 272, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A_lat" + ] + }, + { + "cell_type": "code", + "execution_count": 234, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ -1.38777878e-17, -8.18789481e-16, 7.10542736e-15,\n", + " -6.25064079e-02],\n", + " [ -1.38777878e-17, 8.88178420e-16, -4.44089210e-16,\n", + " 0.00000000e+00],\n", + " [ -6.93889390e-18, 8.32667268e-17, 1.11022302e-16,\n", + " 0.00000000e+00],\n", + " [ 0.00000000e+00, -6.39429055e-03, -7.98365815e-02,\n", + " 0.00000000e+00]])" + ] + }, + "execution_count": 234, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A_lat_0 - A_lat" + ] + }, + { + "cell_type": "code", + "execution_count": 273, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.00000000e+00, 2.77555756e-17, 1.03506245e-01,\n", + " -3.16067172e-11],\n", + " [ -5.55111512e-17, 4.44089210e-16, 1.42108547e-14,\n", + " 4.71280662e-11],\n", + " [ 9.50501660e-24, 0.00000000e+00, 0.00000000e+00,\n", + " 0.00000000e+00],\n", + " [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", + " 0.00000000e+00]])" + ] + }, + "execution_count": 273, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A_long - A_long_0" + ] + }, + { + "cell_type": "code", + "execution_count": 129, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "9.775346835682555" + ] + }, + "execution_count": 129, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "environment.gravity.magnitude*np.cos(trimmed_state.attitude.theta)" + ] + }, + { + "cell_type": "code", + "execution_count": 125, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([-5.58715768+0.j , -0.26874702+1.12000709j,\n", + " -0.26874702-1.12000709j, 0.05183599+0.j ]),\n", + " array([[ 0.13423245+0.j , -0.99952523+0.j ,\n", + " -0.99952523-0.j , 0.96028912+0.j ],\n", + " [ 0.97522803+0.j , 0.01451373+0.00631349j,\n", + " 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0.95819774+0.j ],\n", + " [ 0.97487327+0.j , 0.01443260+0.00632829j,\n", + " 0.01443260-0.00632829j, 0.01044092+0.j ],\n", + " [-0.02373824+0.j , -0.00263322+0.02211495j,\n", + " -0.00263322-0.02211495j, 0.05802270+0.j ],\n", + " [-0.17503917+0.j , 0.00251248-0.01353422j,\n", + " 0.00251248+0.01353422j, 0.27996688+0.j ]]))" + ] + }, + "execution_count": 126, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "nl.eig(A_lat_0)" + ] + }, + { + "cell_type": "code", + "execution_count": 273, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'Lp': -7133.328546452819,\n", + " 'Lq': -1.4654173893683747e-10,\n", + " 'Lr': 2845.5233748002283,\n", + " 'Lu': -1.6283778605817378e-13,\n", + " 'Lv': -93.803403491876296,\n", + " 'Lw': 6.9671154216072033e-11,\n", + " 'Lw_dot': 0.0,\n", + " 'Mp': -1.4695971056655402e-10,\n", + " 'Mq': -5632.7295473571803,\n", + " 'Mr': 2.7867357756854979e-10,\n", + " 'Mu': -2.0745923501323575e-10,\n", + " 'Mv': -9.186545529766439e-12,\n", + " 'Mw': -707.13949139512761,\n", + " 'Mw_dot': 0.0,\n", + " 'Np': -283.31950651682462,\n", + " 'Nq': -2.2527993262196244e-11,\n", + " 'Nr': -895.86253976691603,\n", + " 'Nu': -1.7233602342481363e-12,\n", + " 'Nv': 63.401932933491914,\n", + " 'Nw': 5.2206376490114745e-12,\n", + " 'Nw_dot': 0.0,\n", + " 'Xp': 9.229755496128686e-12,\n", + " 'Xq': -107.9840910856487,\n", + " 'Xr': -4.7292397320312929e-11,\n", + " 'Xu': -81.920634160969684,\n", + " 'Xv': -1.0097458080175065e-10,\n", + " 'Xw': 117.92566393514095,\n", + " 'Xw_dot': 0.0,\n", + " 'Yp': -94.24462738878492,\n", + " 'Yq': -9.2148511043887993e-12,\n", + " 'Yr': 482.90054315893724,\n", + " 'Yu': -8.1046280797636427e-12,\n", + " 'Yv': -126.09881477888743,\n", + " 'Yw': 2.2093438190040615e-11,\n", + " 'Yw_dot': 0.0,\n", + " 'Zp': 0.0,\n", + " 'Zq': -2203.4392987106062,\n", + " 'Zr': 0.0,\n", + " 'Zu': -448.14552058005893,\n", + " 'Zv': 9.0763688408092465e-12,\n", + " 'Zw': -2221.7928894651527,\n", + " 'Zw_dot': 0.0}" + ] + }, + "execution_count": 273, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "aircraft.calculate_derivatives(trimmed_state, environment, trimmed_controls)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" } }, "nbformat": 4, diff --git a/Eigenvalue problem - tests.ipynb b/Eigenvalue problem - tests.ipynb deleted file mode 100644 index eec39b2..0000000 --- a/Eigenvalue problem - tests.ipynb +++ /dev/null @@ -1,864 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Python Flight Mechanics Engine " - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.aircrafts import LinearB747, SimplifiedCessna172\n", - "from pyfme.models import EulerFlatEarth\n", - "import numpy as np\n", - "nl = np.linalg\n", - "import matplotlib.pyplot as plt\n", - "from pyfme.environment.atmosphere import ISA1976\n", - "from pyfme.environment.wind import NoWind\n", - "from pyfme.environment.gravity import VerticalConstant\n", - "from pyfme.environment import Environment\n", - "from pyfme.utils.trimmer import steady_state_trim\n", - "from pyfme.models.state.position import EarthPosition\n", - "from pyfme.simulator import Simulation\n", - "from pyfme.models import EulerFlatEarth" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "%load_ext autoreload\n", - "%autoreload 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Test on Boeing" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "aircraft = LinearB747()" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Aircraft mass: 288660.5504587156 kg\n", - "Aircraft inertia tensor: \n", - " [[ 24700000. 0. -2120000.]\n", - " [ 0. 44900000. 0.]\n", - " [ -2120000. 0. 67300000.]] kg/m²\n" - ] - } - ], - "source": [ - "print(f\"Aircraft mass: {aircraft.mass} kg\")\n", - "print(f\"Aircraft inertia tensor: \\n {aircraft.inertia} kg/m²\")" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "state, environment = aircraft.trimmed_conditions()" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "system = EulerFlatEarth(t0=0, full_state=state)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "A_long, A_lat = system.linearized_model(state, aircraft, environment, None)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[ -6.86619629e-03 1.39437135e-02 0.00000000e+00 -9.80665000e+00]\n", - " [ -9.04964592e-02 -3.14906754e-01 2.35892792e+02 -0.00000000e+00]\n", - " [ 3.89092422e-04 -3.36169904e-03 -4.28171388e-01 0.00000000e+00]\n", - " [ 0.00000000e+00 0.00000000e+00 1.00000000e+00 0.00000000e+00]]\n" - ] - } - ], - "source": [ - "print(f\"{A_long}\")" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "d = aircraft.calculate_derivatives(None, None, None)" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "val, vec = nl.eig(A_long)" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([-0.37168337+0.88692454j, -0.37168337-0.88692454j,\n", - " -0.00328880+0.0671904j , -0.00328880-0.0671904j ])" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "val" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[ -5.57748538e-02 0.00000000e+00 -2.35900000e+02 9.80665000e+00]\n", - " [ -1.27028796e-02 -4.35107741e-01 4.14335937e-01 0.00000000e+00]\n", - " [ 3.56656916e-03 -6.05604146e-03 -1.45800775e-01 0.00000000e+00]\n", - " [ 0.00000000e+00 1.00000000e+00 0.00000000e+00 0.00000000e+00]]\n" - ] - } - ], - "source": [ - "print(f\"{A_lat}\")" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "val, vec = nl.eig(A_lat)" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([-0.03309986+0.94696989j, -0.03309986-0.94696989j,\n", - " -0.56322438+0.j , -0.00725928+0.j ])" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "val" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Eigen values are the same as the ones in Etkin. So the matrix was copy-pasted right in EulerFlatEarth.linearize()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Simplified Cessna: compare response with eigenvalue analysis" - ] - }, - { - "cell_type": "code", - "execution_count": 48, - "metadata": {}, - "outputs": [], - "source": [ - "aircraft = SimplifiedCessna172()" - ] - }, - { - "cell_type": "code", - "execution_count": 49, - "metadata": {}, - "outputs": [], - "source": [ - "atmosphere = ISA1976()\n", - "gravity = VerticalConstant()\n", - "wind = NoWind()\n", - "environment = Environment(atmosphere, gravity, wind)" - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "metadata": {}, - "outputs": [], - "source": [ - "pos = EarthPosition(x=0, y=0, height=1000)\n", - "psi = 0.5 # rad\n", - "TAS = 45 # m/s\n", - "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}\n", - "trimmed_state, trimmed_controls = steady_state_trim(\n", - " aircraft,\n", - " environment,\n", - " pos,\n", - " psi,\n", - " TAS,\n", - " controls0\n", - ")\n", - "environment.update(trimmed_state)" - ] - }, - { - "cell_type": "code", - "execution_count": 51, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" - ] - }, - { - "cell_type": "code", - "execution_count": 52, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{'Lp': -7133.3285464529754,\n", - " 'Lq': -1.3596490723877686e-10,\n", - " 'Lr': 2845.5233747989769,\n", - " 'Lu': -1.5072258133617629e-13,\n", - " 'Lv': -93.803403491879237,\n", - " 'Lw': 6.4642542808689936e-11,\n", - " 'Lw_dot': 0.0,\n", - " 'Mp': -1.3635270481322531e-10,\n", - " 'Mq': -5632.7295473571794,\n", - " 'Mr': 2.5855995439045339e-10,\n", - " 'Mu': -2.0740884413894751e-10,\n", - " 'Mv': -8.5234948148304966e-12,\n", - " 'Mw': -707.13949139550539,\n", - " 'Mw_dot': 0.0,\n", - " 'Np': -283.31950651664334,\n", - " 'Nq': -2.0902086546512417e-11,\n", - " 'Nr': -895.8625397666973,\n", - " 'Nu': -1.600102250108547e-12,\n", - " 'Nv': 63.401932933487544,\n", - " 'Nw': 4.8437512785752048e-12,\n", - " 'Nw_dot': 0.0,\n", - " 'Xp': 8.5635844119039128e-12,\n", - " 'Xq': -107.98409108583664,\n", - " 'Xr': -4.3879010396940393e-11,\n", - " 'Xu': -81.920634161805893,\n", - " 'Xv': -1.0186591357214635e-10,\n", - " 'Xw': 117.92566393495383,\n", - " 'Xw_dot': 0.0,\n", - " 'Yp': -94.244627388807359,\n", - " 'Yq': -8.5635868519158715e-12,\n", - " 'Yr': 482.90054315893269,\n", - " 'Yu': -7.5184642244713184e-12,\n", - " 'Yv': -126.09881477888285,\n", - " 'Yw': 2.053118461568279e-11,\n", - " 'Yw_dot': 0.0,\n", - " 'Zp': 0.0,\n", - " 'Zq': -2203.4392987142378,\n", - " 'Zr': 0.0,\n", - " 'Zu': -448.14552058364376,\n", - " 'Zv': 9.0763684172927728e-12,\n", - " 'Zw': -2221.7928894687734,\n", - " 'Zw_dot': 0.0}" - ] - }, - "execution_count": 52, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "aircraft.calculate_derivatives(trimmed_state, environment=environment, controls=trimmed_controls)" - ] - }, - { - "cell_type": "code", - "execution_count": 53, - "metadata": {}, - "outputs": [], - "source": [ - "A_long, A_lat = system.linearized_model(trimmed_state, aircraft, environment, trimmed_controls)" - ] - }, - { - "cell_type": "code", - "execution_count": 54, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "longitudinal eigenvalues : [[-2.61286215+4.04181191j -2.61286215-4.04181191j -0.03450179+0.26321042j\n", - " -0.03450179-0.26321042j]]\n" - ] - } - ], - "source": [ - "long_val, long_vec=nl.eig(A_long)\n", - "long_val = np.expand_dims(long_val, axis = 0)\n", - "print(f\"longitudinal eigenvalues : {long_val}\")" - ] - }, - { - "cell_type": "code", - "execution_count": 55, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[ -1.20869794e-01 -9.03365248e-02 -4.43934827e+01 9.80665000e+00]\n", - " [ -7.29808437e-02 -5.54986617e+00 2.21387166e+00 0.00000000e+00]\n", - " [ 2.37736990e-02 -1.06235762e-01 -3.35919827e-01 0.00000000e+00]\n", - " [ 0.00000000e+00 1.00000000e+00 0.00000000e+00 0.00000000e+00]]\n" - ] - } - ], - "source": [ - "print(f\"{A_lat}\")" - ] - }, - { - "cell_type": "code", - "execution_count": 56, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "lat eigenvalues : [[-5.54552962+0.j -0.24937803+1.12210093j -0.24937803-1.12210093j\n", - " 0.03762989+0.j ]]\n" - ] - } - ], - "source": [ - "lat_val, lat_vec=nl.eig(A_lat)\n", - "lat_val = np.expand_dims(lat_val, axis = 0)\n", - "print(f\"lat eigenvalues : {lat_val}\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Longitudinal checks" - ] - }, - { - "cell_type": "code", - "execution_count": 57, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Aircraft State \n", - "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", - "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", - "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", - "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", - "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", - "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " - ] - }, - "execution_count": 57, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "trimmed_state" - ] - }, - { - "cell_type": "code", - "execution_count": 58, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "def linear_stab_2_body(long_state=np.zeros(4), lat_state=np.zeros(4), u0=0, theta0=0,alpha0=0, beta0=0):\n", - " # velocities\n", - " v = wind2body(np.array([long_state[0] + u0, lat_state[0], long_state[1]]), alpha=alpha0, beta=beta0)\n", - " # Roll rates\n", - " r = wind2body(np.array([lat_state[1], long_state[2], lat_state[2]]), alpha=alpha0, beta=beta0)\n", - " long_stateB = np.copy(long_state)\n", - " lat_stateB = np.copy(lat_state)\n", - " long_stateB[0] = v[0]\n", - " long_stateB[1] = v[2]\n", - " long_stateB[2] = r[1]\n", - " long_stateB[3] += theta0\n", - " lat_stateB[0] = v[1]\n", - " lat_stateB[1] = r[0]\n", - " lat_stateB[2] = r[2]\n", - " return long_stateB.real, lat_stateB.real" - ] - }, - { - "cell_type": "code", - "execution_count": 59, - "metadata": {}, - "outputs": [], - "source": [ - "from pyfme.utils.coordinates import wind2body, body2wind, stab2body" - ] - }, - { - "cell_type": "code", - "execution_count": 60, - "metadata": {}, - "outputs": [], - "source": [ - "alpha = np.arctan2(trimmed_state.velocity.w, trimmed_state.velocity.u)\n", - "u = trimmed_state.velocity.u*1.0" - ] - }, - { - "cell_type": "code", - "execution_count": 61, - "metadata": {}, - "outputs": [], - "source": [ - "perturbation = (long_vec.T[0] + long_vec.T[1])/10" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Eigenvalue approach" - ] - }, - { - "cell_type": "code", - "execution_count": 62, - "metadata": {}, - "outputs": [], - "source": [ - "C = nl.lstsq(a=long_vec,b=perturbation.real)[0].real" - ] - }, - { - "cell_type": "code", - "execution_count": 63, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# stability axis\n", - "u, v, w = body2wind(trimmed_state.velocity.vel_body, alpha, 0)\n", - "theta0 = trimmed_state.attitude.theta*1.0" - ] - }, - { - "cell_type": "code", - "execution_count": 64, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 4.48563585e+01, -4.08894829e-12, 3.59264617e+00])" - ] - }, - "execution_count": 64, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "trimmed_state.velocity._vel_body" - ] - }, - { - "cell_type": "code", - "execution_count": 65, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 4.48563585e+01, -4.08894829e-12, 3.59264617e+00])" - ] - }, - "execution_count": 65, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "wind2body(np.array([u,v,w]), alpha=alpha, beta=0)" - ] - }, - { - "cell_type": "code", - "execution_count": 66, - "metadata": {}, - "outputs": [], - "source": [ - "t = np.linspace(0,3,100)\n", - "N = len(t)\n", - "X = np.zeros((N,4))\n", - "xx = []\n", - "for i in range(N):\n", - " x_stab = (long_vec*np.exp(long_val*t[i])).dot(C)\n", - " xx.append(x_stab[1])\n", - " X[i,:] = linear_stab_2_body(long_state=x_stab.real, alpha0=alpha, u0=u, theta0 = theta0)[0]" - ] - }, - { - "cell_type": "code", - "execution_count": 67, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(t,X[:,1],'.')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Simulation" - ] - }, - { - "cell_type": "code", - "execution_count": 68, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.utils.input_generator import Constant" - ] - }, - { - "cell_type": "code", - "execution_count": 69, - "metadata": {}, - "outputs": [], - "source": [ - "controls = {\n", - " 'delta_elevator': Constant(trimmed_controls['delta_elevator']),\n", - " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", - " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", - " 'delta_t': Constant(trimmed_controls['delta_t'])\n", - "}" - ] - }, - { - "cell_type": "code", - "execution_count": 78, - "metadata": {}, - "outputs": [], - "source": [ - "# Perturbate\n", - "trimmed_state.cancel_perturbation()\n", - "p = linear_stab_2_body(long_state=perturbation.real, alpha0=alpha)[0]\n", - "trimmed_state.perturbate(np.array([p[0],0,p[1]]), 'velocity')\n", - "trimmed_state.perturbate(np.array([0,p[2],0]), 'angular_vel')\n", - "trimmed_state.perturbate(np.array([0,p[3],0]), 'attitude')" - ] - }, - { - "cell_type": "code", - "execution_count": 79, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Aircraft State \n", - "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", - "theta: 0.080 rad, phi: 0.004 rad, psi: 0.500 rad \n", - "u: 44.84 m/s, v: -0.00 m/s, w: 3.79 m/s \n", - "P: 0.00 rad/s, Q: -0.00 rad/s, R: 0.00 rad/s \n", - "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", - "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " - ] - }, - "execution_count": 79, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "trimmed_state" - ] - }, - { - "cell_type": "code", - "execution_count": 71, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 0.00438011+0.j, 0.19901295+0.j, -0.00220572+0.j, 0.00353290+0.j])" - ] - }, - "execution_count": 71, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "perturbation" - ] - }, - { - "cell_type": "code", - "execution_count": 72, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "environment.update(trimmed_state)\n", - "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" - ] - }, - { - "cell_type": "code", - "execution_count": 73, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "sim = Simulation(aircraft, system, environment, controls)" - ] - }, - { - "cell_type": "code", - "execution_count": 74, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "time: 100%|████████████████████████████████████████████████████████████▉| 9.999999999999831/10 [00:06<00:00, 1.49it/s]\n" - ] - } - ], - "source": [ - "r = sim.propagate(10)" - ] - }, - { - "cell_type": "code", - "execution_count": 75, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Aircraft State \n", - "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", - "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", - "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", - "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", - "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", - "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " - ] - }, - "execution_count": 75, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "trimmed_state.cancel_perturbation()" - ] - }, - { - "cell_type": "code", - "execution_count": 76, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(t,X[:,3],'.')\n", - "plt.plot(r.theta)\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 77, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Aircraft State \n", - "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", - "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", - "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", - "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", - "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", - "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " - ] - }, - "execution_count": 77, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "trimmed_state" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/How it works (modif).ipynb b/How it works (modif).ipynb deleted file mode 100644 index 1a228b7..0000000 --- a/How it works (modif).ipynb +++ /dev/null @@ -1,4991 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Python Flight Mechanics Engine " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Aircraft " - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "import pyfme\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from scipy import stats" - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The autoreload extension is already loaded. To reload it, use:\n", - " %reload_ext autoreload\n" - ] - } - ], - "source": [ - "%load_ext autoreload\n", - "%autoreload 2" - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.aircrafts import SimplifiedCessna172, Cessna172" - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "aircraft = SimplifiedCessna172()" - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "metadata": {}, - "outputs": [ - { - "ename": "AttributeError", - "evalue": "'SimplifiedCessna172' object has no attribute 'full_state'", - "output_type": "error", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[1;31mAttributeError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0maircraft\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfull_state\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", - "\u001b[1;31mAttributeError\u001b[0m: 'SimplifiedCessna172' object has no attribute 'full_state'" - ] - } - ], - "source": [ - "aircraft.full_state" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Aircraft will provide the simulator the forces, moments and inertial properties in order to perform the integration of the dynamic system equations:" - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Aircraft mass: 1043.2616 kg\n", - "Aircraft inertia tensor: \n", - " [[ 1285.3154166 0. 0. ]\n", - " [ 0. 1824.9309607 0. ]\n", - " [ 0. 0. 2666.89390765]] kg/m²\n" - ] - } - ], - "source": [ - "print(f\"Aircraft mass: {aircraft.mass} kg\")\n", - "print(f\"Aircraft inertia tensor: \\n {aircraft.inertia} kg/m²\")" - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "forces: [ 0. 0. 0.] N\n", - "moments: [ 0. 0. 0.] N·m\n" - ] - } - ], - "source": [ - "print(f\"forces: {aircraft.total_forces} N\")\n", - "print(f\"moments: {aircraft.total_moments} N·m\")" - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Stability Derivatives : \n", - "CL_0 = 0.148;\n", - "CM_0 = 0.012068670774609398;\n", - "CL_alpha = 5.44;\n", - "CL_q = 7.281999999999999;\n", - "CL_delta_elev = 0.005677366997294861;\n", - "CM_alpha2 = -0.0008829539354397849;\n", - "CM_alpha = -0.01230758597735665;\n", - "CM_q = -12.464;\n", - "CM_delta_elev = -0.014180595130748421;\n", - "CD_K1 = 0.04394233763124108;\n", - "CD_0 = 0.029537580994030695;\n", - "CL_MAX = 1.889;\n", - "CY_beta = -0.26799999999999996;\n", - "CY_p = -0.05993333333333333;\n", - "CY_r = 0.2143333333333333;\n", - "CY_delta_rud = -0.561;\n", - "Cl_beta = -0.022292500000000003;\n", - "Cl_p = -0.3025083333333333;\n", - "Cl_r_cl = 0.17341925931518656;\n", - "Cl_delta_rud = -0.0027193749999999996;\n", - "Cl_delta_aile = 0.0044410237288135595;\n", - "CN_beta = 0.0126;\n", - "CN_p_al = -0.007206294994140298;\n", - "CN_r_cl = -0.00957535593543321;\n", - "CN_r_0 = -0.027354917660317425;\n", - "CN_delta_rud = 0.016818749999999997;\n", - "CN_delta_aile_cl = -0.0004745447361550377;\n", - "Ct_J2 = -0.16921210379223448;\n", - "Ct_J = 0.03545196433877688;\n", - "C_0 = 0.10446359303931643;\n" - ] - } - ], - "source": [ - "print(\"Stability Derivatives : \")\n", - "for k,val in aircraft.__dict__.items():\n", - " if k.startswith('C') and \"data\" not in k and \"_\" in k:\n", - " print(f\"{k} = {val};\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "For the aircraft, in order to calculate its forces and moments it is necessary to set the controls values within the limits: " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "print(aircraft.controls)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "print(aircraft.control_limits)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "but also to provide and environment (ie. atmosphere, winds, gravity) and the aircraft state, which will also determine the aerodynamic contribution." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Environment " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.environment.atmosphere import ISA1976\n", - "from pyfme.environment.wind import NoWind\n", - "from pyfme.environment.gravity import VerticalConstant" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "atmosphere = ISA1976()\n", - "gravity = VerticalConstant()\n", - "wind = NoWind()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The atmosphere, wind and gravity model make up the environment:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.environment import Environment" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "environment = Environment(atmosphere, gravity, wind)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The environment has an update method which given the state (ie. position, altitude...) updates the environment variables (ie. density, wind magnitude, gravity force...)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "help(environment.update)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## State " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Even if the state can be set manually by giving the position, attitude, velocity, angular velocities... Most of the times, the user will want to trim the aircraft in a stationary condition. The aircraft controls to flight in that condition will be also provided by the trimmer." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.utils.trimmer import steady_state_trim" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "scrolled": true - }, - "outputs": [], - "source": [ - "help(steady_state_trim)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.models.state.position import EarthPosition" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "pos = EarthPosition(x=0, y=0, height=1000)\n", - "psi = 0.5 # rad\n", - "TAS = 45 # m/s\n", - "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "trimmed_state, trimmed_controls = steady_state_trim(\n", - " aircraft,\n", - " environment,\n", - " pos,\n", - " psi,\n", - " TAS,\n", - " controls0\n", - ") " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "trimmed_state" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "trimmed_controls" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now, all the necessary elements in order to calculate forces and moments are available " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# Environment conditions for the current state:\n", - "environment.update(trimmed_state)\n", - "\n", - "# Forces and moments calculation:\n", - "forces, moments = aircraft.calculate_forces_and_moments(trimmed_state, environment, controls0)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "print(\"NDIM forces : \")\n", - "for k,val in aircraft.__dict__.items():\n", - " if k.startswith('C') and \"data\" not in k and \"_\" not in k:\n", - " print(f\"{k} : {val}\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "forces, moments" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The aircraft is trimmed indeed: the total forces and moments (aerodynamics + gravity + thrust) are zero" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Simulation " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In order to simulate the dynamics of the aircraft under certain inputs in an environment, the user can set up a simulation using a dynamic system:" - ] - }, - { - "cell_type": "code", - "execution_count": 739, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.models import EulerFlatEarth" - ] - }, - { - "cell_type": "code", - "execution_count": 740, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Constant Controls " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values." - ] - }, - { - "cell_type": "code", - "execution_count": 741, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.utils.input_generator import Constant" - ] - }, - { - "cell_type": "code", - "execution_count": 742, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "controls = {\n", - " 'delta_elevator': Constant(trimmed_controls['delta_elevator']),\n", - " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", - " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", - " 'delta_t': Constant(trimmed_controls['delta_t'])\n", - "}" - ] - }, - { - "cell_type": "code", - "execution_count": 743, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.simulator import Simulation" - ] - }, - { - "cell_type": "code", - "execution_count": 744, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "sim = Simulation(aircraft, system, environment, controls)" - ] - }, - { - "cell_type": "code", - "execution_count": 745, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "system = EulerFlatEarth(t0=0, full_state=trimmed_state)\n", - "sim = Simulation(aircraft, system, environment, controls)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Once the simulation is set, the propagation can be performed:" - ] - }, - { - "cell_type": "code", - "execution_count": 767, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "\n", - "\n", - "time: 10.0it [00:00, ?it/s]\n", - "\n" - ] - } - ], - "source": [ - "results = sim.propagate(5)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The results are returned in a DataFrame:" - ] - }, - { - "cell_type": "code", - "execution_count": 747, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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FxFyFzMachMxMyMzTASaaileron...thrustuvv_downv_eastv_northwx_earthy_earthz_earth
time
0.011.546141e-111.688011e-160.000000e+000.133756-3.667941e-13-1.355845e-11-1.585097e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.511938e-154.440892e-1621.57414939.4912153.3964640.3949120.215741-1000.0
0.021.546141e-115.250914e-170.000000e+000.133756-3.506913e-13-1.314636e-11-1.347614e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.512042e-154.440892e-1621.57414939.4912153.3964640.7898240.431483-1000.0
0.031.546141e-11-3.441253e-160.000000e+000.133756-3.352723e-13-1.274679e-11-1.121474e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.512218e-154.440892e-1621.57414939.4912153.3964641.1847360.647224-1000.0
0.041.546141e-11-1.008065e-150.000000e+000.133756-3.205078e-13-1.235936e-11-9.062203e-1545.0336.434581-9.644866e-18...0.57799744.87164-3.512470e-154.440892e-1621.57414939.4912153.3964641.5796490.862966-1000.0
0.051.546141e-11-1.926832e-150.000000e+000.133756-3.063696e-13-1.198371e-11-7.014180e-1545.0336.434581-9.644866e-18...0.57799744.87164-3.512798e-154.440892e-1621.57414939.4912153.3964641.9745611.078707-1000.0
0.061.546141e-11-3.088483e-150.000000e+000.133756-2.928307e-13-1.161948e-11-5.066498e-1545.0336.434581-9.644866e-18...0.57799744.87164-3.513206e-154.440892e-1621.57414939.4912153.3964642.3694731.294449-1000.0
0.071.534772e-11-4.481585e-151.818989e-120.133756-2.798654e-13-1.126632e-11-3.215162e-1545.0336.434581-9.644866e-18...0.57799744.87164-3.513695e-154.440892e-1621.57414939.4912153.3964642.7643851.510190-1000.0
0.081.534772e-11-6.095197e-151.818989e-120.133756-2.674490e-13-1.092389e-11-1.456347e-1545.0336.434581-9.644866e-18...0.57799744.87164-3.514266e-154.440892e-1621.57414939.4912153.3964643.1592971.725932-1000.0
0.091.534772e-11-7.918846e-151.818989e-120.133756-2.555579e-13-1.059187e-112.136113e-1645.0336.434581-9.644866e-18...0.57799744.87164-3.514923e-150.000000e+0021.57414939.4912153.3964643.5542091.941673-1000.0
0.101.523404e-11-9.948167e-153.637979e-120.133756-2.441994e-13-9.889790e-121.798616e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.515665e-15-4.440892e-1621.57414939.4912153.3964643.9491222.157415-1000.0
0.111.489298e-11-1.213353e-145.456968e-120.133756-2.331439e-13-9.209049e-122.315148e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.516503e-15-8.881784e-1621.57414939.4912153.3964644.3440342.373156-1000.0
0.121.512035e-11-1.448774e-145.456968e-120.133756-2.225089e-13-8.548998e-122.316617e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.517460e-15-8.881784e-1621.57414939.4912153.3964644.7389462.588898-1000.0
0.131.523404e-11-1.701269e-145.456968e-120.133756-2.123358e-13-8.289160e-122.445525e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.518540e-15-4.440892e-1621.57414939.4912153.3964645.1338582.804639-1000.0
0.141.523404e-11-1.969178e-147.275958e-120.133756-2.025612e-13-7.664615e-123.206469e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.519743e-15-4.440892e-1621.57414939.4912153.3964645.5287703.020381-1000.0
0.151.568878e-11-2.252049e-141.273293e-110.133756-1.931933e-13-7.059053e-122.645450e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.521077e-150.000000e+0021.57414939.4912153.3964645.9236823.236122-1000.0
0.161.580247e-11-2.549911e-141.273293e-110.133756-1.842518e-13-6.844501e-122.752624e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.522536e-150.000000e+0021.57414939.4912153.3964646.3185943.451864-1000.0
0.171.557510e-11-2.861302e-141.637090e-110.133756-1.756801e-13-6.263865e-122.954086e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.524120e-150.000000e+0021.57414939.4912153.3964646.7135073.667605-1000.0
0.181.557510e-11-3.185448e-141.818989e-110.133756-1.674601e-13-5.700878e-123.081479e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.525830e-154.440892e-1621.57414939.4912153.3964647.1084193.883347-1000.0
0.191.557510e-11-3.522797e-141.818989e-110.133756-1.596367e-13-4.782397e-121.923424e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.527666e-154.440892e-1621.57414939.4912153.3964647.5033314.099088-1000.0
0.201.568878e-11-3.873125e-141.818989e-110.133756-1.522040e-13-4.637041e-122.008599e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.529612e-158.881784e-1621.57414939.4912153.3964647.8982434.314830-1000.0
0.211.568878e-11-4.234649e-141.818989e-110.133756-1.450822e-13-4.496103e-122.088193e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.531666e-158.881784e-1621.57414939.4912153.3964648.2931554.530571-1000.0
0.221.546141e-11-4.605667e-142.182787e-110.133756-1.382001e-13-3.986845e-123.475211e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.533831e-158.881784e-1621.57414939.4912153.3964648.6880674.746313-1000.0
0.231.568878e-11-4.985191e-142.182787e-110.133756-1.315377e-13-3.865669e-123.540318e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.536124e-151.332268e-1521.57414939.4912153.3964649.0829804.962054-1000.0
0.241.568878e-11-5.373557e-142.182787e-110.133756-1.251340e-13-3.375572e-124.004200e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.538548e-151.332268e-1521.57414939.4912153.3964649.4778925.177796-1000.0
0.251.568878e-11-5.770391e-142.364686e-110.133756-1.189899e-13-2.900371e-123.721343e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.541109e-151.776357e-1521.57414939.4912153.3964649.8728045.393537-1000.0
0.261.557510e-11-6.175787e-142.546585e-110.133756-1.131234e-13-2.439613e-123.636619e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.543804e-151.776357e-1521.57414939.4912153.39646410.2677165.609279-1000.0
0.271.580247e-11-6.588990e-142.546585e-110.133756-1.075064e-13-2.365464e-123.682321e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.546629e-151.776357e-1521.57414939.4912153.39646410.6626285.825020-1000.0
0.281.568878e-11-7.008588e-142.728484e-110.133756-1.020786e-13-1.920964e-124.699768e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.549585e-152.220446e-1521.57414939.4912153.39646411.0575406.040762-1000.0
0.291.557510e-11-7.434394e-142.910383e-110.133756-9.685431e-14-1.489974e-124.060594e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.552685e-152.220446e-1521.57414939.4912153.39646411.4524526.256503-1000.0
0.301.568878e-11-7.867110e-142.910383e-110.133756-9.187934e-14-1.444688e-124.092412e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.555922e-152.664535e-1521.57414939.4912153.39646411.8473656.472245-1000.0
..................................................................
9.711.479066e-10-5.311047e-124.729372e-110.133756-4.807148e-151.651500e-25-3.956346e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.664932e-155.875300e-1321.57414939.4912153.396464383.459700209.484989-1000.0
9.721.480203e-10-5.318273e-124.729372e-110.133756-4.794496e-151.597792e-25-3.952250e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.666790e-155.884182e-1321.57414939.4912153.396464383.854613209.700731-1000.0
9.731.482476e-10-5.325504e-124.729372e-110.133756-4.781638e-151.544085e-25-3.948197e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.668652e-155.888623e-1321.57414939.4912153.396464384.249525209.916472-1000.0
9.741.483613e-10-5.332739e-124.729372e-110.133756-4.768578e-151.503805e-25-3.944187e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.670518e-155.897505e-1321.57414939.4912153.396464384.644437210.132214-1000.0
9.751.484750e-10-5.339978e-124.729372e-110.133756-4.755319e-151.463524e-25-3.940220e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.672389e-155.901946e-1321.57414939.4912153.396464385.039349210.347955-1000.0
9.761.485887e-10-5.347222e-124.729372e-110.133756-4.741864e-151.409817e-25-3.936298e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.674264e-155.906386e-1321.57414939.4912153.396464385.434261210.563697-1000.0
9.771.488161e-10-5.354470e-124.729372e-110.133756-4.728216e-151.369536e-25-3.932421e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.676144e-155.915268e-1321.57414939.4912153.396464385.829173210.779438-1000.0
9.781.489298e-10-5.361722e-124.729372e-110.133756-4.714378e-151.315829e-25-3.928590e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.678028e-155.919709e-1321.57414939.4912153.396464386.224085210.995180-1000.0
9.791.490434e-10-5.368978e-124.729372e-110.133756-4.700354e-151.275549e-25-3.924805e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.679916e-155.928591e-1321.57414939.4912153.396464386.618998211.210921-1000.0
9.801.491571e-10-5.376239e-124.729372e-110.133756-4.686147e-151.248695e-25-3.921066e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.681810e-155.933032e-1321.57414939.4912153.396464387.013910211.426663-1000.0
9.811.493845e-10-5.383504e-124.729372e-110.133756-4.671759e-151.208414e-25-3.917374e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.683708e-155.937473e-1321.57414939.4912153.396464387.408822211.642404-1000.0
9.821.494982e-10-5.390773e-124.729372e-110.133756-4.657195e-151.181561e-25-3.913730e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.685612e-155.946355e-1321.57414939.4912153.396464387.803734211.858146-1000.0
9.831.496119e-10-5.398046e-124.729372e-110.133756-4.642458e-151.154707e-25-3.910134e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.687520e-155.950795e-1321.57414939.4912153.396464388.198646212.073887-1000.0
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9.861.498393e-10-5.419890e-124.911271e-110.133756-4.597238e-151.047292e-25-3.899641e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.693277e-155.968559e-1321.57414939.4912153.396464389.383383212.721111-1000.0
9.871.500666e-10-5.427180e-124.911271e-110.133756-4.581839e-151.007012e-25-3.896243e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.695207e-155.973000e-1321.57414939.4912153.396464389.778295212.936853-1000.0
9.881.501803e-10-5.434473e-124.911271e-110.133756-4.566283e-159.801583e-26-3.892896e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.697142e-155.981882e-1321.57414939.4912153.396464390.173207213.152594-1000.0
9.891.502940e-10-5.441771e-124.911271e-110.133756-4.550574e-159.533047e-26-3.889600e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.699083e-155.986323e-1321.57414939.4912153.396464390.568119213.368336-1000.0
9.901.504077e-10-5.449072e-124.911271e-110.133756-4.534714e-159.130242e-26-3.886355e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.701029e-155.995204e-1321.57414939.4912153.396464390.963031213.584077-1000.0
9.911.506351e-10-5.456378e-124.911271e-110.133756-4.518707e-158.861705e-26-3.883162e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.702982e-155.999645e-1321.57414939.4912153.396464391.357943213.799819-1000.0
9.921.507487e-10-5.463687e-124.911271e-110.133756-4.502555e-158.458901e-26-3.880022e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.704940e-156.004086e-1321.57414939.4912153.396464391.752856214.015560-1000.0
9.931.508624e-10-5.471000e-124.911271e-110.133756-4.486263e-158.324632e-26-3.876934e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.706904e-156.012968e-1321.57414939.4912153.396464392.147768214.231302-1000.0
9.941.509761e-10-5.478317e-124.911271e-110.133756-4.469834e-158.056096e-26-3.873900e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.708875e-156.017409e-1321.57414939.4912153.396464392.542680214.447043-1000.0
9.951.510898e-10-5.485638e-124.911271e-110.133756-4.453270e-157.921828e-26-3.870920e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.710851e-156.026291e-1321.57414939.4912153.396464392.937592214.662785-1000.0
9.961.514309e-10-5.492963e-124.911271e-110.133756-4.436576e-157.653291e-26-3.867993e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.712834e-156.030731e-1321.57414939.4912153.396464393.332504214.878526-1000.0
9.971.515446e-10-5.500291e-124.911271e-110.133756-4.419754e-157.519023e-26-3.865121e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.714823e-156.035172e-1321.57414939.4912153.396464393.727416215.094268-1000.0
9.981.516582e-10-5.507624e-124.911271e-110.133756-4.402808e-157.250486e-26-3.862304e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.716819e-156.044054e-1321.57414939.4912153.396464394.122329215.310009-1000.0
9.991.517719e-10-5.514960e-124.911271e-110.133756-4.385742e-157.116218e-26-3.859542e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.718821e-156.048495e-1321.57414939.4912153.396464394.517241215.525751-1000.0
10.001.519993e-10-5.522300e-124.911271e-110.133756-4.368557e-156.847682e-26-3.856835e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.720829e-156.057377e-1321.57414939.4912153.396464394.912153215.741492-1000.0
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1000 rows × 35 columns

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" - ], - "text/plain": [ - " Fx Fy Fz Mach Mx \\\n", - "time \n", - "0.01 1.546141e-11 1.688011e-16 0.000000e+00 0.133756 -3.667941e-13 \n", - "0.02 1.546141e-11 5.250914e-17 0.000000e+00 0.133756 -3.506913e-13 \n", - "0.03 1.546141e-11 -3.441253e-16 0.000000e+00 0.133756 -3.352723e-13 \n", - "0.04 1.546141e-11 -1.008065e-15 0.000000e+00 0.133756 -3.205078e-13 \n", - "0.05 1.546141e-11 -1.926832e-15 0.000000e+00 0.133756 -3.063696e-13 \n", - "0.06 1.546141e-11 -3.088483e-15 0.000000e+00 0.133756 -2.928307e-13 \n", - "0.07 1.534772e-11 -4.481585e-15 1.818989e-12 0.133756 -2.798654e-13 \n", - "0.08 1.534772e-11 -6.095197e-15 1.818989e-12 0.133756 -2.674490e-13 \n", - "0.09 1.534772e-11 -7.918846e-15 1.818989e-12 0.133756 -2.555579e-13 \n", - "0.10 1.523404e-11 -9.948167e-15 3.637979e-12 0.133756 -2.441994e-13 \n", - "0.11 1.489298e-11 -1.213353e-14 5.456968e-12 0.133756 -2.331439e-13 \n", - "0.12 1.512035e-11 -1.448774e-14 5.456968e-12 0.133756 -2.225089e-13 \n", - "0.13 1.523404e-11 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-6.175787e-14 2.546585e-11 0.133756 -1.131234e-13 \n", - "0.27 1.580247e-11 -6.588990e-14 2.546585e-11 0.133756 -1.075064e-13 \n", - "0.28 1.568878e-11 -7.008588e-14 2.728484e-11 0.133756 -1.020786e-13 \n", - "0.29 1.557510e-11 -7.434394e-14 2.910383e-11 0.133756 -9.685431e-14 \n", - "0.30 1.568878e-11 -7.867110e-14 2.910383e-11 0.133756 -9.187934e-14 \n", - "... ... ... ... ... ... \n", - "9.71 1.479066e-10 -5.311047e-12 4.729372e-11 0.133756 -4.807148e-15 \n", - "9.72 1.480203e-10 -5.318273e-12 4.729372e-11 0.133756 -4.794496e-15 \n", - "9.73 1.482476e-10 -5.325504e-12 4.729372e-11 0.133756 -4.781638e-15 \n", - "9.74 1.483613e-10 -5.332739e-12 4.729372e-11 0.133756 -4.768578e-15 \n", - "9.75 1.484750e-10 -5.339978e-12 4.729372e-11 0.133756 -4.755319e-15 \n", - "9.76 1.485887e-10 -5.347222e-12 4.729372e-11 0.133756 -4.741864e-15 \n", - "9.77 1.488161e-10 -5.354470e-12 4.729372e-11 0.133756 -4.728216e-15 \n", - "9.78 1.489298e-10 -5.361722e-12 4.729372e-11 0.133756 -4.714378e-15 \n", - "9.79 1.490434e-10 -5.368978e-12 4.729372e-11 0.133756 -4.700354e-15 \n", - "9.80 1.491571e-10 -5.376239e-12 4.729372e-11 0.133756 -4.686147e-15 \n", - "9.81 1.493845e-10 -5.383504e-12 4.729372e-11 0.133756 -4.671759e-15 \n", - "9.82 1.494982e-10 -5.390773e-12 4.729372e-11 0.133756 -4.657195e-15 \n", - "9.83 1.496119e-10 -5.398046e-12 4.729372e-11 0.133756 -4.642458e-15 \n", - "9.84 1.497256e-10 -5.405323e-12 4.911271e-11 0.133756 -4.627550e-15 \n", - "9.85 1.498393e-10 -5.412605e-12 4.911271e-11 0.133756 -4.612476e-15 \n", - "9.86 1.498393e-10 -5.419890e-12 4.911271e-11 0.133756 -4.597238e-15 \n", - "9.87 1.500666e-10 -5.427180e-12 4.911271e-11 0.133756 -4.581839e-15 \n", - "9.88 1.501803e-10 -5.434473e-12 4.911271e-11 0.133756 -4.566283e-15 \n", - "9.89 1.502940e-10 -5.441771e-12 4.911271e-11 0.133756 -4.550574e-15 \n", - "9.90 1.504077e-10 -5.449072e-12 4.911271e-11 0.133756 -4.534714e-15 \n", - "9.91 1.506351e-10 -5.456378e-12 4.911271e-11 0.133756 -4.518707e-15 \n", - "9.92 1.507487e-10 -5.463687e-12 4.911271e-11 0.133756 -4.502555e-15 \n", - "9.93 1.508624e-10 -5.471000e-12 4.911271e-11 0.133756 -4.486263e-15 \n", - "9.94 1.509761e-10 -5.478317e-12 4.911271e-11 0.133756 -4.469834e-15 \n", - "9.95 1.510898e-10 -5.485638e-12 4.911271e-11 0.133756 -4.453270e-15 \n", - "9.96 1.514309e-10 -5.492963e-12 4.911271e-11 0.133756 -4.436576e-15 \n", - "9.97 1.515446e-10 -5.500291e-12 4.911271e-11 0.133756 -4.419754e-15 \n", - "9.98 1.516582e-10 -5.507624e-12 4.911271e-11 0.133756 -4.402808e-15 \n", - "9.99 1.517719e-10 -5.514960e-12 4.911271e-11 0.133756 -4.385742e-15 \n", - "10.00 1.519993e-10 -5.522300e-12 4.911271e-11 0.133756 -4.368557e-15 \n", - "\n", - " My Mz TAS a aileron ... \\\n", - "time ... \n", - "0.01 -1.355845e-11 -1.585097e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.02 -1.314636e-11 -1.347614e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.03 -1.274679e-11 -1.121474e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.04 -1.235936e-11 -9.062203e-15 45.0 336.434581 -9.644866e-18 ... \n", - "0.05 -1.198371e-11 -7.014180e-15 45.0 336.434581 -9.644866e-18 ... \n", - "0.06 -1.161948e-11 -5.066498e-15 45.0 336.434581 -9.644866e-18 ... \n", - "0.07 -1.126632e-11 -3.215162e-15 45.0 336.434581 -9.644866e-18 ... \n", - "0.08 -1.092389e-11 -1.456347e-15 45.0 336.434581 -9.644866e-18 ... \n", - "0.09 -1.059187e-11 2.136113e-16 45.0 336.434581 -9.644866e-18 ... \n", - "0.10 -9.889790e-12 1.798616e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.11 -9.209049e-12 2.315148e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.12 -8.548998e-12 2.316617e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.13 -8.289160e-12 2.445525e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.14 -7.664615e-12 3.206469e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.15 -7.059053e-12 2.645450e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.16 -6.844501e-12 2.752624e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.17 -6.263865e-12 2.954086e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.18 -5.700878e-12 3.081479e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.19 -4.782397e-12 1.923424e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.20 -4.637041e-12 2.008599e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.21 -4.496103e-12 2.088193e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.22 -3.986845e-12 3.475211e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.23 -3.865669e-12 3.540318e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.24 -3.375572e-12 4.004200e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.25 -2.900371e-12 3.721343e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.26 -2.439613e-12 3.636619e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.27 -2.365464e-12 3.682321e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.28 -1.920964e-12 4.699768e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.29 -1.489974e-12 4.060594e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.30 -1.444688e-12 4.092412e-14 45.0 336.434581 -9.644866e-18 ... \n", - "... ... ... ... ... ... ... \n", - "9.71 1.651500e-25 -3.956346e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.72 1.597792e-25 -3.952250e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.73 1.544085e-25 -3.948197e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.74 1.503805e-25 -3.944187e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.75 1.463524e-25 -3.940220e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.76 1.409817e-25 -3.936298e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.77 1.369536e-25 -3.932421e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.78 1.315829e-25 -3.928590e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.79 1.275549e-25 -3.924805e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.80 1.248695e-25 -3.921066e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.81 1.208414e-25 -3.917374e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.82 1.181561e-25 -3.913730e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.83 1.154707e-25 -3.910134e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.84 1.114427e-25 -3.906587e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.85 1.074146e-25 -3.903089e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.86 1.047292e-25 -3.899641e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.87 1.007012e-25 -3.896243e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.88 9.801583e-26 -3.892896e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.89 9.533047e-26 -3.889600e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.90 9.130242e-26 -3.886355e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.91 8.861705e-26 -3.883162e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.92 8.458901e-26 -3.880022e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.93 8.324632e-26 -3.876934e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.94 8.056096e-26 -3.873900e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.95 7.921828e-26 -3.870920e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.96 7.653291e-26 -3.867993e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.97 7.519023e-26 -3.865121e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.98 7.250486e-26 -3.862304e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.99 7.116218e-26 -3.859542e-14 45.0 336.434581 -9.644866e-18 ... \n", - "10.00 6.847682e-26 -3.856835e-14 45.0 336.434581 -9.644866e-18 ... \n", - "\n", - " thrust u v v_down v_east v_north \\\n", - "time \n", - "0.01 0.577997 44.87164 -3.511938e-15 4.440892e-16 21.574149 39.491215 \n", - "0.02 0.577997 44.87164 -3.512042e-15 4.440892e-16 21.574149 39.491215 \n", - "0.03 0.577997 44.87164 -3.512218e-15 4.440892e-16 21.574149 39.491215 \n", - "0.04 0.577997 44.87164 -3.512470e-15 4.440892e-16 21.574149 39.491215 \n", - "0.05 0.577997 44.87164 -3.512798e-15 4.440892e-16 21.574149 39.491215 \n", - "0.06 0.577997 44.87164 -3.513206e-15 4.440892e-16 21.574149 39.491215 \n", - "0.07 0.577997 44.87164 -3.513695e-15 4.440892e-16 21.574149 39.491215 \n", - "0.08 0.577997 44.87164 -3.514266e-15 4.440892e-16 21.574149 39.491215 \n", - "0.09 0.577997 44.87164 -3.514923e-15 0.000000e+00 21.574149 39.491215 \n", - "0.10 0.577997 44.87164 -3.515665e-15 -4.440892e-16 21.574149 39.491215 \n", - "0.11 0.577997 44.87164 -3.516503e-15 -8.881784e-16 21.574149 39.491215 \n", - "0.12 0.577997 44.87164 -3.517460e-15 -8.881784e-16 21.574149 39.491215 \n", - "0.13 0.577997 44.87164 -3.518540e-15 -4.440892e-16 21.574149 39.491215 \n", - "0.14 0.577997 44.87164 -3.519743e-15 -4.440892e-16 21.574149 39.491215 \n", - "0.15 0.577997 44.87164 -3.521077e-15 0.000000e+00 21.574149 39.491215 \n", - "0.16 0.577997 44.87164 -3.522536e-15 0.000000e+00 21.574149 39.491215 \n", - "0.17 0.577997 44.87164 -3.524120e-15 0.000000e+00 21.574149 39.491215 \n", - "0.18 0.577997 44.87164 -3.525830e-15 4.440892e-16 21.574149 39.491215 \n", - "0.19 0.577997 44.87164 -3.527666e-15 4.440892e-16 21.574149 39.491215 \n", - "0.20 0.577997 44.87164 -3.529612e-15 8.881784e-16 21.574149 39.491215 \n", - "0.21 0.577997 44.87164 -3.531666e-15 8.881784e-16 21.574149 39.491215 \n", - "0.22 0.577997 44.87164 -3.533831e-15 8.881784e-16 21.574149 39.491215 \n", - "0.23 0.577997 44.87164 -3.536124e-15 1.332268e-15 21.574149 39.491215 \n", - "0.24 0.577997 44.87164 -3.538548e-15 1.332268e-15 21.574149 39.491215 \n", - "0.25 0.577997 44.87164 -3.541109e-15 1.776357e-15 21.574149 39.491215 \n", - "0.26 0.577997 44.87164 -3.543804e-15 1.776357e-15 21.574149 39.491215 \n", - "0.27 0.577997 44.87164 -3.546629e-15 1.776357e-15 21.574149 39.491215 \n", - "0.28 0.577997 44.87164 -3.549585e-15 2.220446e-15 21.574149 39.491215 \n", - "0.29 0.577997 44.87164 -3.552685e-15 2.220446e-15 21.574149 39.491215 \n", - "0.30 0.577997 44.87164 -3.555922e-15 2.664535e-15 21.574149 39.491215 \n", - "... ... ... ... ... ... ... \n", - "9.71 0.577997 44.87164 -6.664932e-15 5.875300e-13 21.574149 39.491215 \n", - "9.72 0.577997 44.87164 -6.666790e-15 5.884182e-13 21.574149 39.491215 \n", - "9.73 0.577997 44.87164 -6.668652e-15 5.888623e-13 21.574149 39.491215 \n", - "9.74 0.577997 44.87164 -6.670518e-15 5.897505e-13 21.574149 39.491215 \n", - "9.75 0.577997 44.87164 -6.672389e-15 5.901946e-13 21.574149 39.491215 \n", - "9.76 0.577997 44.87164 -6.674264e-15 5.906386e-13 21.574149 39.491215 \n", - "9.77 0.577997 44.87164 -6.676144e-15 5.915268e-13 21.574149 39.491215 \n", - "9.78 0.577997 44.87164 -6.678028e-15 5.919709e-13 21.574149 39.491215 \n", - "9.79 0.577997 44.87164 -6.679916e-15 5.928591e-13 21.574149 39.491215 \n", - "9.80 0.577997 44.87164 -6.681810e-15 5.933032e-13 21.574149 39.491215 \n", - "9.81 0.577997 44.87164 -6.683708e-15 5.937473e-13 21.574149 39.491215 \n", - "9.82 0.577997 44.87164 -6.685612e-15 5.946355e-13 21.574149 39.491215 \n", - "9.83 0.577997 44.87164 -6.687520e-15 5.950795e-13 21.574149 39.491215 \n", - "9.84 0.577997 44.87164 -6.689434e-15 5.964118e-13 21.574149 39.491215 \n", - "9.85 0.577997 44.87164 -6.691353e-15 5.968559e-13 21.574149 39.491215 \n", - "9.86 0.577997 44.87164 -6.693277e-15 5.968559e-13 21.574149 39.491215 \n", - "9.87 0.577997 44.87164 -6.695207e-15 5.973000e-13 21.574149 39.491215 \n", - "9.88 0.577997 44.87164 -6.697142e-15 5.981882e-13 21.574149 39.491215 \n", - "9.89 0.577997 44.87164 -6.699083e-15 5.986323e-13 21.574149 39.491215 \n", - "9.90 0.577997 44.87164 -6.701029e-15 5.995204e-13 21.574149 39.491215 \n", - "9.91 0.577997 44.87164 -6.702982e-15 5.999645e-13 21.574149 39.491215 \n", - "9.92 0.577997 44.87164 -6.704940e-15 6.004086e-13 21.574149 39.491215 \n", - "9.93 0.577997 44.87164 -6.706904e-15 6.012968e-13 21.574149 39.491215 \n", - "9.94 0.577997 44.87164 -6.708875e-15 6.017409e-13 21.574149 39.491215 \n", - "9.95 0.577997 44.87164 -6.710851e-15 6.026291e-13 21.574149 39.491215 \n", - "9.96 0.577997 44.87164 -6.712834e-15 6.030731e-13 21.574149 39.491215 \n", - "9.97 0.577997 44.87164 -6.714823e-15 6.035172e-13 21.574149 39.491215 \n", - "9.98 0.577997 44.87164 -6.716819e-15 6.044054e-13 21.574149 39.491215 \n", - "9.99 0.577997 44.87164 -6.718821e-15 6.048495e-13 21.574149 39.491215 \n", - "10.00 0.577997 44.87164 -6.720829e-15 6.057377e-13 21.574149 39.491215 \n", - "\n", - " w x_earth y_earth z_earth \n", - "time \n", - "0.01 3.396464 0.394912 0.215741 -1000.0 \n", - "0.02 3.396464 0.789824 0.431483 -1000.0 \n", - "0.03 3.396464 1.184736 0.647224 -1000.0 \n", - "0.04 3.396464 1.579649 0.862966 -1000.0 \n", - "0.05 3.396464 1.974561 1.078707 -1000.0 \n", - "0.06 3.396464 2.369473 1.294449 -1000.0 \n", - "0.07 3.396464 2.764385 1.510190 -1000.0 \n", - "0.08 3.396464 3.159297 1.725932 -1000.0 \n", - "0.09 3.396464 3.554209 1.941673 -1000.0 \n", - "0.10 3.396464 3.949122 2.157415 -1000.0 \n", - "0.11 3.396464 4.344034 2.373156 -1000.0 \n", - "0.12 3.396464 4.738946 2.588898 -1000.0 \n", - "0.13 3.396464 5.133858 2.804639 -1000.0 \n", - "0.14 3.396464 5.528770 3.020381 -1000.0 \n", - "0.15 3.396464 5.923682 3.236122 -1000.0 \n", - "0.16 3.396464 6.318594 3.451864 -1000.0 \n", - "0.17 3.396464 6.713507 3.667605 -1000.0 \n", - "0.18 3.396464 7.108419 3.883347 -1000.0 \n", - "0.19 3.396464 7.503331 4.099088 -1000.0 \n", - "0.20 3.396464 7.898243 4.314830 -1000.0 \n", - "0.21 3.396464 8.293155 4.530571 -1000.0 \n", - "0.22 3.396464 8.688067 4.746313 -1000.0 \n", - "0.23 3.396464 9.082980 4.962054 -1000.0 \n", - "0.24 3.396464 9.477892 5.177796 -1000.0 \n", - "0.25 3.396464 9.872804 5.393537 -1000.0 \n", - "0.26 3.396464 10.267716 5.609279 -1000.0 \n", - "0.27 3.396464 10.662628 5.825020 -1000.0 \n", - "0.28 3.396464 11.057540 6.040762 -1000.0 \n", - "0.29 3.396464 11.452452 6.256503 -1000.0 \n", - "0.30 3.396464 11.847365 6.472245 -1000.0 \n", - "... ... ... ... ... \n", - "9.71 3.396464 383.459700 209.484989 -1000.0 \n", - "9.72 3.396464 383.854613 209.700731 -1000.0 \n", - "9.73 3.396464 384.249525 209.916472 -1000.0 \n", - "9.74 3.396464 384.644437 210.132214 -1000.0 \n", - "9.75 3.396464 385.039349 210.347955 -1000.0 \n", - "9.76 3.396464 385.434261 210.563697 -1000.0 \n", - "9.77 3.396464 385.829173 210.779438 -1000.0 \n", - "9.78 3.396464 386.224085 210.995180 -1000.0 \n", - "9.79 3.396464 386.618998 211.210921 -1000.0 \n", - "9.80 3.396464 387.013910 211.426663 -1000.0 \n", - "9.81 3.396464 387.408822 211.642404 -1000.0 \n", - "9.82 3.396464 387.803734 211.858146 -1000.0 \n", - "9.83 3.396464 388.198646 212.073887 -1000.0 \n", - "9.84 3.396464 388.593558 212.289628 -1000.0 \n", - "9.85 3.396464 388.988471 212.505370 -1000.0 \n", - "9.86 3.396464 389.383383 212.721111 -1000.0 \n", - "9.87 3.396464 389.778295 212.936853 -1000.0 \n", - "9.88 3.396464 390.173207 213.152594 -1000.0 \n", - "9.89 3.396464 390.568119 213.368336 -1000.0 \n", - "9.90 3.396464 390.963031 213.584077 -1000.0 \n", - "9.91 3.396464 391.357943 213.799819 -1000.0 \n", - "9.92 3.396464 391.752856 214.015560 -1000.0 \n", - "9.93 3.396464 392.147768 214.231302 -1000.0 \n", - "9.94 3.396464 392.542680 214.447043 -1000.0 \n", - "9.95 3.396464 392.937592 214.662785 -1000.0 \n", - "9.96 3.396464 393.332504 214.878526 -1000.0 \n", - "9.97 3.396464 393.727416 215.094268 -1000.0 \n", - "9.98 3.396464 394.122329 215.310009 -1000.0 \n", - "9.99 3.396464 394.517241 215.525751 -1000.0 \n", - "10.00 3.396464 394.912153 215.741492 -1000.0 \n", - "\n", - "[1000 rows x 35 columns]" - ] - }, - "execution_count": 747, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "results" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "code", - "execution_count": 749, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "kwargs = {'marker': '.',\n", - " 'subplots': True,\n", - " 'sharex': True,\n", - " 'figsize': (12, 6)}" - ] - }, - { - "cell_type": "code", - "execution_count": 750, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\plotting\\_core.py:1716: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n", - " series.name = label\n" - ] - }, - { - "data": { - "image/png": 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1M4OqVcnDsCRJyt2ZoXdXLx3dI7QhK0LYde2ussAwLElSEeQKu9PqptH+Sjtb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\nMCxJJZBS6gR+HhFPAF8YxyX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TQwTniJgC/Az4XGZ+Z5D9zgDOANh3330PXrVq1VCfQaq/yl/Pb9kEG35XnePu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\nSQUYnCVJkqQCDM6SJElSAQZ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kCpr2YcAnKnddZ5pVh/IIxl8GPgR8FegyGEuSlJPx0Lz74WdmfJ1pVhOrajCO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\n6dnVw+W3Fx60e7T/Ud52+9s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000/X/v37PTs3wXkojVulPVv61wOF0jmf8a89AAAA2aZxq7T5m54OrrBixQo9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\n3KTbF92ecNSNuuY6ffbJz9L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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "results.plot(y=['elevator', 'aileron', 'rudder', 'thrust'], **kwargs);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Doublet " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values." - ] - }, - { - "cell_type": "code", - "execution_count": 291, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.utils.input_generator import Doublet" - ] - }, - { - "cell_type": "code", - "execution_count": 292, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "de0 = trimmed_controls['delta_elevator']" - ] - }, - { - "cell_type": "code", - "execution_count": 293, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "controls = controls = {\n", - " 'delta_elevator': Doublet(t_init=2, T=1, A=0.1, offset=de0),\n", - " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", - " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", - " 'delta_t': Constant(trimmed_controls['delta_t'])\n", - "}" - ] - }, - { - "cell_type": "code", - "execution_count": 294, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "sim = Simulation(aircraft, system, environment, controls)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Once the simulation is set, the propagation can be performed:" - ] - }, - { - "cell_type": "code", - "execution_count": 295, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "\n", - "time: 0%| | 0/90 [00:00" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "results.plot(y=['x_earth', 'y_earth', 'height'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": 297, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\plotting\\_core.py:1716: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n", - " series.name = label\n" - ] - }, - { - "data": { - "image/png": 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5RI899ph23z1GqA8IPcyZ0LWHuUdP6bNnSo3zO+9f8VT22gQAAEpXjJ7gHd5d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\nGuYXJR1gZsMlvSdpiqRzsvC6CXt88uN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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "results.plot(y=['v_north', 'v_east', 'v_down'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": 299, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\plotting\\_core.py:1716: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n", - " series.name = label\n" - ] - }, - { - "data": { - "image/png": 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QB2GsqiF3f0TSIynnbuzxfZukGWH0FTunfk5qulfy7sSxd0u73uxxQXLEecwU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\nn5Hp4dXD024qAxzAiDMAACg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uYukpXt9qyj+AkkWpBgCgNF25V6gjR6HgQUWgYFGqAQAob/F6P+ejh3VXe+zS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\nXoJFTvX4RTZIUpukmZJ+J6nJzI509w5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M/vG5zO2vzksvWlPI9AWlq6dIsQnYWT4h6adRFwEAAIAIDF1uPdcDkzGfP7us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\n/52S7sxzrFXSsTn2d0o6tZh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AlI1AFmI2s6WSpksaa2Ztiq0GskjSQ2Z2raS3JM2Jd18haaakjZI+lHS1JLn7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\nUSJSZLc8f0vOfTt7OvX54z6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FxFyFzMachMxMyMzTASaaileron...thrustuvv_downv_eastv_northwx_earthy_earthz_earth
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" - ], - "text/plain": [ - " Fx Fy Fz Mach Mx My \\\n", - "time \n", - "0.05 -2860.288296 -0.000007 -23948.338630 0.133444 3.670972e-06 416.026942 \n", - "0.10 -2841.450134 -0.000007 -23790.055374 0.133135 2.754411e-06 382.934882 \n", - "0.15 -2814.079427 -0.000007 -23634.534640 0.132827 2.070495e-06 344.981012 \n", - "0.20 -2834.053374 -0.000006 -23475.855214 0.132523 1.564206e-06 331.492749 \n", - "0.25 -2844.314793 -0.000006 -23317.511918 0.132216 1.181851e-06 311.810632 \n", - "0.30 -2847.104415 -0.000006 -23160.410509 0.131908 8.962216e-07 288.008616 \n", - "0.35 -2867.759612 -0.000005 -23001.499461 0.131599 6.829096e-07 273.089782 \n", - "0.40 -2883.231719 -0.000005 -22843.131464 0.131287 5.237487e-07 255.164441 \n", - "0.45 -2892.153236 -0.000005 -22685.668716 0.130975 4.056468e-07 234.048222 \n", - "0.50 -2914.835086 -0.000004 -22525.832830 0.130659 3.167348e-07 219.601445 \n", - "0.55 -2921.787769 -0.000004 -22367.332766 0.130340 2.513504e-07 196.935789 \n", - "\n", - " Mz TAS a aileron ... thrust \\\n", - "time ... \n", - "0.05 -0.000001 44.895162 336.434581 2.959742e-10 ... 0.670198 \n", - "0.10 -0.000001 44.791157 336.434574 2.959742e-10 ... 0.670198 \n", - "0.15 -0.000001 44.687646 336.434555 2.959742e-10 ... 0.670198 \n", - "0.20 -0.000001 44.585409 336.434527 2.959742e-10 ... 0.670198 \n", - "0.25 -0.000001 44.482035 336.434473 2.959742e-10 ... 0.670198 \n", - "0.30 -0.000001 44.378277 336.434397 2.959742e-10 ... 0.670198 \n", - "0.35 -0.000001 44.274258 336.434294 2.959742e-10 ... 0.670198 \n", - "0.40 -0.000001 44.169584 336.434162 2.959742e-10 ... 0.670198 \n", - "0.45 -0.000001 44.064366 336.434000 2.959742e-10 ... 0.670198 \n", - "0.50 -0.000001 43.958162 336.433802 2.959742e-10 ... 0.670198 \n", - "0.55 -0.000001 43.850903 336.433567 2.959742e-10 ... 0.670198 \n", - "\n", - " u v v_down v_east v_north w \\\n", - "time \n", - "0.05 44.877493 1.089215e-07 -0.021778 21.523885 39.399206 -1.259451 \n", - "0.10 44.773564 1.085156e-07 -0.059100 21.474006 39.307904 -1.255270 \n", - "0.15 44.670646 1.080774e-07 -0.101132 21.424344 39.216999 -1.232525 \n", - "0.20 44.567449 1.076118e-07 -0.219729 21.375124 39.126902 -1.265389 \n", - "0.25 44.463623 1.071279e-07 -0.339570 21.325202 39.035520 -1.279696 \n", - "0.30 44.359858 1.066288e-07 -0.462223 21.274925 38.943489 -1.278443 \n", - "0.35 44.255295 1.061187e-07 -0.620164 21.224128 38.850505 -1.295661 \n", - "0.40 44.150414 1.056017e-07 -0.781931 21.172708 38.756382 -1.301203 \n", - "0.45 44.045377 1.050805e-07 -0.944579 21.120728 38.661234 -1.293510 \n", - "0.50 43.938927 1.045592e-07 -1.134443 21.067646 38.564068 -1.300252 \n", - "0.55 43.832154 1.040402e-07 -1.311274 21.013841 38.465578 -1.282176 \n", - "\n", - " x_earth y_earth z_earth \n", - "time \n", - "0.05 1.972256 1.077449 -999.999987 \n", - "0.10 3.939933 2.152395 -1000.001805 \n", - "0.15 5.903055 3.224853 -1000.006526 \n", - "0.20 7.861673 4.294852 -1000.013745 \n", - "0.25 9.815738 5.362362 -1000.027650 \n", - "0.30 11.765219 6.427369 -1000.047414 \n", - "0.35 13.710083 7.489853 -1000.073815 \n", - "0.40 15.650273 8.549783 -1000.107951 \n", - "0.45 17.585742 9.607135 -1000.149658 \n", - "0.50 19.516402 10.661859 -1000.200635 \n", - "0.55 21.442166 11.713909 -1000.261205 \n", - "\n", - "[11 rows x 35 columns]" - ] - }, - "execution_count": 76, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "results = sim.propagate(sim.time+dt)\n", - "results" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Notice that `results` will include the previous timesteps as well as the last one. To get just the last one one can use pandas `loc` or `iloc`:" - ] - }, - { - "cell_type": "code", - "execution_count": 77, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Fx -2.921788e+03\n", - "Fy -3.761191e-06\n", - "Fz -2.236733e+04\n", - "Mach 1.303405e-01\n", - "Mx 2.513504e-07\n", - "My 1.969358e+02\n", - "Mz -1.203167e-06\n", - "TAS 4.385090e+01\n", - "a 3.364336e+02\n", - "aileron 2.959742e-10\n", - "alpha -2.924362e-02\n", - "beta 2.372590e-09\n", - "elevator 1.108958e-02\n", - "height 1.000261e+03\n", - "p 6.386588e-10\n", - "phi 2.537379e-10\n", - "pressure 8.987343e+04\n", - "psi 5.000000e-01\n", - "q 9.152033e-02\n", - "q_inf 1.068779e+03\n", - "r 1.349505e-10\n", - "rho 1.111631e+00\n", - "rudder -1.269086e-09\n", - "temperature 2.816493e+02\n", - "theta 6.638492e-04\n", - "thrust 6.701981e-01\n", - "u 4.383215e+01\n", - "v 1.040402e-07\n", - "v_down -1.311274e+00\n", - "v_east 2.101384e+01\n", - "v_north 3.846558e+01\n", - "w -1.282176e+00\n", - "x_earth 2.144217e+01\n", - "y_earth 1.171391e+01\n", - "z_earth -1.000261e+03\n", - "Name: 0.55, dtype: float64" - ] - }, - "execution_count": 77, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "results.iloc[-1] # last time step" - ] - }, - { - "cell_type": "code", - "execution_count": 78, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Fx -2.921788e+03\n", - "Fy -3.761191e-06\n", - "Fz -2.236733e+04\n", - "Mach 1.303405e-01\n", - "Mx 2.513504e-07\n", - "My 1.969358e+02\n", - "Mz -1.203167e-06\n", - "TAS 4.385090e+01\n", - "a 3.364336e+02\n", - "aileron 2.959742e-10\n", - "alpha -2.924362e-02\n", - "beta 2.372590e-09\n", - "elevator 1.108958e-02\n", - "height 1.000261e+03\n", - "p 6.386588e-10\n", - "phi 2.537379e-10\n", - "pressure 8.987343e+04\n", - "psi 5.000000e-01\n", - "q 9.152033e-02\n", - "q_inf 1.068779e+03\n", - "r 1.349505e-10\n", - "rho 1.111631e+00\n", - "rudder -1.269086e-09\n", - "temperature 2.816493e+02\n", - "theta 6.638492e-04\n", - "thrust 6.701981e-01\n", - "u 4.383215e+01\n", - "v 1.040402e-07\n", - "v_down -1.311274e+00\n", - "v_east 2.101384e+01\n", - "v_north 3.846558e+01\n", - "w -1.282176e+00\n", - "x_earth 2.144217e+01\n", - "y_earth 1.171391e+01\n", - "z_earth -1.000261e+03\n", - "Name: 0.55, dtype: float64" - ] - }, - "execution_count": 78, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "results.loc[sim.time] # results for current simulation time" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Test\n" - ] - }, - { - "cell_type": "code", - "execution_count": 984, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "a1 = Cessna172()\n", - "a2 = SimplifiedCessna172()\n", - "e1 = copy.deepcopy(environment)\n", - "e2 = copy.deepcopy(environment)" - ] - }, - { - "cell_type": "code", - "execution_count": 985, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(Aircraft State \n", - " x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", - " theta: 0.076 rad, phi: 0.000 rad, psi: 0.500 rad \n", - " u: 44.87 m/s, v: -0.00 m/s, w: 3.40 m/s \n", - " P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", - " u_dot: 0.00 m/s², v_dot: -0.00 m/s², w_dot: 0.00 m/s² \n", - " P_dot: -0.00 rad/s², Q_dot: 0.00 rad/s², R_dot: -0.00 rad/s² ,\n", - " {'delta_aileron': -1.2190588362567532e-17,\n", - " 'delta_elevator': -0.048951124635254917,\n", - " 'delta_rudder': 7.1787477633953699e-17,\n", - " 'delta_t': 0.57799667845449421})" - ] - }, - "execution_count": 985, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "ts1, tc1 = steady_state_trim(\n", - " a1,\n", - " e1,\n", - " pos,\n", - " psi,\n", - " TAS,\n", - " controls0\n", - ")\n", - "e1.update(ts1)\n", - "ss1 = EulerFlatEarth(t0=0, full_state=ts1)\n", - "ts1, tc1" - ] - }, - { - "cell_type": "code", - "execution_count": 986, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "({'delta_aileron': -3.9966019045688599e-19,\n", - " 'delta_elevator': -0.07729883009616384,\n", - " 'delta_rudder': 2.7133156470881973e-18,\n", - " 'delta_t': 0.57166075967430052},\n", - " Aircraft State \n", - " x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", - " theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", - " u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", - " P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", - " u_dot: 0.00 m/s², v_dot: -0.00 m/s², w_dot: 0.00 m/s² \n", - " P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² )" - ] - }, - "execution_count": 986, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "ts2, tc2 = steady_state_trim(\n", - " a2,\n", - " e2,\n", - " pos,\n", - " psi,\n", - " TAS,\n", - " controls0\n", - ") \n", - "e2.update(ts2)\n", - "ss2 = EulerFlatEarth(t0=0, full_state=ts2)\n", - "tc2, ts2" - ] - }, - { - "cell_type": "code", - "execution_count": 971, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "c1 = {\n", - " 'delta_elevator': Constant(tc1['delta_elevator']),\n", - " 'delta_aileron': Constant(tc1['delta_aileron']),\n", - " 'delta_rudder': Constant(tc1['delta_rudder']),\n", - " 'delta_t': Constant(tc1['delta_t'])\n", - "}\n", - "c2 = {\n", - " 'delta_elevator': Constant(tc2['delta_elevator']),\n", - " 'delta_aileron': Constant(tc2['delta_aileron']),\n", - " 'delta_rudder': Constant(tc2['delta_rudder']),\n", - " 'delta_t': Constant(tc2['delta_t'])\n", - "}\n", - "s1 = Simulation(a1, ss1, e1, c1)\n", - "s2 = Simulation(a2, ss2, e2, c2)\n", - " # Doublet(t_init=3, T=1, A=0.1, offset=0)," - ] - }, - { - "cell_type": "code", - "execution_count": 711, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "s1 = Simulation(aircraft, ss1, e1, c1)" - ] - }, - { - "cell_type": "code", - "execution_count": 712, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "\n", - "\n", - "time: 0%| | 0/5 [00:00]" - ] - }, - "execution_count": 713, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(r1.alpha*180/np.pi)\n", - "plt.plot(r2.alpha*180/np.pi,'.')\n", - "plt.plot(results.alpha*180/np.pi,'.')" - ] - }, - { - "cell_type": "code", - "execution_count": 972, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\plotting\\_core.py:1716: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n", - " series.name = label\n" - ] - }, - { - "data": { - "image/png": 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NgT6DYPB4OLAe6o6e6hKjshdJgIKziIhIuM5ofQlNteENofDWltHeRK5hx8uw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\nZqsxZocx5o5UnltEREREpCNSVqphjAkA24DLgXJ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9XvyUh2qpkBI0pIqxz7+vlZWVfPWrX+Xss8/mc5/7HDfffDNz5sxhxYoVPPPM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\n97k06D6Xhry/zzkNxs65V4C9sdvM7MR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"\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\__init__.py\u001b[0m in \u001b[0;36minner\u001b[1;34m(ax, *args, **kwargs)\u001b[0m\n\u001b[0;32m 1715\u001b[0m warnings.warn(msg % (label_namer, func.__name__),\n\u001b[0;32m 1716\u001b[0m RuntimeWarning, stacklevel=2)\n\u001b[1;32m-> 1717\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0max\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1718\u001b[0m \u001b[0mpre_doc\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0minner\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__doc__\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1719\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mpre_doc\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py\u001b[0m in \u001b[0;36mplot\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m 1370\u001b[0m \u001b[0mkwargs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcbook\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnormalize_kwargs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0m_alias_map\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1371\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1372\u001b[1;33m \u001b[1;32mfor\u001b[0m \u001b[0mline\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_lines\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1373\u001b[0m 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\u001b[1;32mfor\u001b[0m \u001b[0mseg\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_plot_args\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mthis\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 405\u001b[0m \u001b[1;32myield\u001b[0m \u001b[0mseg\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 406\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_base.py\u001b[0m in \u001b[0;36m_plot_args\u001b[1;34m(self, tup, kwargs)\u001b[0m\n\u001b[0;32m 382\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mindex_of\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtup\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 383\u001b[0m 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(a1.alpha_data, a1.CN_delta_aile_data, '.')\n", - "plt.plot(a1.alpha_data, a2.CN_delta_aile_cl*a2.CL + 0*a2.alpha_data)" - ] - }, - { - "cell_type": "code", - "execution_count": 1106, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "-0.069523541636556885" - ] - }, - "execution_count": 1106, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.sum(a2.CL_data*a2.CN_p_data)/np.sum(a2.CL_data**2)" - ] - }, - { - "cell_type": "code", - "execution_count": 1119, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "-0.00027157871300302394" - ] - }, - "execution_count": 1119, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "x = np.reshape(a1.CL_data**2, (1, 12)) * np.reshape(a1.delta_aile_data, (9, 1))\n", - "np.sum(a1.CN_delta_aile_data*x) / np.sum(x**2)" - ] - }, - { - "cell_type": "code", - "execution_count": 1120, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "LinregressResult(slope=-0.00027568577531501706, intercept=0.00072199122345927057, rvalue=-0.94235806962343571, pvalue=3.266896179580671e-52, stderr=9.5077855389690054e-06)" - ] - }, - "execution_count": 1120, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "linregress(x.flatten(), a1.CN_delta_aile_data.flatten())" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 34, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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IIerTMY3/s+HkVnTn3sCTnJMaPfPvK/RFRA5RVkYqM8eewZq+Ewk0ac7xb09g\nRUExkxYWRHxXj7p3REQOg9fVczp0m4abOZjPZ17Ln8puIDmQyOyxfSK2uyekI30zu8jM1ppZgZnd\nUcPrKWY2J/j6MjPLrPLancH1a83swvorXUQkAnQ4m2UZ1/GjhHcYmfA6ZeUV5BZu9buqWtUZ+maW\nCEwCBgI9gBFm1qNaszFAiXOuMzAReCD43h7AcOB44CLgr8HvJyISM5LOuY23XG9+HZjFCYEi+nRM\n87ukWoVypH8qUOCcK3TOlQJPA4OrtRkMzAg+nwf0NzMLrn/aObfPOfcZUBD8fiIiMSMrM40WI5+k\nLOVonmr5GAml30Rs/34ood8G2FBluTi4rsY2zrlyYAeQFuJ7RUSiXu9unWk2aiYpO4v5Yta1/OnV\njyJyDH8ooW81rHMhtgnlvZjZODPLM7O8LVu2hFCSiEgEyjidpZk/5+KE3Ijt3w8l9IuBdlWW2wIb\na2tjZgGgBbAtxPfinJvsnMt2zmWnp6eHXr2ISIRJ6fdLFrmT+HVgFr0C6yOufz+U0F8OdDGzDmaW\njHdiNqdamxxgdPD5UOBN55wLrh8eHN3TAegCvFs/pYuIRJ6szDRajpxKWUoqT6c+TkLZzojq368z\n9IN99BOABcAaYK5zbpWZ3WNmg4LNpgJpZlYA3ALcEXzvKmAusBp4BbjBORfddyAQEanDid060Wzk\nDFK+KaJ45viI6t8P6eIs59x8YH61df9b5fle4PJa3nsfcN8R1CgiEn0yz2BZxnh+vO5vvJVwPM+V\nn0Nu4VbfL9rSNAwiIg0kqd9tvON6ck9gOj8MbIyI/n2FvohIA8nq0Iqmw5/EJTdlXtoTWPle3/v3\nFfoiIg2od/duNBk2hcbb17J2xgT+9OpaX/v3FfoiIg2ty/m81/YqRiS8zgB719fx+wp9EZFwOO8u\n/uM68WDSZDICW33r31foi4iEwckdf4BdPo1GASPnuBlktT2K/KKSsPfxaz59EZEw6dWzN1T8meTn\nrmXjv+5mVH5fSssrSA4khG0Ofh3pi4iE0wnDoPcIjl35KL33r6bCEdY+foW+iEi4XfwQpUe1Z2LS\nJI62nSQFEsLWx6/QFxEJt5SjaDR8Gscl7GBumznMHnMaQFj699WnLyLihzYnY/3vovPrv2XdJ89w\n0Vvtw9K/ryN9ERG/9L0JOpxNm6W/oc3+z8PSv6/QFxHxS0ICXPo4lpTCI0mTaGTlDd6/r9AXEfFT\n89YEhjxKTytkduc3Gnzopvr0RUT81v3HcNr1ZLXqDA08Vl+hLyISCQb+ISw/Rt07IiJxRKEvIhJH\nFPoiInFEoS8iEkcU+iIicURay7mvAAADoElEQVShLyISRxT6IiJxRKEvIhJHzDnndw3fYWZbgKIj\n+BatgK/qqZxoFO/bD9oHoH0A8bcPMpxz6XU1irjQP1Jmluecy/a7Dr/E+/aD9gFoH4D2QW3UvSMi\nEkcU+iIicSQWQ3+y3wX4LN63H7QPQPsAtA9qFHN9+iIiUrtYPNIXEZFaRGXom9lFZrbWzArM7I4a\nXk8xsznB15eZWWb4q2xYIeyDW8xstZn9x8zeMLMMP+psSHXtgyrthpqZM7OYG8kRyj4ws2HB/wur\nzOwf4a6xIYXwe9DezBaa2Yrg78LFftQZUZxzUfUAEoFPgY5AMvA+0KNam58DjwWfDwfm+F23D/vg\nXKBJ8Pn18bgPgu2OAt4CcoFsv+v24f9BF2AFkBpcPsbvusO8/ZOB64PPewDr/K7b70c0HumfChQ4\n5wqdc6XA08Dgam0GAzOCz+cB/c3MwlhjQ6tzHzjnFjrndgcXc4G2Ya6xoYXy/wDgXuBBYG84iwuT\nUPbBtcAk51wJgHNuc5hrbEihbL8DmgeftwA2hrG+iBSNod8G2FBluTi4rsY2zrlyYAfQcLeXD79Q\n9kFVY4CXG7Si8KtzH5jZSUA759yL4SwsjEL5f9AV6GpmS8ws18wuClt1DS+U7f8t8FMzKwbmAzeG\np7TIFY33yK3piL36EKRQ2kSzkLfPzH4KZAP9GrSi8DvoPjCzBGAicHW4CvJBKP8PAnhdPOfg/bX3\ntpn1dM5tb+DawiGU7R8BTHfO/cnMTgdmBbe/ouHLi0zReKRfDLSrstyW7//J9m0bMwvg/Vm3LSzV\nhUco+wAzOx/4H2CQc25fmGoLl7r2wVFAT2CRma0D+gA5MXYyN9TfhX8658qcc58Ba/E+BGJBKNs/\nBpgL4JxbCjTCm5MnbkVj6C8HuphZBzNLxjtRm1OtTQ4wOvh8KPCmC57JiRF17oNg18bjeIEfS/24\nlQ66D5xzO5xzrZxzmc65TLzzGoOcc3n+lNsgQvldeAHvpD5m1gqvu6cwrFU2nFC2fz3QH8DMuuOF\n/pawVhlhoi70g330E4AFwBpgrnNulZndY2aDgs2mAmlmVgDcAtQ6nC8ahbgPHgKaAc+Y2Uozq/7L\nENVC3AcxLcR9sADYamargYXA7c65rf5UXL9C3P5bgWvN7H3gKeDqGDsAPGS6IldEJI5E3ZG+iIgc\nPoW+iEgcUeiLiMQRhb6ISBxR6IuIxBGFvohIHFHoi4jEEYW+iEgc+X+3AsIS92rKUwAAAABJRU5E\nrkJggg==\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(aircraft.J_data,aircraft.Ct_data,'.')\n", - "plt.plot(aircraft.J_data,-0.1692121*aircraft.J_data**2 + 0.03545196*aircraft.J_data +0.10446359)" - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "metadata": {}, - "outputs": [], - "source": [ - "a,b,c = np.polyfit(aircraft.J_data,aircraft.Ct_data,2)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/How it works.ipynb b/How it works.ipynb deleted file mode 100644 index 6160320..0000000 --- a/How it works.ipynb +++ /dev/null @@ -1,938 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Python Flight Mechanics Engine " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Aircraft " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In order to perform a simulation, the first thing we need is an aircraft:" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from pyfme.aircrafts import Cessna172" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "%load_ext autoreload\n", - "%autoreload 2" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "aircraft = Cessna172()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Aircraft will provide the simulator the forces, moments and inertial properties in order to perform the integration of the dynamic system equations:" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Aircraft mass: 1043.2616 kg\n", - "Aircraft inertia tensor: \n", - " [[ 1285.3154166 0. 0. ]\n", - " [ 0. 1824.9309607 0. ]\n", - " [ 0. 0. 2666.89390765]] kg/m²\n" - ] - } - ], - "source": [ - "print(f\"Aircraft mass: {aircraft.mass} kg\")\n", - "print(f\"Aircraft inertia tensor: \\n {aircraft.inertia} kg/m²\")" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "forces: [ 0. 0. 0.] N\n", - "moments: [ 0. 0. 0.] N·m\n" - ] - } - ], - "source": [ - "print(f\"forces: {aircraft.total_forces} N\")\n", - "print(f\"moments: {aircraft.total_moments} N·m\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "For the aircraft, in order to calculate its forces and moments it is necessary to set the controls values within the limits: " - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0}\n" - ] - } - ], - "source": [ - "print(aircraft.controls)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'delta_elevator': (-0.4537856055185257, 0.48869219055841229), 'delta_aileron': (-0.26179938779914941, 0.3490658503988659), 'delta_rudder': (-0.27925268031909273, 0.27925268031909273), 'delta_t': (0, 1)}\n" - ] - } - ], - "source": [ - "print(aircraft.control_limits)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "but also to provide and environment (ie. atmosphere, winds, gravity) and the aircraft state, which will also determine the aerodynamic contribution." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Environment " - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.environment.atmosphere import ISA1976\n", - "from pyfme.environment.wind import NoWind\n", - "from pyfme.environment.gravity import VerticalConstant" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "atmosphere = ISA1976()\n", - "gravity = VerticalConstant()\n", - "wind = NoWind()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The atmosphere, wind and gravity model make up the environment:" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.environment import Environment" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "environment = Environment(atmosphere, gravity, wind)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The environment has an update method which given the state (ie. position, altitude...) updates the environment variables (ie. density, wind magnitude, gravity force...)" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Help on method update in module pyfme.environment.environment:\n", - "\n", - "update(state) method of pyfme.environment.environment.Environment instance\n", - "\n" - ] - } - ], - "source": [ - "help(environment.update)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## State " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Even if the state can be set manually by giving the position, attitude, velocity, angular velocities... Most of the times, the user will want to trim the aircraft in a stationary condition. The aircraft controls to flight in that condition will be also provided by the trimmer." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.utils.trimmer import steady_state_trim" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Help on function steady_state_trim in module pyfme.utils.trimmer:\n", - "\n", - "steady_state_trim(aircraft, environment, pos, psi, TAS, controls, gamma=0, turn_rate=0, exclude=None, verbose=0)\n", - " Finds a combination of values of the state and control variables\n", - " that correspond to a steady-state flight condition.\n", - " \n", - " Steady-state aircraft flight is defined as a condition in which all\n", - " of the motion variables are constant or zero. That is, the linear and\n", - " angular velocity components are constant (or zero), thus all\n", - " acceleration components are zero.\n", - " \n", - " Parameters\n", - " ----------\n", - " aircraft : Aircraft\n", - " Aircraft to be trimmed.\n", - " environment : Environment\n", - " Environment where the aircraft is trimmed including atmosphere,\n", - " gravity and wind.\n", - " pos : Position\n", - " Initial position of the aircraft.\n", - " psi : float, opt\n", - " Initial yaw angle (rad).\n", - " TAS : float\n", - " True Air Speed (m/s).\n", - " controls : dict\n", - " Initial value guess for each control or fixed value if control is\n", - " included in exclude.\n", - " gamma : float, optional\n", - " Flight path angle (rad).\n", - " turn_rate : float, optional\n", - " Turn rate, d(psi)/dt (rad/s).\n", - " exclude : list, optional\n", - " List with controls not to be trimmed. If not given, every control\n", - " is considered in the trim process.\n", - " verbose : {0, 1, 2}, optional\n", - " Level of least_squares verbosity:\n", - " * 0 (default) : work silently.\n", - " * 1 : display a termination report.\n", - " * 2 : display progress during iterations (not supported by 'lm'\n", - " method).\n", - " \n", - " Returns\n", - " -------\n", - " state : AircraftState\n", - " Trimmed aircraft state.\n", - " trimmed_controls : dict\n", - " Trimmed aircraft controls\n", - " \n", - " Notes\n", - " -----\n", - " See section 3.4 in [1] for the algorithm description.\n", - " See section 2.5 in [1] for the definition of steady-state flight\n", - " condition.\n", - " \n", - " References\n", - " ----------\n", - " .. [1] Stevens, BL and Lewis, FL, \"Aircraft Control and Simulation\",\n", - " Wiley-lnterscience.\n", - "\n" - ] - } - ], - "source": [ - "help(steady_state_trim)" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.models.state.position import EarthPosition" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "pos = EarthPosition(x=0, y=0, height=1000)\n", - "psi = 0.5 # rad\n", - "TAS = 45 # m/s\n", - "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [], - "source": [ - "trimmed_state, trimmed_controls = steady_state_trim(\n", - " aircraft,\n", - " environment,\n", - " pos,\n", - " psi,\n", - " TAS,\n", - " controls0\n", - ") " - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{'delta_aileron': 5.6949494207348974e-18,\n", - " 'delta_elevator': -0.048951124635247888,\n", - " 'delta_rudder': -1.4494655727415656e-17,\n", - " 'delta_t': 0.57799667845248459}" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "trimmed_controls" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "environment.update(trimmed_state)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now, all the necessary elements in order to calculate forces and moments are available " - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# Environment conditions for the current state:\n", - "environment.update(trimmed_state)\n", - "\n", - "# Forces and moments calculation:\n", - "forces, moments = aircraft.calculate_forces_and_moments(trimmed_state, environment, controls0)" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(array([ 1.14823706e-11, -6.00938052e-18, -5.45696821e-12]),\n", - " array([ 1.34219095e-13, -1.43613996e-11, -2.41989038e-15]))" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "forces, moments" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The aircraft is trimmed indeed: the total forces and moments (aerodynamics + gravity + thrust) are zero" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Simulation " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In order to simulate the dynamics of the aircraft under certain inputs in an environment, the user can set up a simulation using a dynamic system:" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.models import EulerFlatEarth" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Constant Controls " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values." - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.utils.input_generator import Constant" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "controls = controls = {\n", - " 'delta_elevator': Constant(trimmed_controls['delta_elevator']),\n", - " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", - " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", - " 'delta_t': Constant(trimmed_controls['delta_t'])\n", - "}" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.simulator import Simulation" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "sim = Simulation(aircraft, system, environment, controls)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Once the simulation is set, the propagation can be performed:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results = sim.propagate(10)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The results are returned in a DataFrame:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "kwargs = {'marker': '.',\n", - " 'subplots': True,\n", - " 'sharex': True,\n", - " 'figsize': (12, 6)}" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['x_earth', 'y_earth', 'height'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['psi', 'theta', 'phi'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['v_north', 'v_east', 'v_down'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['p', 'q', 'r'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['alpha', 'beta', 'TAS'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['Fx', 'Fy', 'Fz'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['Mx', 'My', 'Mz'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['elevator', 'aileron', 'rudder', 'thrust'], **kwargs);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Doublet " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.utils.input_generator import Doublet" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "de0 = trimmed_controls['delta_elevator']" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "controls = controls = {\n", - " 'delta_elevator': Doublet(t_init=2, T=1, A=0.1, offset=de0),\n", - " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", - " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", - " 'delta_t': Constant(trimmed_controls['delta_t'])\n", - "}" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "sim = Simulation(aircraft, system, environment, controls)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Once the simulation is set, the propagation can be performed:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results = sim.propagate(90)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['x_earth', 'y_earth', 'height'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['psi', 'theta', 'phi'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['v_north', 'v_east', 'v_down'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['p', 'q', 'r'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['alpha', 'beta', 'TAS'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['Fx', 'Fy', 'Fz'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['Mx', 'My', 'Mz'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['elevator', 'aileron', 'rudder', 'thrust'], **kwargs);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Propagating only one time step" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "dt = 0.05 # seconds\n", - "sim = Simulation(aircraft, system, environment, controls, dt)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results = sim.propagate(0.5)\n", - "results" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can propagate for one time step even once the simulation has been propagated before:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results = sim.propagate(sim.time+dt)\n", - "results" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Notice that `results` will include the previous timesteps as well as the last one. To get just the last one one can use pandas `loc` or `iloc`:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.iloc[-1] # last time step" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.loc[sim.time] # results for current simulation time" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/src/pyfme/aircrafts/boeing_linear.py b/src/pyfme/aircrafts/boeing_linear.py index fcd62d3..402f54f 100644 --- a/src/pyfme/aircrafts/boeing_linear.py +++ b/src/pyfme/aircrafts/boeing_linear.py @@ -67,7 +67,7 @@ def __init__(self): 'Nr': -8.934e6 } - def calculate_derivatives(self, state, environment, controls): + def calculate_derivatives(self, state, environment, controls=None, eps=0): return self.stability_derivatives def trimmed_conditions(self): diff --git a/src/pyfme/aircrafts/cessna_172.py b/src/pyfme/aircrafts/cessna_172.py index 31f8d12..67c8ddb 100644 --- a/src/pyfme/aircrafts/cessna_172.py +++ b/src/pyfme/aircrafts/cessna_172.py @@ -95,6 +95,8 @@ def __init__(self): # Mass & Inertia self.mass = 2300 * lbs2kg # kg self.inertia = np.diag([948, 1346, 1967]) * slugft2_2_kgm2 # kg·m² + self.inertia[0, 2] = - 100*slugft2_2_kgm2 + self.inertia[2, 0] = - 100*slugft2_2_kgm2 # Geometry self.Sw = 16.2 # m2 @@ -362,8 +364,7 @@ def calculate_forces_and_moments(self, state, environment, controls): return self.total_forces, self.total_moments - - def calculate_derivatives(self, state, environment, controls): + def calculate_derivatives(self, state, environment, controls, eps=1e-3): """ Calculate dimensional derivatives of the forces at the vicinity of the state. The output consists in 2 dictionaries, one for force one for moment @@ -377,7 +378,6 @@ def calculate_derivatives(self, state, environment, controls): Fnames = ['X', 'Y', 'Z'] Mnames = ['L', 'M', 'N'] - eps = 1e-3 # F, M = self.calculate_forces_and_moments(state, environment, controls) # Rotation for stability derivatives in stability axis @@ -460,7 +460,6 @@ def __init__(self): self.Cl_delta_rud = .075*np.mean(self.Cl_delta_rud_data) self.Cl_delta_aile = np.sum(self.delta_aile_data*self.Cl_delta_aile_data)/np.sum(self.delta_aile_data**2) - # XXX: Tunned CN_delta_rud self.CN_beta = np.mean(self.CN_beta_data) self.CN_p_al = np.sum(self.alpha_data*self.CN_p_data)/np.sum(self.alpha_data**2) @@ -474,8 +473,6 @@ def __init__(self): self.RPM_idle = 1000 self.Ct_J2, self.Ct_J, self.Ct_0 = np.polyfit(self.J_data, self.Ct_data, 2) - - def _calculate_aero_lon_forces_moments_coeffs(self, state): """ Simplified dynamics for the Cessna 172: strictly linear dynamics. @@ -563,5 +560,4 @@ def _calculate_thrust_forces_moments(self, environment): # We will consider that the engine is aligned along the OX (body) axis Ft = np.array([T, 0, 0]) - return Ft \ No newline at end of file diff --git a/src/pyfme/environment/atmosphere.py b/src/pyfme/environment/atmosphere.py index c09c6fb..1596ef4 100644 --- a/src/pyfme/environment/atmosphere.py +++ b/src/pyfme/environment/atmosphere.py @@ -258,3 +258,9 @@ def __call__(self, h): a = sqrt(gamma * R_a * T) return T, p, rho, a + + +class SeaLevel(ISA1976): + def __call__(self, h): + return super().__call__(h=0.01) + diff --git a/src/pyfme/models/euler_flat_earth.py b/src/pyfme/models/euler_flat_earth.py index a9a2e8c..680979d 100644 --- a/src/pyfme/models/euler_flat_earth.py +++ b/src/pyfme/models/euler_flat_earth.py @@ -15,14 +15,17 @@ import numpy as np from numpy import sin, cos - +from copy import deepcopy as dcp +import pdb from pyfme.models.dynamic_system import AircraftDynamicSystem from pyfme.models.state import ( AircraftState, EarthPosition, EulerAttitude, BodyVelocity, BodyAngularVelocity, BodyAcceleration, BodyAngularAcceleration ) -from pyfme.utils.coordinates import body2wind +from pyfme.utils.coordinates import body2wind, wind2body +import math +_FLOAT_EPS_4 = np.finfo(float).eps * 4.0 class EulerFlatEarth(AircraftDynamicSystem): """Euler Flat Earth Dynamic System. @@ -32,9 +35,12 @@ class EulerFlatEarth(AircraftDynamicSystem): performed on Earth axis. """ - def fun(self, t, x): + def fun(self, t, x=None): + + if x is not None: + # update full state if necessary + self._update_full_system_state_from_state(x, self.state_vector_dot) - self._update_full_system_state_from_state(x, self.state_vector_dot) updated_simulation = self.update_simulation(t, self.full_state) mass = updated_simulation.aircraft.mass @@ -46,10 +52,12 @@ def fun(self, t, x): return rv - def steady_state_trim_fun(self, full_state, environment, aircraft, + def right_hand_side(self, full_state, environment, aircraft, controls): - - environment.update(full_state) + try: + environment.update(full_state) + except: + pdb.set_trace() aircraft.calculate_forces_and_moments(full_state, environment, controls) @@ -61,8 +69,11 @@ def steady_state_trim_fun(self, full_state, environment, aircraft, t0 = 0 x0 = self._get_state_vector_from_full_state(full_state) - rv = _system_equations(t0, x0, mass, inertia, forces, moments) - return rv[:6] + return _system_equations(t0, x0, mass, inertia, forces, moments) + + def steady_state_trim_fun(self, full_state, environment, aircraft, + controls): + return self.right_hand_side(full_state, environment, aircraft, controls)[:6] def _update_full_system_state_from_state(self, state, state_dot): @@ -130,51 +141,235 @@ def _get_state_vector_from_full_state(self, full_state): ) return x0 - def linearized_model(self, state, aircraft, environment, controls): + def linearized_model(self, state, aircraft, environment, controls=None, method="direct", eps=1e-3): """ Outputs matrices A_long and A_lat that are the lateral and longitudinal state matrices for the linearized system. As done in Etkin [2], these matrices are useful in stability axis. - + method can be: + - "direct", in which case we compute the derivative of the accelerations : X_dot = f(X,U), so + Aij = dfi/dxj(X,U) + - "from forces", in which case we compute the dimensional force derivatives and use formulas in Etkin + (/!\ contains assumptions on the point at which we linearize """ - - # get derivatives - d = aircraft.calculate_derivatives(state, environment, controls) - - # get inertias - m = aircraft.mass - Ix = aircraft.inertia[0, 0] - Iy = aircraft.inertia[1, 1] - Iz = aircraft.inertia[2, 2] - Ixz = aircraft.inertia[0, 2] - Ixprime = (Ix*Iz - Ixz**2)/Iz - Izprime = (Ix*Iz - Ixz**2)/Ix - Ixzprime = Ixz/(Ix*Iz - Ixz**2) - - # recover state variables - u, v, w = state.velocity.vel_body - phi, theta, psi = state.attitude.euler_angles - g = environment.gravity_magnitude - - # Longitudinal matrix - # Todo : add alpha_dot derivatives - A1 = np.array([d['Xu'] / m, d['Xw'] / m, 0, -g*np.cos(theta)]) - A2 = np.array([d['Zu'], d['Zw'], d['Zq'] + m*u, -m*g*np.sin(theta)])/(m - d['Zw_dot']) - A3 = (np.array([d['Mu'], d['Mw'], d['Mq'], 0]) + A2*d['Mw_dot']) / Iy - A4 = np.array([0, 0, 1, 0]) - A_long = np.vstack((A1, A2, A3, A4)) - - # Lateral dynamics - A1 = np.array([d['Yv']/m, d['Yp']/m, d['Yr']/m - u, g*np.cos(theta)]) - A2 = np.array([d['Lv']/Ixprime + d['Nv']*Ixzprime, d['Lp']/Ixprime + d['Np']*Ixzprime, - d['Lr']/Ixprime + d['Nr']*Ixzprime, 0]) - A3 = np.array([d['Lv']*Ixzprime + d['Nv']/Izprime, d['Lp']*Ixzprime + d['Np']/Izprime, - d['Lr'] * Ixzprime + d['Nr'] / Izprime, 0]) - A4 = np.array([0, 1, np.tan(theta), 0]) - A_lat = np.vstack((A1, A2, A3, A4)) + if method=="from_forces": + # get derivatives + d = aircraft.calculate_derivatives(state, environment, controls,eps) + + # recover state variables + u, v, w = state.velocity.vel_body + alpha = np.arctan2(w,u) + beta = np.arcsin(v/np.sqrt(u**2 + v**2 + w**2)) + theta = np.copy(state.attitude.theta) - alpha + u, v, w = body2wind(state.velocity.vel_body, alpha, beta) + g = environment.gravity_magnitude + + # get inertias (move them to stability axis) + m = aircraft.mass + Lwb = np.array([[cos(alpha) * cos(beta),sin(beta),sin(alpha) * cos(beta)], + [- cos(alpha) * sin(beta),cos(beta),-sin(alpha) * sin(beta)], + [-sin(alpha), 0, cos(alpha)]]) + I = (Lwb.dot(aircraft.inertia)).dot(Lwb.T) + Ix = I[0,0] + Iy = I[1, 1] + Iz = I[2, 2] + Ixz = - I[0, 2] + Ixprime = (Ix*Iz - Ixz**2)/Iz + Izprime = (Ix*Iz - Ixz**2)/Ix + Ixzprime = Ixz/(Ix*Iz - Ixz**2) + + # Longitudinal matrix + # Todo : add alpha_dot derivatives + A1 = np.array([d['Xu'] / m, d['Xw'] / m, 0, -g*np.cos(theta)]) + A2 = np.array([d['Zu'], d['Zw'], d['Zq'] + m*u, -m*g*np.sin(theta)])/(m - d['Zw_dot']) + A3 = (np.array([d['Mu'], d['Mw'], d['Mq'], 0]) + A2*d['Mw_dot']) / Iy + A4 = np.array([0, 0, 1, 0]) + A_long = np.vstack((A1, A2, A3, A4)) + + # Lateral dynamics + A1 = np.array([d['Yv']/m, d['Yp']/m, d['Yr']/m - u, g*np.cos(theta)]) + A2 = np.array([d['Lv']/Ixprime + d['Nv']*Ixzprime, d['Lp']/Ixprime + d['Np']*Ixzprime, + d['Lr']/Ixprime + d['Nr']*Ixzprime, 0]) + A3 = np.array([d['Lv']*Ixzprime + d['Nv']/Izprime, d['Lp']*Ixzprime + d['Np']/Izprime, + d['Lr'] * Ixzprime + d['Nr'] / Izprime, 0]) + A4 = np.array([0, 1, np.tan(theta), 0]) + A_lat = np.vstack((A1, A2, A3, A4)) + + elif method=="direct": + # Rotation for stability derivatives in stability axis + V = np.sqrt(state.velocity.u ** 2 + state.velocity.v ** 2 + state.velocity.w ** 2) + alpha = np.arctan2(state.velocity.w, state.velocity.u) + beta = np.arcsin(state.velocity.v / V) + + derivatives = {} + for keyword in ['velocity', 'angular_vel', 'attitude']: + derivatives[keyword] = {} + for i in range(3): + derivatives[keyword][i] = {} + eps_v0 = np.zeros(3) + + # plus perturb + eps_v0[i] = eps / 2 + if keyword == 'attitude': + eps_vec = eps_v0 + else: + eps_vec = wind2body(eps_v0, alpha, beta) + state.perturbate(eps_vec, keyword) + state_dot = self.right_hand_side(state, environment, aircraft, controls) + accel_p = body2wind(state_dot[0:3], alpha, beta) + ang_accel_p = body2wind(state_dot[3:6], alpha, beta) + angle_der_p = state_dot[6:9] + state.cancel_perturbation() + + # minus perturb + eps_v0[i] = - eps / 2 + if keyword == 'attitude': + eps_vec = eps_v0 + else: + eps_vec = wind2body(eps_v0, alpha, beta) + state.perturbate(eps_vec, keyword) + state_dot = self.right_hand_side(state, environment, aircraft, controls) + accel_m = body2wind(state_dot[0:3], alpha, beta) + ang_accel_m = body2wind(state_dot[3:6], alpha, beta) + angle_der_m = state_dot[6:9] + state.cancel_perturbation() + + derivatives[keyword][i]["acceleration"] = (accel_p - accel_m)/eps + derivatives[keyword][i]["angular_accel"] = (ang_accel_p - ang_accel_m)/eps + derivatives[keyword][i]["angle_der"] = (angle_der_p - angle_der_m)/eps + + # Longitudinal + # line1 : d(delta_u_dot)/dall + A1 = np.array([derivatives['velocity'][0]["acceleration"][0], derivatives['velocity'][2]["acceleration"][0], + derivatives['angular_vel'][1]["acceleration"][0], derivatives['attitude'][0]["acceleration"][0] + ]) + # line2 : d(w_dot)/dall + A2 = np.array([derivatives['velocity'][0]["acceleration"][2], derivatives['velocity'][2]["acceleration"][2], + derivatives['angular_vel'][1]["acceleration"][2], derivatives['attitude'][0]["acceleration"][2] + ]) + # line3 : d(q_dot)/dall + A3 = np.array([derivatives['velocity'][0]["angular_accel"][1], derivatives['velocity'][2]["angular_accel"][1], + derivatives['angular_vel'][1]["angular_accel"][1], derivatives['attitude'][0]["angular_accel"][1] + ]) + # line4 : d(theta_dot)/dall + A4 = np.array([derivatives['velocity'][0]["angle_der"][0], derivatives['velocity'][2]["angle_der"][0], + derivatives['angular_vel'][1]["angle_der"][0], derivatives['attitude'][0]["angle_der"][0] + ]) + A_long = np.vstack((A1, A2, A3, A4)) + + # Lateral + # line1 d(v_dot)/dall + A1 = np.array([derivatives['velocity'][1]["acceleration"][1], derivatives['angular_vel'][0]["acceleration"][1], + derivatives['angular_vel'][2]["acceleration"][1], derivatives['attitude'][1]["acceleration"][1] + ]) + # line2 d(p_dot)/dall + A2 = np.array([derivatives['velocity'][1]["angular_accel"][0], derivatives['angular_vel'][0]["angular_accel"][0], + derivatives['angular_vel'][2]["angular_accel"][0], derivatives['attitude'][1]["angular_accel"][0] + ]) + # line3 d(r_dot)/dall + A3 = np.array( + [derivatives['velocity'][1]["angular_accel"][2], derivatives['angular_vel'][0]["angular_accel"][2], + derivatives['angular_vel'][2]["angular_accel"][2], derivatives['attitude'][1]["angular_accel"][2] + ]) + # line4 d(phi_dot)/dall + A4 = np.array( + [derivatives['velocity'][1]["angle_der"][1], derivatives['angular_vel'][0]["angle_der"][1], + derivatives['angular_vel'][2]["angle_der"][1], derivatives['attitude'][1]["angle_der"][1] + ]) + A_lat = np.vstack((A1, A2, A3, A4)) + + else: + raise NotImplementedError return A_long, A_lat +def mat2euler(M, cy_thresh=None): + ''' Discover Euler angle vector from 3x3 matrix + + Uses the conventions above. + + Parameters + ---------- + M : array-like, shape (3,3) + cy_thresh : None or scalar, optional + threshold below which to give up on straightforward arctan for + estimating x rotation. If None (default), estimate from + precision of input. + + Returns + ------- + z : scalar + y : scalar + x : scalar + Rotations in radians around z, y, x axes, respectively + + Notes + ----- + If there was no numerical error, the routine could be derived using + Sympy expression for z then y then x rotation matrix, which is:: + + [ cos(y)*cos(z), -cos(y)*sin(z), sin(y)], + [cos(x)*sin(z) + cos(z)*sin(x)*sin(y), cos(x)*cos(z) - sin(x)*sin(y)*sin(z), -cos(y)*sin(x)], + [sin(x)*sin(z) - cos(x)*cos(z)*sin(y), cos(z)*sin(x) + cos(x)*sin(y)*sin(z), cos(x)*cos(y)] + + with the obvious derivations for z, y, and x + + z = atan2(-r12, r11) + y = asin(r13) + x = atan2(-r23, r33) + + Problems arise when cos(y) is close to zero, because both of:: + + z = atan2(cos(y)*sin(z), cos(y)*cos(z)) + x = atan2(cos(y)*sin(x), cos(x)*cos(y)) + + will be close to atan2(0, 0), and highly unstable. + + The ``cy`` fix for numerical instability below is from: *Graphics + Gems IV*, Paul Heckbert (editor), Academic Press, 1994, ISBN: + 0123361559. Specifically it comes from EulerAngles.c by Ken + Shoemake, and deals with the case where cos(y) is close to zero: + + See: http://www.graphicsgems.org/ + + The code appears to be licensed (from the website) as "can be used + without restrictions". + ''' + M = np.asarray(M) + if cy_thresh is None: + try: + cy_thresh = np.finfo(M.dtype).eps * 4 + except ValueError: + cy_thresh = _FLOAT_EPS_4 + r11, r12, r13, r21, r22, r23, r31, r32, r33 = M.flat + # cy: sqrt((cos(y)*cos(z))**2 + (cos(x)*cos(y))**2) + cy = math.sqrt(r33*r33 + r23*r23) + if cy > cy_thresh: # cos(y) not close to zero, standard form + z = math.atan2(-r12, r11) # atan2(cos(y)*sin(z), cos(y)*cos(z)) + y = math.atan2(r13, cy) # atan2(sin(y), cy) + x = math.atan2(-r23, r33) # atan2(cos(y)*sin(x), cos(x)*cos(y)) + else: # cos(y) (close to) zero, so x -> 0.0 (see above) + # so r21 -> sin(z), r22 -> cos(z) and + z = math.atan2(r21, r22) + y = math.atan2(r13, cy) # atan2(sin(y), cy) + x = 0.0 + return z, y, x + +def wind2body4attitude(eps_v0, alpha, beta): + """ + Fix for the fact that theta, phi, psi is the wrong axis order. To use rotation, it has to be phi, theta, psi + """ + eps_vec = np.array([eps_v0[1], eps_v0[0], eps_v0[2]]) + eps_vec = wind2body(eps_vec, alpha, beta) + return np.array([eps_vec[1], eps_vec[0], eps_vec[2]]) + +def body2wind4attitude(eps_v0, alpha, beta): + """ + Fix for the fact that theta, phi, psi is the wrong axis order. To use rotation, it has to be phi, theta, psi + """ + eps_vec = np.array([eps_v0[1], eps_v0[0], eps_v0[2]]) + eps_vec = body2wind(eps_vec, alpha, beta) + return np.array([eps_vec[1], eps_vec[0], eps_vec[2]]) # TODO: numba jit def _system_equations(time, state_vector, mass, inertia, forces, moments): diff --git a/src/pyfme/models/state/aircraft_state.py b/src/pyfme/models/state/aircraft_state.py index 90abec0..c68077e 100644 --- a/src/pyfme/models/state/aircraft_state.py +++ b/src/pyfme/models/state/aircraft_state.py @@ -15,6 +15,7 @@ from .acceleration import BodyAcceleration from .angular_acceleration import BodyAngularAcceleration from pyfme.utils.coordinates import wind2body +from json import dump class AircraftState: @@ -77,3 +78,25 @@ def cancel_perturbation(self): getattr(self, keyword).cancel_perturbation(attitude=self.attitude) return self + + def save_to_json(self, filename): + state = dict() + + state['x_e'] = self.position.x_earth + state['y_e'] = self.position.y_earth + state['z_e'] = self.position.z_earth + + state['phi'] = self.attitude.phi + state['theta'] = self.attitude.theta + state['psi'] = self.attitude.psi + + state['u'] = self.velocity.u + state['v'] = self.velocity.v + state['w'] = self.velocity.w + + state['p'] = self.angular_vel.p + state['q'] = self.angular_vel.q + state['r'] = self.angular_vel.r + + with open(filename, 'w') as f: + dump(state, f) \ No newline at end of file diff --git a/src/pyfme/utils/coordinates.py b/src/pyfme/utils/coordinates.py index ffee070..8f48750 100644 --- a/src/pyfme/utils/coordinates.py +++ b/src/pyfme/utils/coordinates.py @@ -448,27 +448,3 @@ def wind2body(wind_coords, alpha, beta): body_coords = Lbw.dot(wind_coords) return body_coords - - -def body2stab(body_coords, alpha, beta): - return body2wind(body_coords, alpha, beta) - -def stab2body(body_coords, alpha, beta): - check_alpha_beta_range(alpha, beta) - - # Transformation matrix from body to wind - Lwb = np.array([ - [cos(alpha) * cos(beta), - sin(beta), - sin(alpha) * cos(beta)], - [- cos(alpha) * sin(beta), - cos(beta), - -sin(alpha) * sin(beta)], - [-sin(alpha), - 0, - cos(alpha)] - ]) - - wind_coords = np.linalg.lstsq(Lwb, body_coords)[0] - - return wind_coords diff --git a/src/pyfme/utils/export.py b/src/pyfme/utils/export.py new file mode 100644 index 0000000..0ae04a6 --- /dev/null +++ b/src/pyfme/utils/export.py @@ -0,0 +1,18 @@ +# -*- coding: utf-8 -*- +""" +Python Flight Mechanics Engine (PyFME). +Copyright (c) AeroPython Development Team. +Distributed under the terms of the MIT License. + +Export results and state to other formats +---------------- +Creates a few functions to save simulation outputs to other formats +Other functions and methods doing the same thing: + AircraftState.save_to_json() +""" +from scipy.io import savemat + + +def results2matlab(results, filename): + ref = results.to_dict(orient='list') + savemat(filename, ref) diff --git a/validation/PyFME vs Eigenvalue analysis.ipynb b/validation/PyFME vs Eigenvalue analysis.ipynb new file mode 100644 index 0000000..0f95f61 --- /dev/null +++ b/validation/PyFME vs Eigenvalue analysis.ipynb @@ -0,0 +1,1515 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# PyFME Validation : comparing response with eigenvalue analysis" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.aircrafts import LinearB747, Cessna172, SimplifiedCessna172\n", + "from pyfme.models import EulerFlatEarth\n", + "import numpy as np\n", + "nl = np.linalg\n", + "import matplotlib.pyplot as plt\n", + "from pyfme.environment.atmosphere import ISA1976, SeaLevel\n", + "from pyfme.environment.wind import NoWind\n", + "from pyfme.environment.gravity import VerticalConstant\n", + "from pyfme.environment import Environment\n", + "from pyfme.utils.trimmer import steady_state_trim\n", + "from pyfme.models.state.position import EarthPosition\n", + "from pyfme.simulator import Simulation\n", + "from pyfme.utils.coordinates import wind2body, body2wind\n", + "from pyfme.utils.input_generator import Constant" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The autoreload extension is already loaded. To reload it, use:\n", + " %reload_ext autoreload\n" + ] + } + ], + "source": [ + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We start by defining the airplane, the environment and the trim position." + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "aircraft = SimplifiedCessna172()" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "atmosphere = SeaLevel()\n", + "gravity = VerticalConstant()\n", + "wind = NoWind()\n", + "environment = Environment(atmosphere, gravity, wind)" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "pos = EarthPosition(x=0, y=0, height=1000)\n", + "psi = 0.5 # rad\n", + "TAS = 45 # m/s\n", + "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}\n", + "trimmed_state, trimmed_controls = steady_state_trim(\n", + " aircraft,\n", + " environment,\n", + " pos,\n", + " psi,\n", + " TAS,\n", + " controls0\n", + ")\n", + "environment.update(trimmed_state)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then we linearize the model around the trim condition. It gives us two matrices for lateral and longitudinal small perturbations.\n", + "Under the hood, the code computes dimensional stability derivatives using numerical differentiation, and then uses the analytical formulas for the linearized system given in [1]." + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" + ] + }, + { + "cell_type": "code", + "execution_count": 81, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "A_long, A_lat = system.linearized_model(trimmed_state, aircraft, environment, trimmed_controls)" + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Longitudinal eigenvalues : \n", + "(-2.87760089356+4.12505582128j)\n", + "(-2.87760089356-4.12505582128j)\n", + "(-0.03785343075+0.257120129321j)\n", + "(-0.03785343075-0.257120129321j)\n" + ] + } + ], + "source": [ + "long_val, long_vec=nl.eig(A_long)\n", + "long_val = np.expand_dims(long_val, axis = 0)\n", + "print(f\"Longitudinal eigenvalues : \")\n", + "for l in long_val[0]:\n", + " print(l)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As expected we find two damped oscillatory modes in the longitudinal dynamics: phugoid and short period." + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lateral eigenvalues : \n", + "(-6.96516821579+0j)\n", + "(-0.204583217243+1.17359637036j)\n", + "(-0.204583217243-1.17359637036j)\n", + "(0.0324906079983+0j)\n" + ] + } + ], + "source": [ + "lat_val, lat_vec=nl.eig(A_lat)\n", + "lat_val = np.expand_dims(lat_val, axis = 0)\n", + "print(f\"Lateral eigenvalues : \")\n", + "for l in lat_val[0]:\n", + " print(l)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the lateral case, we get one oscillatory mode (dutch roll), a stable rolling convergence and an unstable - but very slow - spiral mode." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Eigenvalue trajectories" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can compute the predicted trajectories for small perturbations." + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# helper function to go from stability to body axis\n", + "def linear_stab_2_body(long_state=np.zeros(4), lat_state=np.zeros(4), u0=0, theta0=0,alpha0=0, beta0=0):\n", + " # velocities\n", + " v = wind2body(np.array([long_state[0] + u0, lat_state[0], long_state[1]]), alpha=alpha0, beta=beta0)\n", + " # Roll rates\n", + " r = wind2body(np.array([lat_state[1], long_state[2], lat_state[2]]), alpha=alpha0, beta=beta0)\n", + " long_stateB = np.copy(long_state)\n", + " lat_stateB = np.copy(lat_state)\n", + " long_stateB[0] = v[0]\n", + " long_stateB[1] = v[2]\n", + " long_stateB[2] = r[1]\n", + " long_stateB[3] += theta0\n", + " lat_stateB[0] = v[1]\n", + " lat_stateB[1] = r[0]\n", + " lat_stateB[2] = r[2]\n", + " return long_stateB.real, lat_stateB.real" + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Reference conditions\n", + "alpha = np.arctan2(trimmed_state.velocity.w, trimmed_state.velocity.u)\n", + "beta = np.arcsin(trimmed_state.velocity.v/nl.norm(trimmed_state.velocity.vel_body))\n", + "u, v, w = body2wind(trimmed_state.velocity.vel_body, alpha, 0)\n", + "theta0 = trimmed_state.attitude.theta*1.0" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Longitudinal case" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can pick any perturbation from the equilibrium. Here I chose something along the eigenvectors of A_long.\n", + "The result will be a weighted sum of eigenvector*exp(eigenvalue*t). The weights are determined by the initial condition." + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "long_perturbation = (long_vec.T[2] + long_vec.T[3])/1000" + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "C = nl.lstsq(a=long_vec,b=long_perturbation.real)[0].real" + ] + }, + { + "cell_type": "code", + "execution_count": 88, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "T = 100;\n", + "t_long = np.linspace(0,T,1000)\n", + "N = len(t_long)\n", + "X_long = np.zeros((N,4))\n", + "for i in range(N):\n", + " x_stab = (long_vec*np.exp(long_val*t_long[i])).dot(C)\n", + " X_long[i,:] = linear_stab_2_body(long_state=x_stab.real, alpha0=alpha, u0=u, theta0 = theta0)[0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Lateral case" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again we can pick any perturbation" + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "lat_perturbation = (lat_vec.T[0])" + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "C = nl.lstsq(a=lat_vec,b=lat_perturbation.real)[0].real" + ] + }, + { + "cell_type": "code", + "execution_count": 91, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "t_lat = np.linspace(0,10,100)\n", + "N = len(t_lat)\n", + "X_lat = np.zeros((N,4))\n", + "for i in range(N):\n", + " x_stab = (lat_vec*np.exp(lat_val*t_lat[i])).dot(C)\n", + " X_lat[i,:] = linear_stab_2_body(lat_state=x_stab.real, beta0=beta, alpha0=alpha, u0=u, theta0 = theta0)[1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 92, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "controls = {\n", + " 'delta_elevator': Constant(trimmed_controls['delta_elevator']),\n", + " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", + " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", + " 'delta_t': Constant(trimmed_controls['delta_t'])\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Longitudinal case" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We perturbate the trimmed state and run the simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 93, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Perturbate the trimmed state\n", + "trimmed_state.cancel_perturbation()\n", + "p = linear_stab_2_body(long_state=long_perturbation.real, alpha0=alpha)[0]\n", + "trimmed_state.perturbate(np.array([p[0],0,p[1]]), 'velocity')\n", + "trimmed_state.perturbate(np.array([0,p[2],0]), 'angular_vel')\n", + "trimmed_state.perturbate(np.array([p[3],0,0]), 'attitude') # /!\\ Convention theta, phi, psi" + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "trimmed_state.save_to_json('long_perturb.json')" + ] + }, + { + "cell_type": "code", + "execution_count": 95, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "environment.update(trimmed_state)\n", + "system = EulerFlatEarth(t0=0, full_state=trimmed_state)\n", + "sim = Simulation(aircraft, system, environment, controls)" + ] + }, + { + "cell_type": "code", + "execution_count": 96, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n", + "time: 0%| | 0/100 [00:00" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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HeO6553A4HIwZM4bOnTsXec3Bgwczfvx4RowYgd1uB+DBBx9k9OjRfP755/Tv35/atWuf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\nM56yweVkiEhZuA8SJQu75uR3ql0v2DVHk3WLGWOMiTgLLsY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9llLqlFJqD7DLV1+xdfru6eOrA1+dQ8/xjKDnOOFiv/KmWxvCJZN08O5Puxlr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\nTF2RitU4ezjJ4jnJdcY6vrB+S7yxmww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7Ujyrzx+owCas6BA/Rl7fG4DmcoiXvt9sJhMahlFjmQBSDnEpmTTWI5xSb45z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\nNnpcSibdbZvIVgdr3Fdhr4D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AegIjre+3Wk1VTuARYDqwDNgN5L/jOIBwoA8wApgsIo0A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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Longitudinal case\n", + "plt.plot(t_long, X_long[:,0], '.', label='eigenvalue analysis')\n", + "plt.plot(r_long.u, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Horizontal velocity\")\n", + "plt.show()\n", + "\n", + "plt.plot(t_long, X_long[:,1], '.', label='eigenvalue analysis')\n", + "plt.plot(r_long.w, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Vertical velocity\")\n", + "plt.show()\n", + "\n", + "plt.plot(t_long, X_long[:,2], '.', label='eigenvalue analysis')\n", + "plt.plot(r_long.q, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Pitch rate\")\n", + "plt.show()\n", + "\n", + "plt.plot(t_long, X_long[:,3], '.', label='eigenvalue analysis')\n", + "plt.plot(r_long.theta, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Pitch angle\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 103, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Lateral case\n", + "plt.plot(t_lat, X_lat[:,0], '.', label='eigenvalue analysis')\n", + "plt.plot(r_lat.v, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Lateral velocity\")\n", + "plt.show()\n", + "\n", + "plt.plot(t_lat, X_lat[:,1], '.', label='eigenvalue analysis')\n", + "plt.plot(r_lat.p, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Roll rate\")\n", + "plt.show()\n", + "\n", + "plt.plot(t_lat, X_lat[:,2], '.', label='eigenvalue analysis')\n", + "plt.plot(r_lat.r, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Yaw rate\")\n", + "plt.show()\n", + "\n", + "plt.plot(t_lat, X_lat[:,3], '.', label='eigenvalue analysis')\n", + "plt.plot(r_lat.phi, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Heading angle\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 105, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1285.3154166 , 0. , -677.908975 ],\n", + " [ 0. , 1824.9309607 , 0. ],\n", + " [ -677.908975 , 0. , 2666.89390765]])" + ] + }, + "execution_count": 105, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "aircraft.inertia\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# References" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Dynamics of Flight, Stability and Control, Etkin and Reid" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/validation/PyFME vs Simulink.ipynb b/validation/PyFME vs Simulink.ipynb new file mode 100644 index 0000000..61293f0 --- /dev/null +++ b/validation/PyFME vs Simulink.ipynb @@ -0,0 +1,440 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# PyFME Validation: comparing response versus Matlab model" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from pyfme.aircrafts import LinearB747, Cessna172, SimplifiedCessna172\n", + "from pyfme.models import EulerFlatEarth\n", + "import numpy as np\n", + "# nl = np.linalg\n", + "import matplotlib.pyplot as plt\n", + "from pyfme.environment.atmosphere import SeaLevel\n", + "from pyfme.environment.wind import NoWind\n", + "from pyfme.environment.gravity import VerticalConstant\n", + "from pyfme.environment import Environment\n", + "from pyfme.utils.trimmer import steady_state_trim\n", + "from pyfme.models.state.position import EarthPosition\n", + "from pyfme.simulator import Simulation\n", + "from pyfme.utils.export import results2matlab\n", + "from scipy.io import savemat, loadmat\n", + "from pyfme.utils.coordinates import wind2body, body2wind\n", + "from pyfme.utils.input_generator import Constant, Doublet, Ramp\n", + "from json import load as jload" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The autoreload extension is already loaded. To reload it, use:\n", + " %reload_ext autoreload\n" + ] + } + ], + "source": [ + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Running a PyFME simulation and save it to a MATLAB readable file" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We start by defining the airplane and the environment." + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [], + "source": [ + "aircraft = SimplifiedCessna172()" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [], + "source": [ + "atmosphere = SeaLevel()\n", + "gravity = VerticalConstant()\n", + "wind = NoWind()\n", + "environment = Environment(atmosphere, gravity, wind)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We then pick a the trim position. We save the trimmed state into a json file." + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "pos = EarthPosition(x=0, y=0, height=1000)\n", + "psi = 0.5 # rad\n", + "TAS = 45 # m/s\n", + "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}\n", + "trimmed_state, trimmed_controls = steady_state_trim(\n", + " aircraft,\n", + " environment,\n", + " pos,\n", + " psi,\n", + " TAS,\n", + " controls0\n", + ")\n", + "environment.update(trimmed_state)" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "trimmed_state.save_to_json('ini_state.json')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "We finally pick a particular time serie of controls and run the simulation." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [], + "source": [ + "controls = {\n", + " 'delta_elevator': Doublet(t_init=2, T=1, A=0.1, offset=trimmed_controls['delta_elevator']),\n", + " 'delta_aileron': Ramp(t_init=1,T=2, A=.2, offset=trimmed_controls['delta_aileron']),\n", + " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", + " 'delta_t': Constant(trimmed_controls['delta_t'])\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "environment.update(trimmed_state)\n", + "system = EulerFlatEarth(t0=0, full_state=trimmed_state)\n", + "sim = Simulation(aircraft, system, environment, controls)" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "T = 10 # seconds" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "time: 100%|████████████████████████████████████████████████████████████▉| 9.999999999999831/10 [00:06<00:00, 1.60it/s]\n" + ] + } + ], + "source": [ + "results = sim.propagate(T)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We save the controls in a Matlab file" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": {}, + "outputs": [], + "source": [ + "N = int(T/sim.dt)\n", + "t= np.arange(N)*sim.dt\n", + "controls4matlab = np.ones((N,4));\n", + "for it in range(N):\n", + " controls4matlab[it,0] = controls['delta_aileron']._fun(t[it])\n", + " controls4matlab[it,1] = controls['delta_elevator']._fun(t[it])\n", + " controls4matlab[it,2] = controls['delta_rudder']._fun(t[it])\n", + " controls4matlab[it,3] = controls['delta_t']._fun(t[it])\n", + "savemat('controls.mat',{'c': controls4matlab, 'dt':sim.dt})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Run the same simulation in Simulink" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The simulink bloc diagram used for comparison uses exactly the same model to compute forces and moments (the method aircraft.compute_forces_and_moments() was translated directly to Matlab). The entire equations of motion integration is done with the %6DOF (Quaternion) % Simulink bloc from the aerospace blocset. Verifying against this tool allows to make sure that there are no mistake in the way the EulerFlatEarth equations of motion are written, and in the way they are integrated.\n", + "\n", + "We run the Simulink model and load the results:" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "dict_keys(['V_body', 'Omega_body', 'Euler', 't'])\n" + ] + } + ], + "source": [ + "with open('../matlab_comparison/matlab_results.json','r') as f:\n", + " mat_states = jload(f)\n", + "mat_states = {k:np.array(el) for k,el in mat_states.items()}\n", + "print(f\"{mat_states.keys()}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Compare outputs" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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TmeavKaKdFLDeNAsNgzyzk76fKxVLnJVtICJTgGwgXUTygUcBF4Ax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\nyhtvvEGbNm244YYbaNiwIYsWLWLz5s3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M1FgwmDp5cfEW2msBQLgpKTmhcf8b5WhvznRyCE7uLa16ptWqI26d0KRtPvzk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\nOUsidt1bZ3/BJOdj+jmbud9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3A/nE7fG5mnbVm+zPxO8dx7WeKXTIe5HfSGBAWhOeuaxdrEMzpkQ2yMuUSmmn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\nfyK3et9lVq2PAfhvsBtvBs9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M2b/qfOVvjDFmPyz5G2NMDVTtkr+I9BaR70RklYj4Yx1P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\nHzT85XhvkfIlAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Longitudinal values\n", + "plt.plot(mat_states['t'], mat_states['V_body'][:,0], '.', label='Simulink output')\n", + "plt.plot(results.u, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Horizontal velocity\")\n", + "plt.show()\n", + "\n", + "plt.plot(mat_states['t'], mat_states['V_body'][:,2], '.', label='Simulink output')\n", + "plt.plot(results.w, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Vertical velocity\")\n", + "plt.show()\n", + "\n", + "plt.plot(mat_states['t'], mat_states['Omega_body'][:,1], '.', label='Simulink output')\n", + "plt.plot(results.q, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Pitch rate\")\n", + "plt.show()\n", + "\n", + "plt.plot(mat_states['t'], mat_states['Euler'][:,1], '.', label='Simulink output')\n", + "plt.plot(results.theta, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Pitch angle\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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86Qyxv6ahbAP8nyaUKk804auIMHjMAipymNs9k5jpa8UC469RVom3S33stg1qYgEvea8h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\neybg7zUfCQaPWUBL2cSF1gY+8F2CCaQ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iW6XD3xjjBUYCM4DVwAfGmJUi8riIDAosNgPYKSKrgG+Ae40xOyu77US3tGA3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\nf+zU1RGrqc+zszg35xP+lvQS9yR9xCR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ernXMcrqFukqqHNEZvqpSeHvpD3SxNgKw3KkccwyTbmyFweILO56eVqrO9lWn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\namJkH+3FO7Q2HJZ53pp1lPt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ACc8i200dVtsNWW3OZ6WdzDLTjDxTj9KGiir79zX4a5skO7nbMZXrHXP5jWq8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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Lateral case\n", + "plt.plot(mat_states['t'], mat_states['V_body'][:,1], '.', label='Simulink output')\n", + "plt.plot(results.v, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Lateral velocity\")\n", + "plt.show()\n", + "\n", + "plt.plot(mat_states['t'], mat_states['Omega_body'][:,0], '.', label='Simulink output')\n", + "plt.plot(results.p, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Roll rate\")\n", + "plt.show()\n", + "\n", + "plt.plot(mat_states['t'], mat_states['Omega_body'][:,2], '.', label='Simulink output')\n", + "plt.plot(results.r, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Yaw rate\")\n", + "plt.show()\n", + "\n", + "plt.plot(mat_states['t'], mat_states['Euler'][:,0], '.', label='Simulink output')\n", + "plt.plot(results.phi, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Heading angle\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 84e70458614b7c0acad9ad01221b5bc87be2247d Mon Sep 17 00:00:00 2001 From: jdebecdelievre Date: Mon, 4 Jun 2018 17:06:35 -0700 Subject: [PATCH 3/5] removed ipython checkpoints --- ...igenvalue problem - tests-checkpoint.ipynb | 1573 ----- .../How it works (modif)-checkpoint.ipynb | 5112 ----------------- .../How it works-checkpoint.ipynb | 938 --- 3 files changed, 7623 deletions(-) delete mode 100644 .ipynb_checkpoints/Eigenvalue problem - tests-checkpoint.ipynb delete mode 100644 .ipynb_checkpoints/How it works (modif)-checkpoint.ipynb delete mode 100644 .ipynb_checkpoints/How it works-checkpoint.ipynb diff --git a/.ipynb_checkpoints/Eigenvalue problem - tests-checkpoint.ipynb b/.ipynb_checkpoints/Eigenvalue problem - tests-checkpoint.ipynb deleted file mode 100644 index d86403e..0000000 --- a/.ipynb_checkpoints/Eigenvalue problem - tests-checkpoint.ipynb +++ /dev/null @@ -1,1573 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Python Flight Mechanics Engine " - ] - }, - { - "cell_type": "code", - "execution_count": 299, - "metadata": {}, - "outputs": [], - "source": [ - "from pyfme.aircrafts import LinearB747, SimplifiedCessna172\n", - "from pyfme.models import EulerFlatEarth\n", - "import numpy as np\n", - "nl = np.linalg\n", - "import matplotlib.pyplot as plt\n", - "from pyfme.environment.atmosphere import ISA1976\n", - "from pyfme.environment.wind import NoWind\n", - "from pyfme.environment.gravity import VerticalConstant\n", - "from pyfme.environment import Environment\n", - "from pyfme.utils.trimmer import steady_state_trim\n", - "from pyfme.models.state.position import EarthPosition\n", - "from pyfme.simulator import Simulation\n", - "from pyfme.models import EulerFlatEarth\n", - "from pyfme.models.euler_flat_earth import wind2body4attitude" - ] - }, - { - "cell_type": "code", - "execution_count": 300, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The autoreload extension is already loaded. To reload it, use:\n", - " %reload_ext autoreload\n" - ] - } - ], - "source": [ - "%load_ext autoreload\n", - "%autoreload 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Test on Boeing" - ] - }, - { - "cell_type": "code", - "execution_count": 301, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "aircraft = LinearB747()" - ] - }, - { - "cell_type": "code", - "execution_count": 302, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Aircraft mass: 288660.5504587156 kg\n", - "Aircraft inertia tensor: \n", - " [[ 24700000. 0. -2120000.]\n", - " [ 0. 44900000. 0.]\n", - " [ -2120000. 0. 67300000.]] kg/m²\n" - ] - } - ], - "source": [ - "print(f\"Aircraft mass: {aircraft.mass} kg\")\n", - "print(f\"Aircraft inertia tensor: \\n {aircraft.inertia} kg/m²\")" - ] - }, - { - "cell_type": "code", - "execution_count": 303, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "state, environment = aircraft.trimmed_conditions()" - ] - }, - { - "cell_type": "code", - "execution_count": 304, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "system = EulerFlatEarth(t0=0, full_state=state)" - ] - }, - { - "cell_type": "code", - "execution_count": 305, - "metadata": {}, - "outputs": [], - "source": [ - "A_long, A_lat = system.linearized_model(state, aircraft, environment, method=\"from_forces\")" - ] - }, - { - "cell_type": "code", - "execution_count": 306, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[ -6.86619629e-03 1.39437135e-02 0.00000000e+00 -9.80665000e+00]\n", - " [ -9.04964592e-02 -3.14906754e-01 2.35892792e+02 -0.00000000e+00]\n", - " [ 3.89092422e-04 -3.36169904e-03 -4.28171388e-01 0.00000000e+00]\n", - " [ 0.00000000e+00 0.00000000e+00 1.00000000e+00 0.00000000e+00]]\n" - ] - } - ], - "source": [ - "print(f\"{A_long}\")" - ] - }, - { - "cell_type": "code", - "execution_count": 307, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "d = aircraft.calculate_derivatives(None, None, None)" - ] - }, - { - "cell_type": "code", - "execution_count": 308, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "val, vec = nl.eig(A_long)" - ] - }, - { - "cell_type": "code", - "execution_count": 309, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([-0.37168337+0.88692454j, -0.37168337-0.88692454j,\n", - " -0.00328880+0.0671904j , -0.00328880-0.0671904j ])" - ] - }, - "execution_count": 309, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "val" - ] - }, - { - "cell_type": "code", - "execution_count": 310, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[ -5.57748538e-02 0.00000000e+00 -2.35900000e+02 9.80665000e+00]\n", - " [ -1.21578588e-02 -4.38509325e-01 3.91486496e-01 0.00000000e+00]\n", - " [ 2.78343743e-03 -3.35756281e-02 -1.20416770e-01 0.00000000e+00]\n", - " [ 0.00000000e+00 1.00000000e+00 0.00000000e+00 0.00000000e+00]]\n" - ] - } - ], - "source": [ - "print(f\"{A_lat}\")" - ] - }, - { - "cell_type": "code", - "execution_count": 311, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "val, vec = nl.eig(A_lat)" - ] - }, - { - "cell_type": "code", - "execution_count": 312, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 0.01992122+0.88015949j, 0.01992122-0.88015949j,\n", - " -0.64722566+0.j , -0.00731773+0.j ])" - ] - }, - "execution_count": 312, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "val" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Eigen values are the same as the ones in Etkin. So the matrix was copy-pasted right in EulerFlatEarth.linearize()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Simplified Cessna: compare response with eigenvalue analysis" - ] - }, - { - "cell_type": "code", - "execution_count": 313, - "metadata": {}, - "outputs": [], - "source": [ - "aircraft = SimplifiedCessna172()" - ] - }, - { - "cell_type": "code", - "execution_count": 314, - "metadata": {}, - "outputs": [], - "source": [ - "atmosphere = ISA1976()\n", - "gravity = VerticalConstant()\n", - "wind = NoWind()\n", - "environment = Environment(atmosphere, gravity, wind)" - ] - }, - { - "cell_type": "code", - "execution_count": 315, - "metadata": {}, - "outputs": [], - "source": [ - "pos = EarthPosition(x=0, y=0, height=1000)\n", - "psi = 0.5 # rad\n", - "TAS = 45 # m/s\n", - "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}\n", - "trimmed_state, trimmed_controls = steady_state_trim(\n", - " aircraft,\n", - " environment,\n", - " pos,\n", - " psi,\n", - " TAS,\n", - " controls0\n", - ")\n", - "environment.update(trimmed_state)" - ] - }, - { - "cell_type": "code", - "execution_count": 316, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Aircraft State \n", - "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", - "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", - "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", - "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", - "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", - "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " - ] - }, - "execution_count": 316, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "trimmed_state" - ] - }, - { - "cell_type": "code", - "execution_count": 317, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" - ] - }, - { - "cell_type": "code", - "execution_count": 318, - "metadata": {}, - "outputs": [], - "source": [ - "A_long, A_lat = system.linearized_model(trimmed_state, aircraft, environment, trimmed_controls, method=\"from_forces\",eps=1e-10)" - ] - }, - { - "cell_type": "code", - "execution_count": 319, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "longitudinal eigenvalues : [[-2.61284085+4.04869466j -2.61284085-4.04869466j -0.03452750+0.26286901j\n", - " -0.03452750-0.26286901j]]\n" - ] - } - ], - "source": [ - "long_val, long_vec=nl.eig(A_long)\n", - "long_val = np.expand_dims(long_val, axis = 0)\n", - "print(f\"longitudinal eigenvalues : {long_val}\")" - ] - }, - { - "cell_type": "code", - "execution_count": 320, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "def linear_stab_2_body(long_state=np.zeros(4), lat_state=np.zeros(4), u0=0, theta0=0,alpha0=0, beta0=0):\n", - " # velocities\n", - " v = wind2body(np.array([long_state[0] + u0, lat_state[0], long_state[1]]), alpha=alpha0, beta=beta0)\n", - " # Roll rates\n", - " r = wind2body(np.array([lat_state[1], long_state[2], lat_state[2]]), alpha=alpha0, beta=beta0)\n", - " # attitude\n", - " ang = wind2body4attitude(np.array([long_state[3], lat_state[3], 0]), alpha=alpha0, beta=beta0)\n", - " long_stateB = np.copy(long_state)\n", - " lat_stateB = np.copy(lat_state)\n", - " long_stateB[0] = v[0]\n", - " long_stateB[1] = v[2]\n", - " long_stateB[2] = r[1]\n", - " long_stateB[3] += theta0\n", - " lat_stateB[0] = v[1]\n", - " lat_stateB[1] = r[0]\n", - " lat_stateB[2] = r[2]\n", - " return long_stateB.real, lat_stateB.real" - ] - }, - { - "cell_type": "code", - "execution_count": 321, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Aircraft State \n", - "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", - "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", - "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", - "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", - "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", - "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " - ] - }, - "execution_count": 321, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "trimmed_state" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Longitudinal checks" - ] - }, - { - "cell_type": "code", - "execution_count": 322, - "metadata": {}, - "outputs": [], - "source": [ - "from pyfme.utils.coordinates import wind2body, body2wind" - ] - }, - { - "cell_type": "code", - "execution_count": 323, - "metadata": {}, - "outputs": [], - "source": [ - "alpha = np.arctan2(trimmed_state.velocity.w, trimmed_state.velocity.u)\n", - "u = trimmed_state.velocity.u*1.0" - ] - }, - { - "cell_type": "code", - "execution_count": 324, - "metadata": {}, - "outputs": [], - "source": [ - "perturbation = (long_vec.T[0] + long_vec.T[1])/1000" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Eigenvalue approach" - ] - }, - { - "cell_type": "code", - "execution_count": 325, - "metadata": {}, - "outputs": [], - "source": [ - "C = nl.lstsq(a=long_vec,b=perturbation.real)[0].real" - ] - }, - { - "cell_type": "code", - "execution_count": 326, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# stability axis\n", - "u, v, w = body2wind(trimmed_state.velocity.vel_body, alpha, 0)\n", - "theta0 = trimmed_state.attitude.theta*1.0" - ] - }, - { - "cell_type": "code", - "execution_count": 327, - "metadata": {}, - "outputs": [], - "source": [ - "t = np.linspace(0,3,100)\n", - "N = len(t)\n", - "X = np.zeros((N,4))\n", - "xx = []\n", - "for i in range(N):\n", - " x_stab = (long_vec*np.exp(long_val*t[i])).dot(C)\n", - " xx.append(x_stab[1])\n", - " X[i,:] = linear_stab_2_body(long_state=x_stab.real, alpha0=alpha, u0=u, theta0 = theta0)[0]" - ] - }, - { - "cell_type": "code", - "execution_count": 328, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(t,X[:,0],'.')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Simulation" - ] - }, - { - "cell_type": "code", - "execution_count": 329, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.utils.input_generator import Constant" - ] - }, - { - "cell_type": "code", - "execution_count": 330, - "metadata": {}, - "outputs": [], - "source": [ - "controls = {\n", - " 'delta_elevator': Constant(trimmed_controls['delta_elevator']),\n", - " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", - " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", - " 'delta_t': Constant(trimmed_controls['delta_t'])\n", - "}" - ] - }, - { - "cell_type": "code", - "execution_count": 331, - "metadata": {}, - "outputs": [], - "source": [ - "# Perturbate\n", - "trimmed_state.cancel_perturbation()\n", - "p = linear_stab_2_body(long_state=perturbation.real, alpha0=alpha)[0]\n", - "trimmed_state.perturbate(np.array([p[0],0,p[1]]), 'velocity')\n", - "trimmed_state.perturbate(np.array([0,p[2],0]), 'angular_vel')\n", - "trimmed_state.perturbate(np.array([p[3],0,0]), 'attitude') # /!\\ Convention theta, phi, psi" - ] - }, - { - "cell_type": "code", - "execution_count": 332, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Aircraft State \n", - "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", - "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", - "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", - "P: 0.00 rad/s, Q: -0.00 rad/s, R: 0.00 rad/s \n", - "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", - "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " - ] - }, - "execution_count": 332, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "trimmed_state" - ] - }, - { - "cell_type": "code", - "execution_count": 333, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 4.35247324e-05+0.j, 1.99016773e-03+0.j, -2.19846816e-05+0.j,\n", - " 3.52384151e-05+0.j])" - ] - }, - "execution_count": 333, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "perturbation" - ] - }, - { - "cell_type": "code", - "execution_count": 334, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ -1.15502388e-04, 1.98728991e-03, -2.19846816e-05,\n", - " 3.52384151e-05])" - ] - }, - "execution_count": 334, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "p" - ] - }, - { - "cell_type": "code", - "execution_count": 335, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "environment.update(trimmed_state)\n", - "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" - ] - }, - { - "cell_type": "code", - "execution_count": 336, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "sim = Simulation(aircraft, system, environment, controls)" - ] - }, - { - "cell_type": "code", - "execution_count": 337, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "time: 100%|████████████████████████████████████████████████████████████▉| 9.999999999999831/10 [00:07<00:00, 1.31it/s]\n" - ] - } - ], - "source": [ - "r = sim.propagate(10)" - ] - }, - { - "cell_type": "code", - "execution_count": 338, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Aircraft State \n", - "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", - "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", - "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", - "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", - "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", - "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " - ] - }, - "execution_count": 338, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "trimmed_state.cancel_perturbation()" - ] - }, - { - "cell_type": "code", - "execution_count": 339, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "2.9988658738488994e-06" - ] - }, - "execution_count": 339, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "r.u[0.01] - X[0,0]" - ] - }, - { - "cell_type": "code", - "execution_count": 340, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "-0.00045841006027558251" - ] - }, - "execution_count": 340, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "44.855900 - X[-1,0]" - ] - }, - { - "cell_type": "code", - "execution_count": 175, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(t,X[:,3],'.')\n", - "plt.plot(r.theta)\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 176, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Aircraft State \n", - "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", - "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", - "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", - "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", - "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", - "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " - ] - }, - "execution_count": 176, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "trimmed_state" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Lateral Checks" - ] - }, - { - "cell_type": "code", - "execution_count": 277, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[ -1.20869794e-01 -9.03365248e-02 -4.45371242e+01 9.80665000e+00]\n", - " [ -7.47735120e-02 -5.52245304e+00 2.23529676e+00 0.00000000e+00]\n", - " [ 2.69453703e-02 1.21841526e-01 -4.29492904e-01 0.00000000e+00]\n", - " [ 0.00000000e+00 1.00000000e+00 0.00000000e+00 0.00000000e+00]]\n" - ] - } - ], - "source": [ - "print(f\"{A_lat}\")" - ] - }, - { - "cell_type": "code", - "execution_count": 278, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "lat eigenvalues : [[-5.58724126+0.j -0.26870849+1.12020645j -0.26870849-1.12020645j\n", - " 0.05184251+0.j ]]\n" - ] - } - ], - "source": [ - "lat_val, lat_vec=nl.eig(A_lat_0)\n", - "lat_val = np.expand_dims(lat_val, axis = 0)\n", - "print(f\"lat eigenvalues : {lat_val}\")" - ] - }, - { - "cell_type": "code", - "execution_count": 279, - "metadata": {}, - "outputs": [], - "source": [ - "# # Normalize eigvec to have delta_psi=1\n", - "# delta_psi = lat_vec[2]/np.cos(theta0)\n", - "# lat_vec /= delta_psi\n", - "# print(f\"{lat_vec.T}\")" - ] - }, - { - "cell_type": "code", - "execution_count": 280, - "metadata": {}, - "outputs": [], - "source": [ - "alpha = np.arctan2(trimmed_state.velocity.w, trimmed_state.velocity.u)\n", - "V = np.sqrt(trimmed_state.velocity.w**2 + trimmed_state.velocity.v**2 + trimmed_state.velocity.u**2)\n", - "beta = np.arcsin(trimmed_state.velocity.v/V)\n", - "u = trimmed_state.velocity.u*1.0" - ] - }, - { - "cell_type": "code", - "execution_count": 281, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([[-5.58724126+0.j , -0.26870849+1.12020645j,\n", - " -0.26870849-1.12020645j, 0.05184251+0.j ]])" - ] - }, - "execution_count": 281, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "lat_val" - ] - }, - { - "cell_type": "code", - "execution_count": 282, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# perturbation = (lat_vec.T[1] + lat_vec.T[2])/1000\n", - "perturbation = (lat_vec.T[3])/10000" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Eigenvalue approach" - ] - }, - { - "cell_type": "code", - "execution_count": 283, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "C = nl.lstsq(a=lat_vec,b=perturbation.real)[0].real" - ] - }, - { - "cell_type": "code", - "execution_count": 284, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# stability axis\n", - "u, v, w = body2wind(trimmed_state.velocity.vel_body, alpha, 0)\n", - "theta0 = trimmed_state.attitude.theta*1.0" - ] - }, - { - "cell_type": "code", - "execution_count": 285, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "t = np.linspace(0,10,100)\n", - "N = len(t)\n", - "X = np.zeros((N,4))\n", - "xx = []\n", - "for i in range(N):\n", - " x_stab = (lat_vec*np.exp(lat_val*t[i])).dot(C)\n", - " xx.append(x_stab[1])\n", - " X[i,:] = linear_stab_2_body(lat_state=x_stab.real, beta0=beta, alpha0=alpha, u0=u, theta0 = theta0)[1]" - ] - }, - { - "cell_type": "code", - "execution_count": 286, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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NR96Ykp4DLgWWpj4PpHHXpXAZsRX4fM5aFwE/jog3q3hfE8Kn0czMyqsmdKYB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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(t,X[:,3],'.')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Simulation" - ] - }, - { - "cell_type": "code", - "execution_count": 287, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.utils.input_generator import Constant" - ] - }, - { - "cell_type": "code", - "execution_count": 288, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "controls = {\n", - " 'delta_elevator': Constant(trimmed_controls['delta_elevator']),\n", - " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", - " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", - " 'delta_t': Constant(trimmed_controls['delta_t'])\n", - "}" - ] - }, - { - "cell_type": "code", - "execution_count": 289, - "metadata": {}, - "outputs": [], - "source": [ - "# Perturbate\n", - "trimmed_state.cancel_perturbation()\n", - "p = linear_stab_2_body(lat_state=perturbation.real, alpha0=alpha, beta0=beta)[1]\n", - "trimmed_state.perturbate(np.array([0,p[0],0]), 'velocity')\n", - "trimmed_state.perturbate(np.array([p[1],0,p[2]]), 'angular_vel')\n", - "trimmed_state.perturbate(np.array([0,p[3],0]), 'attitude') # /!\\ Convention theta, phi, psi" - ] - }, - { - "cell_type": "code", - "execution_count": 290, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Aircraft State \n", - "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", - "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", - "u: 44.86 m/s, v: 0.00 m/s, w: 3.59 m/s \n", - "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", - "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", - "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " - ] - }, - "execution_count": 290, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "trimmed_state" - ] - }, - { - "cell_type": "code", - "execution_count": 291, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 9.60060356e-05, 5.13657549e-07, 5.67794858e-06,\n", - " 2.73923016e-05])" - ] - }, - "execution_count": 291, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "p" - ] - }, - { - "cell_type": "code", - "execution_count": 292, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "environment.update(trimmed_state)\n", - "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" - ] - }, - { - "cell_type": "code", - "execution_count": 293, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "sim = Simulation(aircraft, system, environment, controls)" - ] - }, - { - "cell_type": "code", - "execution_count": 294, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "time: 100%|████████████████████████████████████████████████████████████▉| 9.999999999999831/10 [00:06<00:00, 1.64it/s]\n" - ] - } - ], - "source": [ - "r = sim.propagate(10)" - ] - }, - { - "cell_type": "code", - "execution_count": 295, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Aircraft State \n", - "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", - "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", - "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", - "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", - "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", - "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " - ] - }, - "execution_count": 295, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "trimmed_state.cancel_perturbation()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "plt.plot(r2.r)\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 296, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(t,X[:,2],'.')\n", - "plt.plot(r.r)\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 200, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Aircraft State \n", - "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", - "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", - "u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", - "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", - "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", - "P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² " - ] - }, - "execution_count": 200, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "trimmed_state" - ] - }, - { - "cell_type": "code", - "execution_count": 201, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([[-5.54556785+0.j , -0.24930832+1.12369875j,\n", - " -0.24930832-1.12369875j, 0.03752870+0.j ]])" - ] - }, - "execution_count": 201, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "lat_val" - ] - }, - { - "cell_type": "code", - "execution_count": 202, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([ 0.43547942+0.j, 0.88576915+0.j, 0.01607544+0.j, -0.15972560+0.j])" - ] - }, - "execution_count": 202, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "lat_vec.T[0]" - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "0.0" - ] - }, - "execution_count": 43, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "trimmed_state.angular_vel." - ] - }, - { - "cell_type": "code", - "execution_count": 269, - "metadata": {}, - "outputs": [], - "source": [ - "A_long, A_lat = system.linearized_model(aircraft=aircraft, environment=environment, controls=trimmed_controls, state=trimmed_state, method='from_forces',eps=1e-5)" - ] - }, - { - "cell_type": "code", - "execution_count": 276, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "> c:\\users\\jean\\box sync\\recherche\\aeropython\\pyfme\\pyfme\\src\\pyfme\\models\\euler_flat_earth.py(240)linearized_model()\n", - "-> derivatives[keyword][i][\"acceleration\"] = (accel_p - accel_m)/eps\n", - "(Pdb) eps_vec\n", - "array([ -4.98403983e-06, 4.54327588e-19, -3.99182908e-07])\n", - "(Pdb) angle_der_p\n", - "array([ 2.90510260e-21, 5.03197145e-06, -1.27828591e-09])\n", - "(Pdb) angle_der_m\n", - "array([ -2.90510260e-21, -5.03197145e-06, 1.27828591e-09])\n", - "(Pdb) (angle_der_p - angle_der_m)/eps\n", - "array([ 5.81020520e-16, 1.00639429e+00, -2.55657183e-04])\n", - "(Pdb) body2wind4attitude(np.array([ 5.81020520e-16, 1.00639429e+00, -2.55657183e-04]), alpha,0)\n", - "array([ 5.81020520e-16, 1.00316143e+00, -8.06019209e-02])\n", - "(Pdb) body2wind(np.array([ 5.81020520e-16, 1.00639429e+00, -2.55657183e-04]), alpha,0)\n", - "array([ -2.04107955e-05, 1.00639429e+00, -2.54841116e-04])\n", - "(Pdb) body2wind(np.array([ 5.81020520e-16, -2.55657183e-04, 1.00639429e+00]), alpha,0)\n", - "array([ 8.03470798e-02, -2.55657183e-04, 1.00318184e+00])\n", - "(Pdb) body2wind(np.array([1.00639429e+00, 5.81020520e-16, -2.55657183e-04]), alpha,0)\n", - "array([ 1.00316143e+00, 5.81020520e-16, -8.06019209e-02])\n", - "(Pdb) body2wind4attitude(np.array([ 5.81020520e-16, 1.00639429e+00, -2.55657183e-04]), alpha,0)\n", - "array([ 5.81020520e-16, 1.00316143e+00, -8.06019209e-02])\n", - "(Pdb) body2wind4attitude(np.array([ 5.81020520e-16, 1.00316143e+00, -8.06019209e-02]), alpha,0)\n", - "array([ 5.81020520e-16, 9.93524322e-01, -1.60433616e-01])\n", - "(Pdb) q\n" - ] - }, - { - "ename": "BdbQuit", - "evalue": "", - "output_type": "error", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[1;31mBdbQuit\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mA_long_0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mA_lat_0\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msystem\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlinearized_model\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0maircraft\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0maircraft\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0menvironment\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0menvironment\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcontrols\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mtrimmed_controls\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstate\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mtrimmed_state\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'direct'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0meps\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1e-5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", - "\u001b[1;32mc:\\users\\jean\\box sync\\recherche\\aeropython\\pyfme\\pyfme\\src\\pyfme\\models\\euler_flat_earth.py\u001b[0m in \u001b[0;36mlinearized_model\u001b[1;34m(self, state, aircraft, environment, controls, method, eps)\u001b[0m\n\u001b[0;32m 238\u001b[0m \u001b[0mpdb\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mset_trace\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 239\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 240\u001b[1;33m \u001b[0mderivatives\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mkeyword\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m\"acceleration\"\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m 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\u001b[1;34m'call'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 50\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdispatch_call\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mframe\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0marg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\bdb.py\u001b[0m in \u001b[0;36mdispatch_line\u001b[1;34m(self, frame)\u001b[0m\n\u001b[0;32m 65\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstop_here\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mframe\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mbreak_here\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mframe\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 66\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0muser_line\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mframe\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 67\u001b[1;33m \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mquitting\u001b[0m\u001b[1;33m:\u001b[0m \u001b[1;32mraise\u001b[0m \u001b[0mBdbQuit\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 68\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtrace_dispatch\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;31mBdbQuit\u001b[0m: " - ] - } - ], - "source": [ - "A_long_0, A_lat_0 = system.linearized_model(aircraft=aircraft, environment=environment, controls=trimmed_controls, state=trimmed_state, method='direct',eps=1e-5)" - ] - }, - { - "cell_type": "code", - "execution_count": 271, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - 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"output_type": "execute_result" - } - ], - "source": [ - "A_lat" - ] - }, - { - "cell_type": "code", - "execution_count": 234, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([[ -1.38777878e-17, -8.18789481e-16, 7.10542736e-15,\n", - " -6.25064079e-02],\n", - " [ -1.38777878e-17, 8.88178420e-16, -4.44089210e-16,\n", - " 0.00000000e+00],\n", - " [ -6.93889390e-18, 8.32667268e-17, 1.11022302e-16,\n", - " 0.00000000e+00],\n", - " [ 0.00000000e+00, -6.39429055e-03, -7.98365815e-02,\n", - " 0.00000000e+00]])" - ] - }, - "execution_count": 234, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "A_lat_0 - A_lat" - ] - }, - { - "cell_type": "code", - "execution_count": 273, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([[ 0.00000000e+00, 2.77555756e-17, 1.03506245e-01,\n", - " -3.16067172e-11],\n", - " [ -5.55111512e-17, 4.44089210e-16, 1.42108547e-14,\n", - " 4.71280662e-11],\n", - " [ 9.50501660e-24, 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'Zw_dot': 0.0}" - ] - }, - "execution_count": 273, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "aircraft.calculate_derivatives(trimmed_state, environment, trimmed_controls)" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/.ipynb_checkpoints/How it works (modif)-checkpoint.ipynb b/.ipynb_checkpoints/How it works (modif)-checkpoint.ipynb deleted file mode 100644 index 7557a20..0000000 --- a/.ipynb_checkpoints/How it works (modif)-checkpoint.ipynb +++ /dev/null @@ -1,5112 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Python Flight Mechanics Engine " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Aircraft " - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "import pyfme\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from scipy import stats" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "%load_ext autoreload\n", - "%autoreload 2" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.aircrafts import SimplifiedCessna172, Cessna172" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "aircraft = SimplifiedCessna172()" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "ename": "AttributeError", - "evalue": "'SimplifiedCessna172' object has no attribute 'full_state'", - "output_type": "error", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[1;31mAttributeError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0maircraft\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfull_state\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", - "\u001b[1;31mAttributeError\u001b[0m: 'SimplifiedCessna172' object has no attribute 'full_state'" - ] - } - ], - "source": [ - "aircraft.full_state" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Aircraft will provide the simulator the forces, moments and inertial properties in order to perform the integration of the dynamic system equations:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "print(f\"Aircraft mass: {aircraft.mass} kg\")\n", - "print(f\"Aircraft inertia tensor: \\n {aircraft.inertia} kg/m²\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "print(f\"forces: {aircraft.total_forces} N\")\n", - "print(f\"moments: {aircraft.total_moments} N·m\")" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Stability Derivatives : \n", - "CL_0 = 0.148;\n", - "CM_0 = 0.012068670774609398;\n", - "CL_alpha = 5.44;\n", - "CL_q = 7.281999999999999;\n", - "CL_delta_elev = 0.005677366997294861;\n", - "CM_alpha2 = -0.0008829539354397849;\n", - "CM_alpha = -0.01230758597735665;\n", - "CM_q = -12.464;\n", - "CM_delta_elev = -0.014180595130748421;\n", - "CD_K1 = 0.04394233763124108;\n", - "CD_0 = 0.029537580994030695;\n", - "CL_MAX = 1.889;\n", - "CY_beta = -0.26799999999999996;\n", - "CY_p = -0.05993333333333333;\n", - "CY_r = 0.2143333333333333;\n", - "CY_delta_rud = -0.561;\n", - "Cl_beta = -0.022292500000000003;\n", - "Cl_p = -0.3025083333333333;\n", - "Cl_r_cl = 0.17341925931518656;\n", - "Cl_delta_rud = -0.0027193749999999996;\n", - "Cl_delta_aile = 0.0044410237288135595;\n", - "CN_beta = 0.0126;\n", - "CN_p_al = -0.007206294994140298;\n", - "CN_r_cl = -0.00957535593543321;\n", - "CN_r_0 = -0.027354917660317425;\n", - "CN_delta_rud = 0.016818749999999997;\n", - "CN_delta_aile_cl = -0.0004745447361550377;\n" - ] - } - ], - "source": [ - "print(\"Stability Derivatives : \")\n", - "for k,val in aircraft.__dict__.items():\n", - " if k.startswith('C') and \"data\" not in k and \"_\" in k:\n", - " print(f\"{k} = {val};\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "For the aircraft, in order to calculate its forces and moments it is necessary to set the controls values within the limits: " - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0}\n" - ] - } - ], - "source": [ - "print(aircraft.controls)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'delta_elevator': (-0.4537856055185257, 0.48869219055841229), 'delta_aileron': (-0.26179938779914941, 0.3490658503988659), 'delta_rudder': (-0.27925268031909273, 0.27925268031909273), 'delta_t': (0, 1)}\n" - ] - } - ], - "source": [ - "print(aircraft.control_limits)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "but also to provide and environment (ie. atmosphere, winds, gravity) and the aircraft state, which will also determine the aerodynamic contribution." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Environment " - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.environment.atmosphere import ISA1976\n", - "from pyfme.environment.wind import NoWind\n", - "from pyfme.environment.gravity import VerticalConstant" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "atmosphere = ISA1976()\n", - "gravity = VerticalConstant()\n", - "wind = NoWind()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The atmosphere, wind and gravity model make up the environment:" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.environment import Environment" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "environment = Environment(atmosphere, gravity, wind)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The environment has an update method which given the state (ie. position, altitude...) updates the environment variables (ie. density, wind magnitude, gravity force...)" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Help on method update in module pyfme.environment.environment:\n", - "\n", - "update(state) method of pyfme.environment.environment.Environment instance\n", - "\n" - ] - } - ], - "source": [ - "help(environment.update)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## State " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Even if the state can be set manually by giving the position, attitude, velocity, angular velocities... Most of the times, the user will want to trim the aircraft in a stationary condition. The aircraft controls to flight in that condition will be also provided by the trimmer." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.utils.trimmer import steady_state_trim" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Help on function steady_state_trim in module pyfme.utils.trimmer:\n", - "\n", - "steady_state_trim(aircraft, environment, pos, psi, TAS, controls, gamma=0, turn_rate=0, exclude=None, verbose=0)\n", - " Finds a combination of values of the state and control variables\n", - " that correspond to a steady-state flight condition.\n", - " \n", - " Steady-state aircraft flight is defined as a condition in which all\n", - " of the motion variables are constant or zero. That is, the linear and\n", - " angular velocity components are constant (or zero), thus all\n", - " acceleration components are zero.\n", - " \n", - " Parameters\n", - " ----------\n", - " aircraft : Aircraft\n", - " Aircraft to be trimmed.\n", - " environment : Environment\n", - " Environment where the aircraft is trimmed including atmosphere,\n", - " gravity and wind.\n", - " pos : Position\n", - " Initial position of the aircraft.\n", - " psi : float, opt\n", - " Initial yaw angle (rad).\n", - " TAS : float\n", - " True Air Speed (m/s).\n", - " controls : dict\n", - " Initial value guess for each control or fixed value if control is\n", - " included in exclude.\n", - " gamma : float, optional\n", - " Flight path angle (rad).\n", - " turn_rate : float, optional\n", - " Turn rate, d(psi)/dt (rad/s).\n", - " exclude : list, optional\n", - " List with controls not to be trimmed. If not given, every control\n", - " is considered in the trim process.\n", - " verbose : {0, 1, 2}, optional\n", - " Level of least_squares verbosity:\n", - " * 0 (default) : work silently.\n", - " * 1 : display a termination report.\n", - " * 2 : display progress during iterations (not supported by 'lm'\n", - " method).\n", - " \n", - " Returns\n", - " -------\n", - " state : AircraftState\n", - " Trimmed aircraft state.\n", - " trimmed_controls : dict\n", - " Trimmed aircraft controls\n", - " \n", - " Notes\n", - " -----\n", - " See section 3.4 in [1] for the algorithm description.\n", - " See section 2.5 in [1] for the definition of steady-state flight\n", - " condition.\n", - " \n", - " References\n", - " ----------\n", - " .. [1] Stevens, BL and Lewis, FL, \"Aircraft Control and Simulation\",\n", - " Wiley-lnterscience.\n", - "\n" - ] - } - ], - "source": [ - "help(steady_state_trim)" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.models.state.position import EarthPosition" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "pos = EarthPosition(x=0, y=0, height=1000)\n", - "psi = 0.5 # rad\n", - "TAS = 45 # m/s\n", - "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "trimmed_state, trimmed_controls = steady_state_trim(\n", - " aircraft,\n", - " environment,\n", - " pos,\n", - " psi,\n", - " TAS,\n", - " controls0\n", - ") " - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Aircraft State \n", - "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", - "theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", - "u: 44.86 m/s, v: 0.00 m/s, w: 3.61 m/s \n", - "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", - "u_dot: -0.80 m/s², v_dot: 0.00 m/s², w_dot: -0.80 m/s² \n", - "P_dot: -0.00 rad/s², Q_dot: 0.00 rad/s², R_dot: 0.00 rad/s² " - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "trimmed_state" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{'delta_aileron': 4.8196779769121189e-07,\n", - " 'delta_elevator': -0.077707734980732135,\n", - " 'delta_rudder': -3.746264248090009e-06,\n", - " 'delta_t': 4.2875481736583809e-17}" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "trimmed_controls" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now, all the necessary elements in order to calculate forces and moments are available " - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# Environment conditions for the current state:\n", - "environment.update(trimmed_state)\n", - "\n", - "# Forces and moments calculation:\n", - "forces, moments = aircraft.calculate_forces_and_moments(trimmed_state, environment, controls0)" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "NDIM forces : \n", - "CL : 0.5590400736551502\n", - "CD : 0.043270695389780164\n", - "Cm : 0\n", - "CY : 5.022312452897911e-07\n", - "Cl : -2.164295485216534e-10\n", - "Cn : 0\n", - "Ct : 0\n", - "CAS : 42.87850158964442\n", - "CM : 3.8407025219899804e-07\n", - "CN : 4.86337495461688e-09\n" - ] - } - ], - "source": [ - "print(\"NDIM forces : \")\n", - "for k,val in aircraft.__dict__.items():\n", - " if k.startswith('C') and \"data\" not in k and \"_\" not in k:\n", - " print(f\"{k} : {val}\")" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(array([ -8.33931929e+02, 4.44894756e-03, -2.59679525e+01]),\n", - " array([ -4.30622210e-05, 1.04593235e-02, 9.67648497e-04]))" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "forces, moments" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The aircraft is trimmed indeed: the total forces and moments (aerodynamics + gravity + thrust) are zero" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Simulation " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In order to simulate the dynamics of the aircraft under certain inputs in an environment, the user can set up a simulation using a dynamic system:" - ] - }, - { - "cell_type": "code", - "execution_count": 739, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.models import EulerFlatEarth" - ] - }, - { - "cell_type": "code", - "execution_count": 740, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Constant Controls " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values." - ] - }, - { - "cell_type": "code", - "execution_count": 741, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.utils.input_generator import Constant" - ] - }, - { - "cell_type": "code", - "execution_count": 742, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "controls = {\n", - " 'delta_elevator': Constant(trimmed_controls['delta_elevator']),\n", - " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", - " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", - " 'delta_t': Constant(trimmed_controls['delta_t'])\n", - "}" - ] - }, - { - "cell_type": "code", - "execution_count": 743, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.simulator import Simulation" - ] - }, - { - "cell_type": "code", - "execution_count": 744, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "sim = Simulation(aircraft, system, environment, controls)" - ] - }, - { - "cell_type": "code", - "execution_count": 745, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "system = EulerFlatEarth(t0=0, full_state=trimmed_state)\n", - "sim = Simulation(aircraft, system, environment, controls)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Once the simulation is set, the propagation can be performed:" - ] - }, - { - "cell_type": "code", - "execution_count": 767, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "\n", - "\n", - "time: 10.0it [00:00, ?it/s]\n", - "\n" - ] - } - ], - "source": [ - "results = sim.propagate(5)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The results are returned in a DataFrame:" - ] - }, - { - "cell_type": "code", - "execution_count": 747, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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FxFyFzMachMxMyMzTASaaileron...thrustuvv_downv_eastv_northwx_earthy_earthz_earth
time
0.011.546141e-111.688011e-160.000000e+000.133756-3.667941e-13-1.355845e-11-1.585097e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.511938e-154.440892e-1621.57414939.4912153.3964640.3949120.215741-1000.0
0.021.546141e-115.250914e-170.000000e+000.133756-3.506913e-13-1.314636e-11-1.347614e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.512042e-154.440892e-1621.57414939.4912153.3964640.7898240.431483-1000.0
0.031.546141e-11-3.441253e-160.000000e+000.133756-3.352723e-13-1.274679e-11-1.121474e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.512218e-154.440892e-1621.57414939.4912153.3964641.1847360.647224-1000.0
0.041.546141e-11-1.008065e-150.000000e+000.133756-3.205078e-13-1.235936e-11-9.062203e-1545.0336.434581-9.644866e-18...0.57799744.87164-3.512470e-154.440892e-1621.57414939.4912153.3964641.5796490.862966-1000.0
0.051.546141e-11-1.926832e-150.000000e+000.133756-3.063696e-13-1.198371e-11-7.014180e-1545.0336.434581-9.644866e-18...0.57799744.87164-3.512798e-154.440892e-1621.57414939.4912153.3964641.9745611.078707-1000.0
0.061.546141e-11-3.088483e-150.000000e+000.133756-2.928307e-13-1.161948e-11-5.066498e-1545.0336.434581-9.644866e-18...0.57799744.87164-3.513206e-154.440892e-1621.57414939.4912153.3964642.3694731.294449-1000.0
0.071.534772e-11-4.481585e-151.818989e-120.133756-2.798654e-13-1.126632e-11-3.215162e-1545.0336.434581-9.644866e-18...0.57799744.87164-3.513695e-154.440892e-1621.57414939.4912153.3964642.7643851.510190-1000.0
0.081.534772e-11-6.095197e-151.818989e-120.133756-2.674490e-13-1.092389e-11-1.456347e-1545.0336.434581-9.644866e-18...0.57799744.87164-3.514266e-154.440892e-1621.57414939.4912153.3964643.1592971.725932-1000.0
0.091.534772e-11-7.918846e-151.818989e-120.133756-2.555579e-13-1.059187e-112.136113e-1645.0336.434581-9.644866e-18...0.57799744.87164-3.514923e-150.000000e+0021.57414939.4912153.3964643.5542091.941673-1000.0
0.101.523404e-11-9.948167e-153.637979e-120.133756-2.441994e-13-9.889790e-121.798616e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.515665e-15-4.440892e-1621.57414939.4912153.3964643.9491222.157415-1000.0
0.111.489298e-11-1.213353e-145.456968e-120.133756-2.331439e-13-9.209049e-122.315148e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.516503e-15-8.881784e-1621.57414939.4912153.3964644.3440342.373156-1000.0
0.121.512035e-11-1.448774e-145.456968e-120.133756-2.225089e-13-8.548998e-122.316617e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.517460e-15-8.881784e-1621.57414939.4912153.3964644.7389462.588898-1000.0
0.131.523404e-11-1.701269e-145.456968e-120.133756-2.123358e-13-8.289160e-122.445525e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.518540e-15-4.440892e-1621.57414939.4912153.3964645.1338582.804639-1000.0
0.141.523404e-11-1.969178e-147.275958e-120.133756-2.025612e-13-7.664615e-123.206469e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.519743e-15-4.440892e-1621.57414939.4912153.3964645.5287703.020381-1000.0
0.151.568878e-11-2.252049e-141.273293e-110.133756-1.931933e-13-7.059053e-122.645450e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.521077e-150.000000e+0021.57414939.4912153.3964645.9236823.236122-1000.0
0.161.580247e-11-2.549911e-141.273293e-110.133756-1.842518e-13-6.844501e-122.752624e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.522536e-150.000000e+0021.57414939.4912153.3964646.3185943.451864-1000.0
0.171.557510e-11-2.861302e-141.637090e-110.133756-1.756801e-13-6.263865e-122.954086e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.524120e-150.000000e+0021.57414939.4912153.3964646.7135073.667605-1000.0
0.181.557510e-11-3.185448e-141.818989e-110.133756-1.674601e-13-5.700878e-123.081479e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.525830e-154.440892e-1621.57414939.4912153.3964647.1084193.883347-1000.0
0.191.557510e-11-3.522797e-141.818989e-110.133756-1.596367e-13-4.782397e-121.923424e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.527666e-154.440892e-1621.57414939.4912153.3964647.5033314.099088-1000.0
0.201.568878e-11-3.873125e-141.818989e-110.133756-1.522040e-13-4.637041e-122.008599e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.529612e-158.881784e-1621.57414939.4912153.3964647.8982434.314830-1000.0
0.211.568878e-11-4.234649e-141.818989e-110.133756-1.450822e-13-4.496103e-122.088193e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.531666e-158.881784e-1621.57414939.4912153.3964648.2931554.530571-1000.0
0.221.546141e-11-4.605667e-142.182787e-110.133756-1.382001e-13-3.986845e-123.475211e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.533831e-158.881784e-1621.57414939.4912153.3964648.6880674.746313-1000.0
0.231.568878e-11-4.985191e-142.182787e-110.133756-1.315377e-13-3.865669e-123.540318e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.536124e-151.332268e-1521.57414939.4912153.3964649.0829804.962054-1000.0
0.241.568878e-11-5.373557e-142.182787e-110.133756-1.251340e-13-3.375572e-124.004200e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.538548e-151.332268e-1521.57414939.4912153.3964649.4778925.177796-1000.0
0.251.568878e-11-5.770391e-142.364686e-110.133756-1.189899e-13-2.900371e-123.721343e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.541109e-151.776357e-1521.57414939.4912153.3964649.8728045.393537-1000.0
0.261.557510e-11-6.175787e-142.546585e-110.133756-1.131234e-13-2.439613e-123.636619e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.543804e-151.776357e-1521.57414939.4912153.39646410.2677165.609279-1000.0
0.271.580247e-11-6.588990e-142.546585e-110.133756-1.075064e-13-2.365464e-123.682321e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.546629e-151.776357e-1521.57414939.4912153.39646410.6626285.825020-1000.0
0.281.568878e-11-7.008588e-142.728484e-110.133756-1.020786e-13-1.920964e-124.699768e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.549585e-152.220446e-1521.57414939.4912153.39646411.0575406.040762-1000.0
0.291.557510e-11-7.434394e-142.910383e-110.133756-9.685431e-14-1.489974e-124.060594e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.552685e-152.220446e-1521.57414939.4912153.39646411.4524526.256503-1000.0
0.301.568878e-11-7.867110e-142.910383e-110.133756-9.187934e-14-1.444688e-124.092412e-1445.0336.434581-9.644866e-18...0.57799744.87164-3.555922e-152.664535e-1521.57414939.4912153.39646411.8473656.472245-1000.0
..................................................................
9.711.479066e-10-5.311047e-124.729372e-110.133756-4.807148e-151.651500e-25-3.956346e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.664932e-155.875300e-1321.57414939.4912153.396464383.459700209.484989-1000.0
9.721.480203e-10-5.318273e-124.729372e-110.133756-4.794496e-151.597792e-25-3.952250e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.666790e-155.884182e-1321.57414939.4912153.396464383.854613209.700731-1000.0
9.731.482476e-10-5.325504e-124.729372e-110.133756-4.781638e-151.544085e-25-3.948197e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.668652e-155.888623e-1321.57414939.4912153.396464384.249525209.916472-1000.0
9.741.483613e-10-5.332739e-124.729372e-110.133756-4.768578e-151.503805e-25-3.944187e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.670518e-155.897505e-1321.57414939.4912153.396464384.644437210.132214-1000.0
9.751.484750e-10-5.339978e-124.729372e-110.133756-4.755319e-151.463524e-25-3.940220e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.672389e-155.901946e-1321.57414939.4912153.396464385.039349210.347955-1000.0
9.761.485887e-10-5.347222e-124.729372e-110.133756-4.741864e-151.409817e-25-3.936298e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.674264e-155.906386e-1321.57414939.4912153.396464385.434261210.563697-1000.0
9.771.488161e-10-5.354470e-124.729372e-110.133756-4.728216e-151.369536e-25-3.932421e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.676144e-155.915268e-1321.57414939.4912153.396464385.829173210.779438-1000.0
9.781.489298e-10-5.361722e-124.729372e-110.133756-4.714378e-151.315829e-25-3.928590e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.678028e-155.919709e-1321.57414939.4912153.396464386.224085210.995180-1000.0
9.791.490434e-10-5.368978e-124.729372e-110.133756-4.700354e-151.275549e-25-3.924805e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.679916e-155.928591e-1321.57414939.4912153.396464386.618998211.210921-1000.0
9.801.491571e-10-5.376239e-124.729372e-110.133756-4.686147e-151.248695e-25-3.921066e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.681810e-155.933032e-1321.57414939.4912153.396464387.013910211.426663-1000.0
9.811.493845e-10-5.383504e-124.729372e-110.133756-4.671759e-151.208414e-25-3.917374e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.683708e-155.937473e-1321.57414939.4912153.396464387.408822211.642404-1000.0
9.821.494982e-10-5.390773e-124.729372e-110.133756-4.657195e-151.181561e-25-3.913730e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.685612e-155.946355e-1321.57414939.4912153.396464387.803734211.858146-1000.0
9.831.496119e-10-5.398046e-124.729372e-110.133756-4.642458e-151.154707e-25-3.910134e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.687520e-155.950795e-1321.57414939.4912153.396464388.198646212.073887-1000.0
9.841.497256e-10-5.405323e-124.911271e-110.133756-4.627550e-151.114427e-25-3.906587e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.689434e-155.964118e-1321.57414939.4912153.396464388.593558212.289628-1000.0
9.851.498393e-10-5.412605e-124.911271e-110.133756-4.612476e-151.074146e-25-3.903089e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.691353e-155.968559e-1321.57414939.4912153.396464388.988471212.505370-1000.0
9.861.498393e-10-5.419890e-124.911271e-110.133756-4.597238e-151.047292e-25-3.899641e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.693277e-155.968559e-1321.57414939.4912153.396464389.383383212.721111-1000.0
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9.901.504077e-10-5.449072e-124.911271e-110.133756-4.534714e-159.130242e-26-3.886355e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.701029e-155.995204e-1321.57414939.4912153.396464390.963031213.584077-1000.0
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9.931.508624e-10-5.471000e-124.911271e-110.133756-4.486263e-158.324632e-26-3.876934e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.706904e-156.012968e-1321.57414939.4912153.396464392.147768214.231302-1000.0
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9.961.514309e-10-5.492963e-124.911271e-110.133756-4.436576e-157.653291e-26-3.867993e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.712834e-156.030731e-1321.57414939.4912153.396464393.332504214.878526-1000.0
9.971.515446e-10-5.500291e-124.911271e-110.133756-4.419754e-157.519023e-26-3.865121e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.714823e-156.035172e-1321.57414939.4912153.396464393.727416215.094268-1000.0
9.981.516582e-10-5.507624e-124.911271e-110.133756-4.402808e-157.250486e-26-3.862304e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.716819e-156.044054e-1321.57414939.4912153.396464394.122329215.310009-1000.0
9.991.517719e-10-5.514960e-124.911271e-110.133756-4.385742e-157.116218e-26-3.859542e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.718821e-156.048495e-1321.57414939.4912153.396464394.517241215.525751-1000.0
10.001.519993e-10-5.522300e-124.911271e-110.133756-4.368557e-156.847682e-26-3.856835e-1445.0336.434581-9.644866e-18...0.57799744.87164-6.720829e-156.057377e-1321.57414939.4912153.396464394.912153215.741492-1000.0
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1000 rows × 35 columns

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" - ], - "text/plain": [ - " Fx Fy Fz Mach Mx \\\n", - "time \n", - "0.01 1.546141e-11 1.688011e-16 0.000000e+00 0.133756 -3.667941e-13 \n", - "0.02 1.546141e-11 5.250914e-17 0.000000e+00 0.133756 -3.506913e-13 \n", - "0.03 1.546141e-11 -3.441253e-16 0.000000e+00 0.133756 -3.352723e-13 \n", - "0.04 1.546141e-11 -1.008065e-15 0.000000e+00 0.133756 -3.205078e-13 \n", - "0.05 1.546141e-11 -1.926832e-15 0.000000e+00 0.133756 -3.063696e-13 \n", - "0.06 1.546141e-11 -3.088483e-15 0.000000e+00 0.133756 -2.928307e-13 \n", - "0.07 1.534772e-11 -4.481585e-15 1.818989e-12 0.133756 -2.798654e-13 \n", - "0.08 1.534772e-11 -6.095197e-15 1.818989e-12 0.133756 -2.674490e-13 \n", - "0.09 1.534772e-11 -7.918846e-15 1.818989e-12 0.133756 -2.555579e-13 \n", - "0.10 1.523404e-11 -9.948167e-15 3.637979e-12 0.133756 -2.441994e-13 \n", - "0.11 1.489298e-11 -1.213353e-14 5.456968e-12 0.133756 -2.331439e-13 \n", - "0.12 1.512035e-11 -1.448774e-14 5.456968e-12 0.133756 -2.225089e-13 \n", - "0.13 1.523404e-11 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"9.79 1.490434e-10 -5.368978e-12 4.729372e-11 0.133756 -4.700354e-15 \n", - "9.80 1.491571e-10 -5.376239e-12 4.729372e-11 0.133756 -4.686147e-15 \n", - "9.81 1.493845e-10 -5.383504e-12 4.729372e-11 0.133756 -4.671759e-15 \n", - "9.82 1.494982e-10 -5.390773e-12 4.729372e-11 0.133756 -4.657195e-15 \n", - "9.83 1.496119e-10 -5.398046e-12 4.729372e-11 0.133756 -4.642458e-15 \n", - "9.84 1.497256e-10 -5.405323e-12 4.911271e-11 0.133756 -4.627550e-15 \n", - "9.85 1.498393e-10 -5.412605e-12 4.911271e-11 0.133756 -4.612476e-15 \n", - "9.86 1.498393e-10 -5.419890e-12 4.911271e-11 0.133756 -4.597238e-15 \n", - "9.87 1.500666e-10 -5.427180e-12 4.911271e-11 0.133756 -4.581839e-15 \n", - "9.88 1.501803e-10 -5.434473e-12 4.911271e-11 0.133756 -4.566283e-15 \n", - "9.89 1.502940e-10 -5.441771e-12 4.911271e-11 0.133756 -4.550574e-15 \n", - "9.90 1.504077e-10 -5.449072e-12 4.911271e-11 0.133756 -4.534714e-15 \n", - "9.91 1.506351e-10 -5.456378e-12 4.911271e-11 0.133756 -4.518707e-15 \n", - "9.92 1.507487e-10 -5.463687e-12 4.911271e-11 0.133756 -4.502555e-15 \n", - "9.93 1.508624e-10 -5.471000e-12 4.911271e-11 0.133756 -4.486263e-15 \n", - "9.94 1.509761e-10 -5.478317e-12 4.911271e-11 0.133756 -4.469834e-15 \n", - "9.95 1.510898e-10 -5.485638e-12 4.911271e-11 0.133756 -4.453270e-15 \n", - "9.96 1.514309e-10 -5.492963e-12 4.911271e-11 0.133756 -4.436576e-15 \n", - "9.97 1.515446e-10 -5.500291e-12 4.911271e-11 0.133756 -4.419754e-15 \n", - "9.98 1.516582e-10 -5.507624e-12 4.911271e-11 0.133756 -4.402808e-15 \n", - "9.99 1.517719e-10 -5.514960e-12 4.911271e-11 0.133756 -4.385742e-15 \n", - "10.00 1.519993e-10 -5.522300e-12 4.911271e-11 0.133756 -4.368557e-15 \n", - "\n", - " My Mz TAS a aileron ... \\\n", - "time ... \n", - "0.01 -1.355845e-11 -1.585097e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.02 -1.314636e-11 -1.347614e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.03 -1.274679e-11 -1.121474e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.04 -1.235936e-11 -9.062203e-15 45.0 336.434581 -9.644866e-18 ... \n", - "0.05 -1.198371e-11 -7.014180e-15 45.0 336.434581 -9.644866e-18 ... \n", - "0.06 -1.161948e-11 -5.066498e-15 45.0 336.434581 -9.644866e-18 ... \n", - "0.07 -1.126632e-11 -3.215162e-15 45.0 336.434581 -9.644866e-18 ... \n", - "0.08 -1.092389e-11 -1.456347e-15 45.0 336.434581 -9.644866e-18 ... \n", - "0.09 -1.059187e-11 2.136113e-16 45.0 336.434581 -9.644866e-18 ... \n", - "0.10 -9.889790e-12 1.798616e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.11 -9.209049e-12 2.315148e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.12 -8.548998e-12 2.316617e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.13 -8.289160e-12 2.445525e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.14 -7.664615e-12 3.206469e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.15 -7.059053e-12 2.645450e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.16 -6.844501e-12 2.752624e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.17 -6.263865e-12 2.954086e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.18 -5.700878e-12 3.081479e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.19 -4.782397e-12 1.923424e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.20 -4.637041e-12 2.008599e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.21 -4.496103e-12 2.088193e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.22 -3.986845e-12 3.475211e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.23 -3.865669e-12 3.540318e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.24 -3.375572e-12 4.004200e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.25 -2.900371e-12 3.721343e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.26 -2.439613e-12 3.636619e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.27 -2.365464e-12 3.682321e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.28 -1.920964e-12 4.699768e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.29 -1.489974e-12 4.060594e-14 45.0 336.434581 -9.644866e-18 ... \n", - "0.30 -1.444688e-12 4.092412e-14 45.0 336.434581 -9.644866e-18 ... \n", - "... ... ... ... ... ... ... \n", - "9.71 1.651500e-25 -3.956346e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.72 1.597792e-25 -3.952250e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.73 1.544085e-25 -3.948197e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.74 1.503805e-25 -3.944187e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.75 1.463524e-25 -3.940220e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.76 1.409817e-25 -3.936298e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.77 1.369536e-25 -3.932421e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.78 1.315829e-25 -3.928590e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.79 1.275549e-25 -3.924805e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.80 1.248695e-25 -3.921066e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.81 1.208414e-25 -3.917374e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.82 1.181561e-25 -3.913730e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.83 1.154707e-25 -3.910134e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.84 1.114427e-25 -3.906587e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.85 1.074146e-25 -3.903089e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.86 1.047292e-25 -3.899641e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.87 1.007012e-25 -3.896243e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.88 9.801583e-26 -3.892896e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.89 9.533047e-26 -3.889600e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.90 9.130242e-26 -3.886355e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.91 8.861705e-26 -3.883162e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.92 8.458901e-26 -3.880022e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.93 8.324632e-26 -3.876934e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.94 8.056096e-26 -3.873900e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.95 7.921828e-26 -3.870920e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.96 7.653291e-26 -3.867993e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.97 7.519023e-26 -3.865121e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.98 7.250486e-26 -3.862304e-14 45.0 336.434581 -9.644866e-18 ... \n", - "9.99 7.116218e-26 -3.859542e-14 45.0 336.434581 -9.644866e-18 ... \n", - "10.00 6.847682e-26 -3.856835e-14 45.0 336.434581 -9.644866e-18 ... \n", - "\n", - " thrust u v v_down v_east v_north \\\n", - "time \n", - "0.01 0.577997 44.87164 -3.511938e-15 4.440892e-16 21.574149 39.491215 \n", - "0.02 0.577997 44.87164 -3.512042e-15 4.440892e-16 21.574149 39.491215 \n", - "0.03 0.577997 44.87164 -3.512218e-15 4.440892e-16 21.574149 39.491215 \n", - "0.04 0.577997 44.87164 -3.512470e-15 4.440892e-16 21.574149 39.491215 \n", - "0.05 0.577997 44.87164 -3.512798e-15 4.440892e-16 21.574149 39.491215 \n", - "0.06 0.577997 44.87164 -3.513206e-15 4.440892e-16 21.574149 39.491215 \n", - "0.07 0.577997 44.87164 -3.513695e-15 4.440892e-16 21.574149 39.491215 \n", - "0.08 0.577997 44.87164 -3.514266e-15 4.440892e-16 21.574149 39.491215 \n", - "0.09 0.577997 44.87164 -3.514923e-15 0.000000e+00 21.574149 39.491215 \n", - "0.10 0.577997 44.87164 -3.515665e-15 -4.440892e-16 21.574149 39.491215 \n", - "0.11 0.577997 44.87164 -3.516503e-15 -8.881784e-16 21.574149 39.491215 \n", - "0.12 0.577997 44.87164 -3.517460e-15 -8.881784e-16 21.574149 39.491215 \n", - "0.13 0.577997 44.87164 -3.518540e-15 -4.440892e-16 21.574149 39.491215 \n", - "0.14 0.577997 44.87164 -3.519743e-15 -4.440892e-16 21.574149 39.491215 \n", - "0.15 0.577997 44.87164 -3.521077e-15 0.000000e+00 21.574149 39.491215 \n", - "0.16 0.577997 44.87164 -3.522536e-15 0.000000e+00 21.574149 39.491215 \n", - "0.17 0.577997 44.87164 -3.524120e-15 0.000000e+00 21.574149 39.491215 \n", - "0.18 0.577997 44.87164 -3.525830e-15 4.440892e-16 21.574149 39.491215 \n", - "0.19 0.577997 44.87164 -3.527666e-15 4.440892e-16 21.574149 39.491215 \n", - "0.20 0.577997 44.87164 -3.529612e-15 8.881784e-16 21.574149 39.491215 \n", - "0.21 0.577997 44.87164 -3.531666e-15 8.881784e-16 21.574149 39.491215 \n", - "0.22 0.577997 44.87164 -3.533831e-15 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39.491215 \n", - "9.75 0.577997 44.87164 -6.672389e-15 5.901946e-13 21.574149 39.491215 \n", - "9.76 0.577997 44.87164 -6.674264e-15 5.906386e-13 21.574149 39.491215 \n", - "9.77 0.577997 44.87164 -6.676144e-15 5.915268e-13 21.574149 39.491215 \n", - "9.78 0.577997 44.87164 -6.678028e-15 5.919709e-13 21.574149 39.491215 \n", - "9.79 0.577997 44.87164 -6.679916e-15 5.928591e-13 21.574149 39.491215 \n", - "9.80 0.577997 44.87164 -6.681810e-15 5.933032e-13 21.574149 39.491215 \n", - "9.81 0.577997 44.87164 -6.683708e-15 5.937473e-13 21.574149 39.491215 \n", - "9.82 0.577997 44.87164 -6.685612e-15 5.946355e-13 21.574149 39.491215 \n", - "9.83 0.577997 44.87164 -6.687520e-15 5.950795e-13 21.574149 39.491215 \n", - "9.84 0.577997 44.87164 -6.689434e-15 5.964118e-13 21.574149 39.491215 \n", - "9.85 0.577997 44.87164 -6.691353e-15 5.968559e-13 21.574149 39.491215 \n", - "9.86 0.577997 44.87164 -6.693277e-15 5.968559e-13 21.574149 39.491215 \n", - "9.87 0.577997 44.87164 -6.695207e-15 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4.099088 -1000.0 \n", - "0.20 3.396464 7.898243 4.314830 -1000.0 \n", - "0.21 3.396464 8.293155 4.530571 -1000.0 \n", - "0.22 3.396464 8.688067 4.746313 -1000.0 \n", - "0.23 3.396464 9.082980 4.962054 -1000.0 \n", - "0.24 3.396464 9.477892 5.177796 -1000.0 \n", - "0.25 3.396464 9.872804 5.393537 -1000.0 \n", - "0.26 3.396464 10.267716 5.609279 -1000.0 \n", - "0.27 3.396464 10.662628 5.825020 -1000.0 \n", - "0.28 3.396464 11.057540 6.040762 -1000.0 \n", - "0.29 3.396464 11.452452 6.256503 -1000.0 \n", - "0.30 3.396464 11.847365 6.472245 -1000.0 \n", - "... ... ... ... ... \n", - "9.71 3.396464 383.459700 209.484989 -1000.0 \n", - "9.72 3.396464 383.854613 209.700731 -1000.0 \n", - "9.73 3.396464 384.249525 209.916472 -1000.0 \n", - "9.74 3.396464 384.644437 210.132214 -1000.0 \n", - "9.75 3.396464 385.039349 210.347955 -1000.0 \n", - "9.76 3.396464 385.434261 210.563697 -1000.0 \n", - "9.77 3.396464 385.829173 210.779438 -1000.0 \n", - "9.78 3.396464 386.224085 210.995180 -1000.0 \n", - "9.79 3.396464 386.618998 211.210921 -1000.0 \n", - "9.80 3.396464 387.013910 211.426663 -1000.0 \n", - "9.81 3.396464 387.408822 211.642404 -1000.0 \n", - "9.82 3.396464 387.803734 211.858146 -1000.0 \n", - "9.83 3.396464 388.198646 212.073887 -1000.0 \n", - "9.84 3.396464 388.593558 212.289628 -1000.0 \n", - "9.85 3.396464 388.988471 212.505370 -1000.0 \n", - "9.86 3.396464 389.383383 212.721111 -1000.0 \n", - "9.87 3.396464 389.778295 212.936853 -1000.0 \n", - "9.88 3.396464 390.173207 213.152594 -1000.0 \n", - "9.89 3.396464 390.568119 213.368336 -1000.0 \n", - "9.90 3.396464 390.963031 213.584077 -1000.0 \n", - "9.91 3.396464 391.357943 213.799819 -1000.0 \n", - "9.92 3.396464 391.752856 214.015560 -1000.0 \n", - "9.93 3.396464 392.147768 214.231302 -1000.0 \n", - "9.94 3.396464 392.542680 214.447043 -1000.0 \n", - "9.95 3.396464 392.937592 214.662785 -1000.0 \n", - "9.96 3.396464 393.332504 214.878526 -1000.0 \n", - "9.97 3.396464 393.727416 215.094268 -1000.0 \n", - "9.98 3.396464 394.122329 215.310009 -1000.0 \n", - "9.99 3.396464 394.517241 215.525751 -1000.0 \n", - "10.00 3.396464 394.912153 215.741492 -1000.0 \n", - "\n", - "[1000 rows x 35 columns]" - ] - }, - "execution_count": 747, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "results" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "code", - "execution_count": 749, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "kwargs = {'marker': '.',\n", - " 'subplots': True,\n", - " 'sharex': True,\n", - " 'figsize': (12, 6)}" - ] - }, - { - "cell_type": "code", - "execution_count": 750, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\plotting\\_core.py:1716: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n", - " series.name = label\n" - ] - }, - { - "data": { - "image/png": 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1M4OqVcnDsCRJyt2ZoXdXLx3dI7QhK0LYde2ussAwLElSEeQKu9PqptH+Sjtb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\nMCxJJZBS6gR+HhFPAF8YxyX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TQwTniJgC/Az4XGZ+Z5D9zgDOANh3330PXrVq1VCfQaq/yl/Pb9kEG35XnePu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\nSQUYnCVJkqQCDM6SJElSAQZ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kCpr2YcAnKnddZ5pVh/IIxl8GPgR8FegyGEuSlJPx0Lz74WdmfJ1pVhOrajCO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\n6dnVw+W3Fx60e7T/Ud52+9s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000/X/v37PTs3wXkojVulPVv61wOF0jmf8a89AAAA2aZxq7T5m54OrrBixQo9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\n3KTbF92ecNSNuuY6ffbJz9L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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "results.plot(y=['elevator', 'aileron', 'rudder', 'thrust'], **kwargs);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Doublet " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values." - ] - }, - { - "cell_type": "code", - "execution_count": 291, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.utils.input_generator import Doublet" - ] - }, - { - "cell_type": "code", - "execution_count": 292, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "de0 = trimmed_controls['delta_elevator']" - ] - }, - { - "cell_type": "code", - "execution_count": 293, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "controls = controls = {\n", - " 'delta_elevator': Doublet(t_init=2, T=1, A=0.1, offset=de0),\n", - " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", - " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", - " 'delta_t': Constant(trimmed_controls['delta_t'])\n", - "}" - ] - }, - { - "cell_type": "code", - "execution_count": 294, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "sim = Simulation(aircraft, system, environment, controls)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Once the simulation is set, the propagation can be performed:" - ] - }, - { - "cell_type": "code", - "execution_count": 295, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "\n", - "time: 0%| | 0/90 [00:00" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "results.plot(y=['x_earth', 'y_earth', 'height'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": 297, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\plotting\\_core.py:1716: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n", - " series.name = label\n" - ] - }, - { - "data": { - "image/png": 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5RI899ph23z1GqA8IPcyZ0LWHuUdP6bNnSo3zO+9f8VT22gQAAEpXjJ7gHd5d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\nGuYXJR1gZsMlvSdpiqRzsvC6CXt88uN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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "results.plot(y=['v_north', 'v_east', 'v_down'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": 299, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\plotting\\_core.py:1716: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n", - " series.name = label\n" - ] - }, - { - "data": { - "image/png": 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QB2GsqiF3f0TSIynnbuzxfZukGWH0FTunfk5qulfy7sSxd0u73uxxQXLEecwU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\nn5Hp4dXD024qAxzAiDMAACg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uYukpXt9qyj+AkkWpBgCgNF25V6gjR6HgQUWgYFGqAQAob/F6P+ejh3VXe+zS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\nXoJFTvX4RTZIUpukmZJ+J6nJzI509w5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M/vG5zO2vzksvWlPI9AWlq6dIsQnYWT4h6adRFwEAAIAIDF1uPdcDkzGfP7us\nDzma2S8kHZzj0OXufldwzuWSWiR9yPMUZ2YrJK2QpIULFy7ZtGlTiSoGAAAAEjyLiJmdL+liSae6\n++5Rfk+HpCgS9kJJmyN4XcQf9wYK4f5APtwbyId7Ix4Wufvc0ZwYm4BtZmdKWi3pne7eEXU9IzGz\njtH+JaO6cG+gEO4P5MO9gXy4N5InNtP0SbpWUr2kB82s3cy+H3VBI9gx8imoUtwbKIT7A/lwbyAf\n7o2Eic1Dju5+RNQ1jFFX1AUgtrg3UAj3B/Lh3kA+3BsJE6cR7KRZE3UBiC3uDRTC/YF8uDeQD/dG\nwsSmBxsAAACoBIxgAwAAACEiYAMAAAAhImADAAAAISJgAwAAACEiYAMAAAAhImADAAAAISJgAwAA\nACEiYAMAAAAhImADAAAAISJgAwAAACEiYAMAAAAhmhB1AcWaM2eONzY2Rl0GAAAAKlhbW9s2d587\nmnMTH7AbGxvV2toadRkAAACoYGa2abTn0iISkdWtq/W+n79Pq1tXR10KAAAAQkTAjsDq1tW65elb\ntLl7s255+hZ96oFPRV0SAAAAQkLAjsC6Desytn/7ym91x7N3RFQNAAAAwpT4HuwkmjJhirbv3Z6x\n79+e+TctP3p5RBUBAACEr7e3V6lUSj09PVGXMmp1dXVqaGjQxIkTx30NAnYELlp8ka589MqMfTv3\n7oyoGgAAgNJIpVKqr69XY2OjzCzqckbk7urs7FQqlVJTU9O4r0OLSASWH71ck2omZeybVDspz9kA\nAADJ1NPTo9mzZyciXEuSmWn27NlFj7gTsCNy4KQDM7YPOeCQiCoBAAAonaSE60Fh1EvAjoi7Z2xP\nnzw9okoAAAAQJnqwI9D+ars693ZGXQYAAEDFq62t1eLFi/dvr1u3TqVeBZyAHYG7/3R31CUAAABU\nhSlTpqi9vb2sr0mLSAQ27tgYdQkAAACx1P5qu25cf6PaXy1dKL7ooovU3Nys5uZmzZ07V1dccUWo\n12cEOwLZc2ADAABUum88/g398bU/Fjxn175denb7s3K5TKajZx6taZOm5T3/TbPepM8v/XzBa+7Z\ns0fNzc2SpKamJq1du1Y33nijJGnTpk0644wzdMEFF4ztDzMCAnYEZk6eOWzf7CmzI6gEAAAgPrp7\nu+VKTwThcnX3dhcM2KORr0Wkp6dHy5cv17XXXqtFixYV9RrZCNgRyDVjyDGzjomgEgAAgPIYaaRZ\nSreHfPKBT6p3oFcTayZq1Umr1DyvuST1XHzxxfrQhz6k0047LfRrE7Aj0DfQN2zfIy8/wlLpAACg\nqjXPa9YNp9+g1q2tajmopWTdHcc0AAAR60lEQVTh+rrrrlN3d7dWrlxZkusTsCOQ6k4N2/efqf9U\n+6vtJbuRAAAAkqB5XnPJ89A3v/lNTZw4cX9v9sUXX6yLL744tOsTsMvsjmfv0Madw2cRGfABtW5t\nJWADAACEaNeuXcP2vfDCCyV9zaKn6TOzBWb2KzN7xsyeNrNLg/1fMbOXzaw9+PXeId/zBTPbYGbP\nmtkZQ/afGezbYGalGbOP2M83/Dznfpdr+iRWcwQAAEi6MEaw+yT9vbv/zszqJbWZ2YPBsW+7+zeH\nnmxmb5Z0rqS3SJov6RdmdlRw+DpJyySlJD1hZne7+x9CqDE2JtdMzntspKlrAAAAEH9FB2x3f0XS\nK8HX3Wb2jKRDC3zLWZJuc/e9kl4wsw2SlgbHNrj7Rkkys9uCcysqYOeaQWTQ4LQ0AAAAlcLdZWZR\nlzFq7sXnsVBXcjSzRklvlfRYsOsSM/u9md1sZoOTPx8q6aUh35YK9uXbn+t1VphZq5m1dnR0hPgn\niBZT9QEAgEpSV1enzs7OUEJrObi7Ojs7VVdXV9R1QnvI0cymSbpT0mXuvtPMrpf0VUke/P4tSZ+Q\nlOtHGFfusJ/zv4a7r5G0RpJaWlqS8V9sFGgRAQAAlaShoUGpVEpJGhCtq6tTQ0NDUdcIJWCb2USl\nw/WP3f3nkuTuW4ccv0HSPcFmStKCId/eIGlL8HW+/VWBFhEAAFBJJk6cqKampqjLKLswZhExSTdJ\nesbdVw/Zf8iQ086W9FTw9d2SzjWzyWbWJOlISY9LekLSkWbWZGaTlH4Q8u5i60sSWkQAAACSL4wR\n7BMkfUzSejMbXOj9i5L+h5k1K93m8aKkT0mSuz9tZrcr/fBin6TPuHu/JJnZJZLul1Qr6WZ3fzqE\n+hKDFhEAAIDkC2MWkUeUu6/6vgLfc5Wkq3Lsv6/Q91U6WkQAAACSL9RZRFAcWkQAAACSj4BdZv0D\n/Tn3m0xd+7rKXA0AAADCRsAusz7vy7mfpdIBAAAqAwG7zF7b81reYzzkCAAAkHwE7DJqf7Vdz2x/\nJu9xHnIEAABIPgJ2Gd3y1C0Fj/OQIwAAQPIRsMvoxZ0vZmzXT6zf/zUPOQIAAFQGAnYZzZw8M3O7\n7o1tHnIEAACoDATsMpo+OTNA9w1kzijCQ44AAADJR8COER5yBAAASD4CdoTqJ9VnbPOQIwAAQPIR\nsCPUO9Cbsc1DjgAAAMlHwC6jrr2ZATq7B3vn3p3lLAcAAAAlMCHqAqrJ9r3bM7a793VnbP/rH/5V\npyw8Rc3zmjP2n7X2LG3cuXH/9gG1B+jRjz5aukIBAAAwboxgl9GBEw/M2J43dZ5qrXb/dr/3q3Vr\na8Y52eFakl7vf12Lf7i4dIUCAABg3AjYZZTdYz1t4jS9v+n9+7dzzYWdHa6HOv7fjg+3QAAAABQt\ndgHbzM40s2fNbIOZrYy6nrC0v9quF3a+kLFv38A+zaibsX87ezXH1a2rC17z9f7XtfLhivkrAgAA\nqAix6sE2s1pJ10laJikl6Qkzu9vd/xBtZZlWPrxS975wb9HXOfuIs7Wrd9f+7ewR7J8++9MRr3Hv\nC/dq1cmrhu1f3bpatzx9S9E1Ipkm2SS1ndeW81jzD5vVr/4yVwQAQHjmT52v+5ffH3UZecUqYEta\nKmmDu2+UJDO7TdJZkmITsMMK13W1dVp+9HJd9+R1+/dlj2D39PWM6lr0YyPbPt/HfQEAqFhbdm/R\nGXecEduQHbcWkUMlvTRkOxXsy2BmK8ys1cxaOzo6ylacJD3y8iOhXGdwir7ZU2bv35erB3sok4Xy\n2gAAAEm3ZfeWqEvIK24BO1eCHLZ+uLuvcfcWd2+ZO3duGcp6w4mHnhjKdSbWTJQkPb/9+Yz9f3zt\nj5LSPdsDGsg4Nqlmktafvz6U1wcAAEiy+VPnR11CXnEL2ClJC4ZsN0iK1Y8nq05epfc1va/o6wx4\nOjx71s8Pg9u3PDW8f3pwtJuQDQAAqhk92GPzhKQjzaxJ0suSzpX0kWhLGm7VyatyPlhYyDt+8g51\n976xsMyk2kmSpGNmHZNx3uD24Ej2UBctvmj/1+vPXz+qh9Xqaur0xMeeGFOtSK47nr1DVz565Yjn\n1apW7ee3l6EiAACqT6wCtrv3mdklku6XVCvpZnd/OuKyQvHhoz6cMavHh4/6sKTMubGHPuS4r39f\nxvcfMOEALT96ecY+AhKyLT96+bD7BAAAlFesArYkuft9ku6Luo6wfa7lc5KkhzY/pFMXnrp/e+hD\njYUecpwyYUrpiwQAAEDRYhewK9nnWj63P1gPym4FydUaAgAAgOSI20OOVSffQ469A71RlAMAAIAi\nEbAjlushx/ZX2zN6s6U3HooEAABAvBGwI5brIcdcU/S9adabylkWAAAAxomAHbFcDzm+uPPFYed9\n/NiPl7EqAAAAjBcBO2K5HnIcXOVx0ML6hWqe11zOsgAAADBOBOyI5XrIsXtfd8a+voG+cpYEAACA\nIhCwI5ZvJUcAAAAkEwE7YrkecqyfVJ9xTvY2AAAA4ouAHbFcDzlmz4HNnNgAAADJQcCO2Ggecsze\nBgAAQHwRsCOW6yHHjj0dGfsYwQYAAEgOAnbEsh9q3N27W6/1vJaxr/HAxjJWBAAAgGIQsCPWta9L\nJpOUfsixdWvrsHNYZAYAACA5CNgRazmoZX+P9YSaCZpcOznjOIvMAAAAJAsBO2LN85p19TuvliQd\nN/e4YYvKTKiZEEVZAAAAGKeiAraZXW1mfzSz35vZWjObEexvNLM9ZtYe/Pr+kO9ZYmbrzWyDmX3X\nzCzYP8vMHjSz54PfZxb3R0uOugl1kqTfbf2dtry+JeMYM4gAAAAkS7Ej2A9KOtbdj5P0nKQvDDn2\nJ3dvDn5dPGT/9ZJWSDoy+HVmsH+lpIfc/UhJDwXbVWF9x3pJw2cUkTRs2XQAAADEW1EB290fcPfB\nnoZHJTUUOt/MDpF0oLv/t7u7pB9J+mBw+CxJPwy+/uGQ/RVvVt2sqEsAAABASMLswf6EpH8fst1k\nZk+a2X+a2UnBvkMlpYackwr2SdJB7v6KJAW/z8v3Qma2wsxazay1o6Mj32mJkb3YzFAskw4AAJAs\nIz5BZ2a/kHRwjkOXu/tdwTmXS+qT9OPg2CuSFrp7p5ktkbTOzN4iBfPRZRreFzECd18jaY0ktbS0\njPn742bbnm15j7HIDAAAQLKMGLDd/bRCx83sfEnvl3Rq0PYhd98raW/wdZuZ/UnSUUqPWA9tI2mQ\nNPhU31YzO8TdXwlaSV4d6x+mEs2cXDXPegIAAFSEYmcROVPS5yX9tbvvHrJ/rpnVBl8fpvTDjBuD\n1o9uMzs+mD3kPEl3Bd92t6Tzg6/PH7K/qh0+4/CoSwAAAMAYFDvJ8rWSJkt6MJht79FgxpCTJV1p\nZn2S+iVd7O6D63//raRbJU1Rumd7sG97laTbzexCSZslLS+ytorwgcM/EHUJAAAAGIOiAra7H5Fn\n/52S7sxzrFXSsTn2d0o6tZh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AlI1AFmI2s6WSpksaa2Ztiq0GskjSQ2Z2raS3JM2Jd18haaakjZI+lHS1JLn7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\nUSJSZLc8f0vOfTt7OvX54z6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FxFyFzMachMxMyMzTASaaileron...thrustuvv_downv_eastv_northwx_earthy_earthz_earth
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" - ], - "text/plain": [ - " Fx Fy Fz Mach Mx My \\\n", - "time \n", - "0.05 -2860.288296 -0.000007 -23948.338630 0.133444 3.670972e-06 416.026942 \n", - "0.10 -2841.450134 -0.000007 -23790.055374 0.133135 2.754411e-06 382.934882 \n", - "0.15 -2814.079427 -0.000007 -23634.534640 0.132827 2.070495e-06 344.981012 \n", - "0.20 -2834.053374 -0.000006 -23475.855214 0.132523 1.564206e-06 331.492749 \n", - "0.25 -2844.314793 -0.000006 -23317.511918 0.132216 1.181851e-06 311.810632 \n", - "0.30 -2847.104415 -0.000006 -23160.410509 0.131908 8.962216e-07 288.008616 \n", - "0.35 -2867.759612 -0.000005 -23001.499461 0.131599 6.829096e-07 273.089782 \n", - "0.40 -2883.231719 -0.000005 -22843.131464 0.131287 5.237487e-07 255.164441 \n", - "0.45 -2892.153236 -0.000005 -22685.668716 0.130975 4.056468e-07 234.048222 \n", - "0.50 -2914.835086 -0.000004 -22525.832830 0.130659 3.167348e-07 219.601445 \n", - "0.55 -2921.787769 -0.000004 -22367.332766 0.130340 2.513504e-07 196.935789 \n", - "\n", - " Mz TAS a aileron ... thrust \\\n", - "time ... \n", - "0.05 -0.000001 44.895162 336.434581 2.959742e-10 ... 0.670198 \n", - "0.10 -0.000001 44.791157 336.434574 2.959742e-10 ... 0.670198 \n", - "0.15 -0.000001 44.687646 336.434555 2.959742e-10 ... 0.670198 \n", - "0.20 -0.000001 44.585409 336.434527 2.959742e-10 ... 0.670198 \n", - "0.25 -0.000001 44.482035 336.434473 2.959742e-10 ... 0.670198 \n", - "0.30 -0.000001 44.378277 336.434397 2.959742e-10 ... 0.670198 \n", - "0.35 -0.000001 44.274258 336.434294 2.959742e-10 ... 0.670198 \n", - "0.40 -0.000001 44.169584 336.434162 2.959742e-10 ... 0.670198 \n", - "0.45 -0.000001 44.064366 336.434000 2.959742e-10 ... 0.670198 \n", - "0.50 -0.000001 43.958162 336.433802 2.959742e-10 ... 0.670198 \n", - "0.55 -0.000001 43.850903 336.433567 2.959742e-10 ... 0.670198 \n", - "\n", - " u v v_down v_east v_north w \\\n", - "time \n", - "0.05 44.877493 1.089215e-07 -0.021778 21.523885 39.399206 -1.259451 \n", - "0.10 44.773564 1.085156e-07 -0.059100 21.474006 39.307904 -1.255270 \n", - "0.15 44.670646 1.080774e-07 -0.101132 21.424344 39.216999 -1.232525 \n", - "0.20 44.567449 1.076118e-07 -0.219729 21.375124 39.126902 -1.265389 \n", - "0.25 44.463623 1.071279e-07 -0.339570 21.325202 39.035520 -1.279696 \n", - "0.30 44.359858 1.066288e-07 -0.462223 21.274925 38.943489 -1.278443 \n", - "0.35 44.255295 1.061187e-07 -0.620164 21.224128 38.850505 -1.295661 \n", - "0.40 44.150414 1.056017e-07 -0.781931 21.172708 38.756382 -1.301203 \n", - "0.45 44.045377 1.050805e-07 -0.944579 21.120728 38.661234 -1.293510 \n", - "0.50 43.938927 1.045592e-07 -1.134443 21.067646 38.564068 -1.300252 \n", - "0.55 43.832154 1.040402e-07 -1.311274 21.013841 38.465578 -1.282176 \n", - "\n", - " x_earth y_earth z_earth \n", - "time \n", - "0.05 1.972256 1.077449 -999.999987 \n", - "0.10 3.939933 2.152395 -1000.001805 \n", - "0.15 5.903055 3.224853 -1000.006526 \n", - "0.20 7.861673 4.294852 -1000.013745 \n", - "0.25 9.815738 5.362362 -1000.027650 \n", - "0.30 11.765219 6.427369 -1000.047414 \n", - "0.35 13.710083 7.489853 -1000.073815 \n", - "0.40 15.650273 8.549783 -1000.107951 \n", - "0.45 17.585742 9.607135 -1000.149658 \n", - "0.50 19.516402 10.661859 -1000.200635 \n", - "0.55 21.442166 11.713909 -1000.261205 \n", - "\n", - "[11 rows x 35 columns]" - ] - }, - "execution_count": 76, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "results = sim.propagate(sim.time+dt)\n", - "results" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Notice that `results` will include the previous timesteps as well as the last one. To get just the last one one can use pandas `loc` or `iloc`:" - ] - }, - { - "cell_type": "code", - "execution_count": 77, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Fx -2.921788e+03\n", - "Fy -3.761191e-06\n", - "Fz -2.236733e+04\n", - "Mach 1.303405e-01\n", - "Mx 2.513504e-07\n", - "My 1.969358e+02\n", - "Mz -1.203167e-06\n", - "TAS 4.385090e+01\n", - "a 3.364336e+02\n", - "aileron 2.959742e-10\n", - "alpha -2.924362e-02\n", - "beta 2.372590e-09\n", - "elevator 1.108958e-02\n", - "height 1.000261e+03\n", - "p 6.386588e-10\n", - "phi 2.537379e-10\n", - "pressure 8.987343e+04\n", - "psi 5.000000e-01\n", - "q 9.152033e-02\n", - "q_inf 1.068779e+03\n", - "r 1.349505e-10\n", - "rho 1.111631e+00\n", - "rudder -1.269086e-09\n", - "temperature 2.816493e+02\n", - "theta 6.638492e-04\n", - "thrust 6.701981e-01\n", - "u 4.383215e+01\n", - "v 1.040402e-07\n", - "v_down -1.311274e+00\n", - "v_east 2.101384e+01\n", - "v_north 3.846558e+01\n", - "w -1.282176e+00\n", - "x_earth 2.144217e+01\n", - "y_earth 1.171391e+01\n", - "z_earth -1.000261e+03\n", - "Name: 0.55, dtype: float64" - ] - }, - "execution_count": 77, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "results.iloc[-1] # last time step" - ] - }, - { - "cell_type": "code", - "execution_count": 78, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Fx -2.921788e+03\n", - "Fy -3.761191e-06\n", - "Fz -2.236733e+04\n", - "Mach 1.303405e-01\n", - "Mx 2.513504e-07\n", - "My 1.969358e+02\n", - "Mz -1.203167e-06\n", - "TAS 4.385090e+01\n", - "a 3.364336e+02\n", - "aileron 2.959742e-10\n", - "alpha -2.924362e-02\n", - "beta 2.372590e-09\n", - "elevator 1.108958e-02\n", - "height 1.000261e+03\n", - "p 6.386588e-10\n", - "phi 2.537379e-10\n", - "pressure 8.987343e+04\n", - "psi 5.000000e-01\n", - "q 9.152033e-02\n", - "q_inf 1.068779e+03\n", - "r 1.349505e-10\n", - "rho 1.111631e+00\n", - "rudder -1.269086e-09\n", - "temperature 2.816493e+02\n", - "theta 6.638492e-04\n", - "thrust 6.701981e-01\n", - "u 4.383215e+01\n", - "v 1.040402e-07\n", - "v_down -1.311274e+00\n", - "v_east 2.101384e+01\n", - "v_north 3.846558e+01\n", - "w -1.282176e+00\n", - "x_earth 2.144217e+01\n", - "y_earth 1.171391e+01\n", - "z_earth -1.000261e+03\n", - "Name: 0.55, dtype: float64" - ] - }, - "execution_count": 78, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "results.loc[sim.time] # results for current simulation time" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Test\n" - ] - }, - { - "cell_type": "code", - "execution_count": 984, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "a1 = Cessna172()\n", - "a2 = SimplifiedCessna172()\n", - "e1 = copy.deepcopy(environment)\n", - "e2 = copy.deepcopy(environment)" - ] - }, - { - "cell_type": "code", - "execution_count": 985, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(Aircraft State \n", - " x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", - " theta: 0.076 rad, phi: 0.000 rad, psi: 0.500 rad \n", - " u: 44.87 m/s, v: -0.00 m/s, w: 3.40 m/s \n", - " P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", - " u_dot: 0.00 m/s², v_dot: -0.00 m/s², w_dot: 0.00 m/s² \n", - " P_dot: -0.00 rad/s², Q_dot: 0.00 rad/s², R_dot: -0.00 rad/s² ,\n", - " {'delta_aileron': -1.2190588362567532e-17,\n", - " 'delta_elevator': -0.048951124635254917,\n", - " 'delta_rudder': 7.1787477633953699e-17,\n", - " 'delta_t': 0.57799667845449421})" - ] - }, - "execution_count": 985, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "ts1, tc1 = steady_state_trim(\n", - " a1,\n", - " e1,\n", - " pos,\n", - " psi,\n", - " TAS,\n", - " controls0\n", - ")\n", - "e1.update(ts1)\n", - "ss1 = EulerFlatEarth(t0=0, full_state=ts1)\n", - "ts1, tc1" - ] - }, - { - "cell_type": "code", - "execution_count": 986, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "({'delta_aileron': -3.9966019045688599e-19,\n", - " 'delta_elevator': -0.07729883009616384,\n", - " 'delta_rudder': 2.7133156470881973e-18,\n", - " 'delta_t': 0.57166075967430052},\n", - " Aircraft State \n", - " x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", - " theta: 0.080 rad, phi: 0.000 rad, psi: 0.500 rad \n", - " u: 44.86 m/s, v: -0.00 m/s, w: 3.59 m/s \n", - " P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", - " u_dot: 0.00 m/s², v_dot: -0.00 m/s², w_dot: 0.00 m/s² \n", - " P_dot: -0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: -0.00 rad/s² )" - ] - }, - "execution_count": 986, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "ts2, tc2 = steady_state_trim(\n", - " a2,\n", - " e2,\n", - " pos,\n", - " psi,\n", - " TAS,\n", - " controls0\n", - ") \n", - "e2.update(ts2)\n", - "ss2 = EulerFlatEarth(t0=0, full_state=ts2)\n", - "tc2, ts2" - ] - }, - { - "cell_type": "code", - "execution_count": 971, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "c1 = {\n", - " 'delta_elevator': Constant(tc1['delta_elevator']),\n", - " 'delta_aileron': Constant(tc1['delta_aileron']),\n", - " 'delta_rudder': Constant(tc1['delta_rudder']),\n", - " 'delta_t': Constant(tc1['delta_t'])\n", - "}\n", - "c2 = {\n", - " 'delta_elevator': Constant(tc2['delta_elevator']),\n", - " 'delta_aileron': Constant(tc2['delta_aileron']),\n", - " 'delta_rudder': Constant(tc2['delta_rudder']),\n", - " 'delta_t': Constant(tc2['delta_t'])\n", - "}\n", - "s1 = Simulation(a1, ss1, e1, c1)\n", - "s2 = Simulation(a2, ss2, e2, c2)\n", - " # Doublet(t_init=3, T=1, A=0.1, offset=0)," - ] - }, - { - "cell_type": "code", - "execution_count": 711, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "s1 = Simulation(aircraft, ss1, e1, c1)" - ] - }, - { - "cell_type": "code", - "execution_count": 712, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "\n", - "\n", - "time: 0%| | 0/5 [00:00]" - ] - }, - "execution_count": 713, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(r1.alpha*180/np.pi)\n", - "plt.plot(r2.alpha*180/np.pi,'.')\n", - "plt.plot(results.alpha*180/np.pi,'.')" - ] - }, - { - "cell_type": "code", - "execution_count": 972, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\pandas\\plotting\\_core.py:1716: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n", - " series.name = label\n" - ] - }, - { - "data": { - "image/png": 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NgT6DYPB4OLAe6o6e6hKjshdJgIKziIhIuM5ofQlNteENofDWltHeRK5hx8uw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\nZqsxZocx5o5UnltEREREpCNSVqphjAkA24DLgXJ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9XvyUh2qpkBI0pIqxz7+vlZWVfPWrX+Xss8/mc5/7HDfffDNz5sxhxYoVPPPM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\n97k06D6Xhry/zzkNxs65V4C9sdvM7MR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"\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\__init__.py\u001b[0m in \u001b[0;36minner\u001b[1;34m(ax, *args, **kwargs)\u001b[0m\n\u001b[0;32m 1715\u001b[0m warnings.warn(msg % (label_namer, func.__name__),\n\u001b[0;32m 1716\u001b[0m RuntimeWarning, stacklevel=2)\n\u001b[1;32m-> 1717\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0max\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1718\u001b[0m \u001b[0mpre_doc\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0minner\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__doc__\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1719\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mpre_doc\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py\u001b[0m in \u001b[0;36mplot\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m 1370\u001b[0m \u001b[0mkwargs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcbook\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnormalize_kwargs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0m_alias_map\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 1371\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1372\u001b[1;33m \u001b[1;32mfor\u001b[0m \u001b[0mline\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_lines\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 1373\u001b[0m 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\u001b[1;32mfor\u001b[0m \u001b[0mseg\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_plot_args\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mthis\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 405\u001b[0m \u001b[1;32myield\u001b[0m \u001b[0mseg\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 406\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;32mC:\\ProgramData\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_base.py\u001b[0m in \u001b[0;36m_plot_args\u001b[1;34m(self, tup, kwargs)\u001b[0m\n\u001b[0;32m 382\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mindex_of\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtup\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 383\u001b[0m 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(a1.alpha_data, a1.CN_delta_aile_data, '.')\n", - "plt.plot(a1.alpha_data, a2.CN_delta_aile_cl*a2.CL + 0*a2.alpha_data)" - ] - }, - { - "cell_type": "code", - "execution_count": 1106, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "-0.069523541636556885" - ] - }, - "execution_count": 1106, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.sum(a2.CL_data*a2.CN_p_data)/np.sum(a2.CL_data**2)" - ] - }, - { - "cell_type": "code", - "execution_count": 1119, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "-0.00027157871300302394" - ] - }, - "execution_count": 1119, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "x = np.reshape(a1.CL_data**2, (1, 12)) * np.reshape(a1.delta_aile_data, (9, 1))\n", - "np.sum(a1.CN_delta_aile_data*x) / np.sum(x**2)" - ] - }, - { - "cell_type": "code", - "execution_count": 1120, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "LinregressResult(slope=-0.00027568577531501706, intercept=0.00072199122345927057, rvalue=-0.94235806962343571, pvalue=3.266896179580671e-52, stderr=9.5077855389690054e-06)" - ] - }, - "execution_count": 1120, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "linregress(x.flatten(), a1.CN_delta_aile_data.flatten())" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 34, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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IIerTMY3/s+HkVnTn3sCTnJMaPfPvK/RFRA5RVkYqM8eewZq+Ewk0ac7xb09g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\nrkJggg==\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(aircraft.J_data,aircraft.Ct_data,'.')\n", - "plt.plot(aircraft.J_data,-0.1692121*aircraft.J_data**2 + 0.03545196*aircraft.J_data +0.10446359)" - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "metadata": {}, - "outputs": [], - "source": [ - "a,b,c = np.polyfit(aircraft.J_data,aircraft.Ct_data,2)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/.ipynb_checkpoints/How it works-checkpoint.ipynb b/.ipynb_checkpoints/How it works-checkpoint.ipynb deleted file mode 100644 index 6160320..0000000 --- a/.ipynb_checkpoints/How it works-checkpoint.ipynb +++ /dev/null @@ -1,938 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Python Flight Mechanics Engine " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Aircraft " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In order to perform a simulation, the first thing we need is an aircraft:" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "from pyfme.aircrafts import Cessna172" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "%load_ext autoreload\n", - "%autoreload 2" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "aircraft = Cessna172()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Aircraft will provide the simulator the forces, moments and inertial properties in order to perform the integration of the dynamic system equations:" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Aircraft mass: 1043.2616 kg\n", - "Aircraft inertia tensor: \n", - " [[ 1285.3154166 0. 0. ]\n", - " [ 0. 1824.9309607 0. ]\n", - " [ 0. 0. 2666.89390765]] kg/m²\n" - ] - } - ], - "source": [ - "print(f\"Aircraft mass: {aircraft.mass} kg\")\n", - "print(f\"Aircraft inertia tensor: \\n {aircraft.inertia} kg/m²\")" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "forces: [ 0. 0. 0.] N\n", - "moments: [ 0. 0. 0.] N·m\n" - ] - } - ], - "source": [ - "print(f\"forces: {aircraft.total_forces} N\")\n", - "print(f\"moments: {aircraft.total_moments} N·m\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "For the aircraft, in order to calculate its forces and moments it is necessary to set the controls values within the limits: " - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0}\n" - ] - } - ], - "source": [ - "print(aircraft.controls)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{'delta_elevator': (-0.4537856055185257, 0.48869219055841229), 'delta_aileron': (-0.26179938779914941, 0.3490658503988659), 'delta_rudder': (-0.27925268031909273, 0.27925268031909273), 'delta_t': (0, 1)}\n" - ] - } - ], - "source": [ - "print(aircraft.control_limits)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "but also to provide and environment (ie. atmosphere, winds, gravity) and the aircraft state, which will also determine the aerodynamic contribution." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Environment " - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.environment.atmosphere import ISA1976\n", - "from pyfme.environment.wind import NoWind\n", - "from pyfme.environment.gravity import VerticalConstant" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "atmosphere = ISA1976()\n", - "gravity = VerticalConstant()\n", - "wind = NoWind()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The atmosphere, wind and gravity model make up the environment:" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.environment import Environment" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "environment = Environment(atmosphere, gravity, wind)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The environment has an update method which given the state (ie. position, altitude...) updates the environment variables (ie. density, wind magnitude, gravity force...)" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Help on method update in module pyfme.environment.environment:\n", - "\n", - "update(state) method of pyfme.environment.environment.Environment instance\n", - "\n" - ] - } - ], - "source": [ - "help(environment.update)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## State " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Even if the state can be set manually by giving the position, attitude, velocity, angular velocities... Most of the times, the user will want to trim the aircraft in a stationary condition. The aircraft controls to flight in that condition will be also provided by the trimmer." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.utils.trimmer import steady_state_trim" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Help on function steady_state_trim in module pyfme.utils.trimmer:\n", - "\n", - "steady_state_trim(aircraft, environment, pos, psi, TAS, controls, gamma=0, turn_rate=0, exclude=None, verbose=0)\n", - " Finds a combination of values of the state and control variables\n", - " that correspond to a steady-state flight condition.\n", - " \n", - " Steady-state aircraft flight is defined as a condition in which all\n", - " of the motion variables are constant or zero. That is, the linear and\n", - " angular velocity components are constant (or zero), thus all\n", - " acceleration components are zero.\n", - " \n", - " Parameters\n", - " ----------\n", - " aircraft : Aircraft\n", - " Aircraft to be trimmed.\n", - " environment : Environment\n", - " Environment where the aircraft is trimmed including atmosphere,\n", - " gravity and wind.\n", - " pos : Position\n", - " Initial position of the aircraft.\n", - " psi : float, opt\n", - " Initial yaw angle (rad).\n", - " TAS : float\n", - " True Air Speed (m/s).\n", - " controls : dict\n", - " Initial value guess for each control or fixed value if control is\n", - " included in exclude.\n", - " gamma : float, optional\n", - " Flight path angle (rad).\n", - " turn_rate : float, optional\n", - " Turn rate, d(psi)/dt (rad/s).\n", - " exclude : list, optional\n", - " List with controls not to be trimmed. If not given, every control\n", - " is considered in the trim process.\n", - " verbose : {0, 1, 2}, optional\n", - " Level of least_squares verbosity:\n", - " * 0 (default) : work silently.\n", - " * 1 : display a termination report.\n", - " * 2 : display progress during iterations (not supported by 'lm'\n", - " method).\n", - " \n", - " Returns\n", - " -------\n", - " state : AircraftState\n", - " Trimmed aircraft state.\n", - " trimmed_controls : dict\n", - " Trimmed aircraft controls\n", - " \n", - " Notes\n", - " -----\n", - " See section 3.4 in [1] for the algorithm description.\n", - " See section 2.5 in [1] for the definition of steady-state flight\n", - " condition.\n", - " \n", - " References\n", - " ----------\n", - " .. [1] Stevens, BL and Lewis, FL, \"Aircraft Control and Simulation\",\n", - " Wiley-lnterscience.\n", - "\n" - ] - } - ], - "source": [ - "help(steady_state_trim)" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.models.state.position import EarthPosition" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "pos = EarthPosition(x=0, y=0, height=1000)\n", - "psi = 0.5 # rad\n", - "TAS = 45 # m/s\n", - "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [], - "source": [ - "trimmed_state, trimmed_controls = steady_state_trim(\n", - " aircraft,\n", - " environment,\n", - " pos,\n", - " psi,\n", - " TAS,\n", - " controls0\n", - ") " - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{'delta_aileron': 5.6949494207348974e-18,\n", - " 'delta_elevator': -0.048951124635247888,\n", - " 'delta_rudder': -1.4494655727415656e-17,\n", - " 'delta_t': 0.57799667845248459}" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "trimmed_controls" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "environment.update(trimmed_state)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now, all the necessary elements in order to calculate forces and moments are available " - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# Environment conditions for the current state:\n", - "environment.update(trimmed_state)\n", - "\n", - "# Forces and moments calculation:\n", - "forces, moments = aircraft.calculate_forces_and_moments(trimmed_state, environment, controls0)" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(array([ 1.14823706e-11, -6.00938052e-18, -5.45696821e-12]),\n", - " array([ 1.34219095e-13, -1.43613996e-11, -2.41989038e-15]))" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "forces, moments" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The aircraft is trimmed indeed: the total forces and moments (aerodynamics + gravity + thrust) are zero" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Simulation " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In order to simulate the dynamics of the aircraft under certain inputs in an environment, the user can set up a simulation using a dynamic system:" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.models import EulerFlatEarth" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "system = EulerFlatEarth(t0=0, full_state=trimmed_state)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Constant Controls " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values." - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.utils.input_generator import Constant" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "controls = controls = {\n", - " 'delta_elevator': Constant(trimmed_controls['delta_elevator']),\n", - " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", - " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", - " 'delta_t': Constant(trimmed_controls['delta_t'])\n", - "}" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.simulator import Simulation" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "sim = Simulation(aircraft, system, environment, controls)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Once the simulation is set, the propagation can be performed:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results = sim.propagate(10)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The results are returned in a DataFrame:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "%matplotlib inline" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "kwargs = {'marker': '.',\n", - " 'subplots': True,\n", - " 'sharex': True,\n", - " 'figsize': (12, 6)}" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['x_earth', 'y_earth', 'height'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['psi', 'theta', 'phi'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['v_north', 'v_east', 'v_down'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['p', 'q', 'r'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['alpha', 'beta', 'TAS'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['Fx', 'Fy', 'Fz'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['Mx', 'My', 'Mz'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['elevator', 'aileron', 'rudder', 'thrust'], **kwargs);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Doublet " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from pyfme.utils.input_generator import Doublet" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "de0 = trimmed_controls['delta_elevator']" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "controls = controls = {\n", - " 'delta_elevator': Doublet(t_init=2, T=1, A=0.1, offset=de0),\n", - " 'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n", - " 'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n", - " 'delta_t': Constant(trimmed_controls['delta_t'])\n", - "}" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "sim = Simulation(aircraft, system, environment, controls)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Once the simulation is set, the propagation can be performed:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results = sim.propagate(90)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['x_earth', 'y_earth', 'height'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['psi', 'theta', 'phi'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['v_north', 'v_east', 'v_down'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['p', 'q', 'r'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['alpha', 'beta', 'TAS'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['Fx', 'Fy', 'Fz'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['Mx', 'My', 'Mz'], **kwargs);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.plot(y=['elevator', 'aileron', 'rudder', 'thrust'], **kwargs);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Propagating only one time step" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "dt = 0.05 # seconds\n", - "sim = Simulation(aircraft, system, environment, controls, dt)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results = sim.propagate(0.5)\n", - "results" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can propagate for one time step even once the simulation has been propagated before:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results = sim.propagate(sim.time+dt)\n", - "results" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Notice that `results` will include the previous timesteps as well as the last one. To get just the last one one can use pandas `loc` or `iloc`:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.iloc[-1] # last time step" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "results.loc[sim.time] # results for current simulation time" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} From 90836af56cb2f5d967f36d27acde484e540b516b Mon Sep 17 00:00:00 2001 From: jdebecdelievre Date: Wed, 6 Jun 2018 11:26:08 -0700 Subject: [PATCH 4/5] connection to avl --- src/pyfme/aero/E205.txt | 54 +++++++ src/pyfme/aero/__init__.py | 1 + src/pyfme/aero/avl.py | 205 +++++++++++++++++++++++++++ src/pyfme/aero/hypo.avl | 132 +++++++++++++++++ src/pyfme/aircrafts/E205.txt | 54 +++++++ src/pyfme/aircrafts/MeterSpanUAV.pkl | Bin 0 -> 790700 bytes src/pyfme/aircrafts/__init__.py | 2 + src/pyfme/aircrafts/aircraft.py | 55 +++++++ src/pyfme/aircrafts/cessna_172.py | 8 -- src/pyfme/aircrafts/uav.py | 201 ++++++++++++++++++++++++++ 10 files changed, 704 insertions(+), 8 deletions(-) create mode 100644 src/pyfme/aero/E205.txt create mode 100644 src/pyfme/aero/__init__.py create mode 100644 src/pyfme/aero/avl.py create mode 100644 src/pyfme/aero/hypo.avl create mode 100644 src/pyfme/aircrafts/E205.txt create mode 100644 src/pyfme/aircrafts/MeterSpanUAV.pkl create mode 100644 src/pyfme/aircrafts/uav.py diff --git a/src/pyfme/aero/E205.txt b/src/pyfme/aero/E205.txt new file mode 100644 index 0000000..0651fbe --- /dev/null +++ b/src/pyfme/aero/E205.txt @@ -0,0 +1,54 @@ +1.00000 0.00000 +0.99974 0.00085 +0.99392 0.00159 +0.98578 0.00307 +0.97290 0.00499 +0.94617 0.00876 +0.91866 0.01274 +0.88020 0.01864 +0.83393 0.02611 +0.79263 0.03228 +0.73829 0.04008 +0.68535 0.04742 +0.63333 0.05440 +0.58021 0.06127 +0.53232 0.06738 +0.48264 0.07291 +0.44197 0.07676 +0.38814 0.08039 +0.32774 0.08186 +0.26612 0.08023 +0.21066 0.07548 +0.14521 0.06478 +0.09684 0.05300 +0.06230 0.04164 +0.04043 0.03241 +0.02021 0.02210 +0.01003 0.01499 +0.00152 0.00614 +0.00000 0.00000 +0.00089 -.00334 +0.00310 -.00596 +0.00816 -.00968 +0.01807 -.01343 +0.03718 -.01680 +0.07273 -.02114 +0.13766 -.02413 +0.20297 -.02449 +0.26877 -.02305 +0.34581 -.02057 +0.42989 -.01762 +0.49449 -.01526 +0.56883 -.01258 +0.63816 -.01012 +0.69937 -.00831 +0.75692 -.00681 +0.82133 -.00505 +0.87969 -.00361 +0.92076 -.00233 +0.96116 -.00099 +0.98546 -.00048 +0.98991 -.00068 +0.99485 -.00044 +0.99873 -.00063 +1.00000 0.00000 \ No newline at end of file diff --git a/src/pyfme/aero/__init__.py b/src/pyfme/aero/__init__.py new file mode 100644 index 0000000..b38c44f --- /dev/null +++ b/src/pyfme/aero/__init__.py @@ -0,0 +1 @@ +from .avl import avl_run \ No newline at end of file diff --git a/src/pyfme/aero/avl.py b/src/pyfme/aero/avl.py new file mode 100644 index 0000000..d02dbe4 --- /dev/null +++ b/src/pyfme/aero/avl.py @@ -0,0 +1,205 @@ +import numpy as np +nl = np.linalg +import os +import subprocess +import sys +import pandas as pd + +FORCES = ['CL', 'CD', 'CY', 'Cl', 'Cm', 'Cn'] +STAB = [F+d for F in ['CL', 'CY', 'Cl', 'Cm', 'Cn'] for d in ['a', 'b', 'p', 'q', 'r']] +CONT = [F+d for F in ['CL', 'CY', 'Cl', 'Cm', 'Cn'] for d in ['d1', 'd2', 'd3']] +# Note: missing drag + +class avl_run(): + def __init__(self, geom_file, num_control_surfaces, run_file="runs", path_to_avl='.'): + self.geom_file = geom_file + self.run_file = run_file + self.avl = path_to_avl + self.num_ctrl = num_control_surfaces + + def run(self, state, controls): + """ + State is a stack of [alpha, beta, phat, qhat, rhat] horizontal vectors + Controls is a [elevator, aileron, rudder] + """ + if controls.ndim > 1: + assert controls.shape[0] == state.shape[0] + + else: + state = np.expand_dims(state, 0) + controls = np.expand_dims(controls, 0) + N = controls.shape[0] + + # Modify run file + f = open(self.run_file, 'w') + for i in range(N): + print(state[i]) + alpha, beta, phat, qhat, rhat = state[i] + elevator, aileron, rudder = controls[i] + f.write(f""" + +--------------------------------------------- +Run case {i+1}: -unnamed- + +alpha -> alpha = {alpha} +beta -> beta = {beta} +pb/2V -> pb/2V = {phat} +qc/2V -> qc/2V = {qhat} +rb/2V -> rb/2V = {rhat} +elevator -> elevator = {elevator} +aileron -> aileron = {aileron} +rudder -> rudder = {rudder} + +alpha = {alpha} deg +beta = {beta} deg +pb/2V = {phat} +qc/2V = {qhat} +rb/2V = {rhat} +CL = 0.310719 +CDo = 0.00000 +bank = 0.00000 deg +elevation = 0.00000 deg +heading = 0.00000 deg +Mach = 0.00000 +velocity = 5.00000 Lunit/Tunit +density = 1.12500 Munit/Lunit^3 +grav.acc. = 9.81000 Lunit/Tunit^2 +turn_rad. = 0.00000 Lunit +load_fac. = 1.00000 +X_cg = 0.300000 Lunit +Y_cg = 0.00000 Lunit +Z_cg = 0.00000 Lunit +mass = 5.00000 Munit +Ixx = 1.00000 Munit-Lunit^2 +Iyy = 0.02000 Munit-Lunit^2 +Izz = 1.00000 Munit-Lunit^2 +Ixy = 0.00000 Munit-Lunit^2 +Iyz = 0.00000 Munit-Lunit^2 +Izx = 0.00000 Munit-Lunit^2 +visc CL_a = 0.00000 +visc CL_u = 0.00000 +visc CM_a = 0.00000 +visc CM_u = 0.00000 +""") + f.close() + + # Create bash script + f = open('cmd_file.run', 'w') + # f.write(f"LOAD {self.geom_file}\n") # load geom file + f.write(f'PLOP\ng\n\n') # disable graphics + f.write(f"CASE {self.run_file}\nOPER\n") + for i in range(N): + results_file = f"rslt_{i}.stab" + f.write(f"{i+1}\nx\nst\n{results_file}\n") + f.write("\n\nQUIT") + f.close() + + # Run bash + with open('cmd_file.run', 'r') as commands: + avl_run = subprocess.Popen([f"{self.avl}\\avl.exe", self.geom_file], + stderr=sys.stderr, + stdout=open(os.devnull, 'w'), + stdin=subprocess.PIPE) + for line in commands: + avl_run.stdin.write(line.encode('utf-8')) + avl_run.communicate() + avl_run.wait() + + # sort out results + data = pd.DataFrame({k: 0.0 for k in FORCES + STAB + CONT}, index=np.arange(N)) + data['de'] = controls[:, 0] + data['da'] = controls[:, 1] + data['dr'] = controls[:, 2] + data['alpha'] = state[:, 0] + data['beta'] = state[:, 1] + data['p'] = state[:, 2] + data['q'] = state[:, 3] + data['r'] = state[:, 4] + + for i in range(N): + with open(f"rslt_{i}.stab", 'r') as f: + lines = f.readlines() + data.Cl[i] = float(lines[19][33:41].strip()) + data.Cm[i] = float(lines[20][33:41].strip()) + data.Cn[i] = float(lines[21][33:41].strip()) + + data.CL[i] = float(lines[23][10:20].strip()) + data.CD[i] = float(lines[24][10:20].strip()) + data.CY[i] = float(lines[20][10:20].strip()) + + num_ctrl = self.num_ctrl # number of control surfaces + data.CLa[i] = float(lines[36 + num_ctrl][24:34].strip()) # CL_a + data.CYa[i] = float(lines[37 + num_ctrl][24:34].strip()) # CY_a + data.Cla[i] = float(lines[38 + num_ctrl][24:34].strip()) # Cl_a + data.Cma[i] = float(lines[39 + num_ctrl][24:34].strip()) # Cm_a + data.Cna[i] = float(lines[40 + num_ctrl][24:34].strip()) # Cn_a + data.CLb[i] = float(lines[36 + num_ctrl][43:54].strip()) # CL_b + data.CYb[i] = float(lines[37 + num_ctrl][43:54].strip()) # CY_b + data.Clb[i] = float(lines[38 + num_ctrl][43:54].strip()) # Cl_b + data.Cmb[i] = float(lines[39 + num_ctrl][43:54].strip()) # Cm_b + data.Cnb[i] = float(lines[40 + num_ctrl][43:54].strip()) # Cn_b + + data.CLp[i] = float(lines[44 + num_ctrl][24:34].strip()) + data.CLq[i] = float(lines[44 + num_ctrl][43:54].strip()) + data.CLr[i] = float(lines[44 + num_ctrl][65:74].strip()) + data.CYp[i] = float(lines[45 + num_ctrl][24:34].strip()) + data.CYq[i] = float(lines[45 + num_ctrl][43:54].strip()) + data.CYr[i] = float(lines[45 + num_ctrl][65:74].strip()) + data.Clp[i] = float(lines[46 + num_ctrl][24:34].strip()) + data.Clq[i] = float(lines[46 + num_ctrl][43:54].strip()) + data.Clr[i] = float(lines[44 + num_ctrl][65:74].strip()) + data.Cmp[i] = float(lines[47 + num_ctrl][24:34].strip()) + data.Cmq[i] = float(lines[47 + num_ctrl][43:54].strip()) + data.Cmr[i] = float(lines[44 + num_ctrl][65:74].strip()) + data.Cnp[i] = float(lines[48 + num_ctrl][24:34].strip()) + data.Cnq[i] = float(lines[48 + num_ctrl][43:54].strip()) + data.Cnr[i] = float(lines[48 + num_ctrl][65:74].strip()) + + INI = [24,43,65] + FIN = [34,54,74] + for n_ctrl in range(num_ctrl): + data['CLd'+str(n_ctrl + 1)][i] = float(lines[52 + num_ctrl] + [INI[n_ctrl]:FIN[n_ctrl]].strip()) # CL_a + data['CYd'+str(n_ctrl + 1)][i] = float(lines[53 + num_ctrl] + [INI[n_ctrl]:FIN[n_ctrl]].strip()) # CY_a + data['Cld'+str(n_ctrl + 1)][i] = float(lines[54 + num_ctrl] + [INI[n_ctrl]:FIN[n_ctrl]].strip()) # Cl_a + data['Cmd'+str(n_ctrl + 1)][i] = float(lines[55 + num_ctrl] + [INI[n_ctrl]:FIN[n_ctrl]].strip()) # Cm_a + data['Cnd'+str(n_ctrl + 1)][i] = float(lines[56 + num_ctrl] + [INI[n_ctrl]:FIN[n_ctrl]].strip()) # Cn_a + + os.remove(f"rslt_{i}.stab") + os.remove(self.run_file) + os.remove('cmd_file.run') + return(data) + +##### TODO : try to see if I can leave an AVL session open + +# def count_control_surfaces(geomfile): +# with open(geomfile,'r') as f: +# for line in f: +# + + +if __name__ == "__main__": + states = [] + controls = [] + for al in np.linspace(-10,20,30): + # for de in np.linspace(-26,28,10): + # controls.append(np.array([de,0,0])) + # states.append(np.array([al,0,0,0,0])) + # for da in np.linspace(-15, 10): + # controls.append(np.array([0,da,0])) + # states.append(np.array([al,0,0,0,0])) + # for dr in np.linspace(-5,5,10): + # controls.append(np.array([0,0,dr])) + states.append(np.array([al,0,0,0,0])) + controls.append(np.array([0,0,0])) + states = np.array(states) + controls = np.array(controls) + # states = np.array([np.arange(5)/100, np.arange(5)/600]) + # controls = np.array([np.arange(3)/3, np.arange(3)/4]) + a = avl_run(num_control_surfaces=3, geom_file='hypo', run_file='runs') + data = a.run(states, controls) + data.to_pickle('MeterSpanUAV.pkl') \ No newline at end of file diff --git a/src/pyfme/aero/hypo.avl b/src/pyfme/aero/hypo.avl new file mode 100644 index 0000000..4e4a9a9 --- /dev/null +++ b/src/pyfme/aero/hypo.avl @@ -0,0 +1,132 @@ +Hypothetical Airplane +#Mach + 0.0 +#IYsym IZsym Zsym + 0 0 0.0 +#Sref Cref Bref +0.135 0.15 0.9 +#Xref Yref Zref +0.35 0.0 0.0 +# +# +#==================================================================== +SURFACE +Wing +#Nchordwise Cspace Nspanwise Sspace +10 0.0 20 0.0 +# +YDUPLICATE +0.0 +# +ANGLE +0.0 +# +TRANSLATE +0.3 0.0 0.01 +# + +#------------------------------------------------------------- +SECTION +#Xle Yle Zle Chord Ainc Nspanwise Sspace +0.00 0. 0. 0.1875 2.0 0 0 + +AFILE +E205.txt + +CLAF +0.927097 + +CDCL +-.25 .02 .877 .0116 1.099 .028 + +#------------------------------------------------------------- +SECTION +#Xle Yle Zle Chord Ainc Nspanwise Sspace +0.01875 .45 0. 0.1125 0.0 0 0 + +AFILE +E205.txt + +CLAF +0.927097 + +CDCL +-.25 .02 .877 .0116 1.099 .028 +#==================================================================== +SURFACE +H-stab +#Nchordwise Cspace Nspanwise Sspace +5 0.0 10 0.0 +# +YDUPLICATE +0.0 +# +TRANSLATE +0.9 0.0 0.01 +# + +#------------------------------------------------------------- +SECTION +#Xle Yle Zle Chord Ainc Nspanwise Sspace +0.0 0.0 0.0 0.0913 0. 0 0 + +CLAF +0.938569 + +CDCL +-.56 .0202 .528 .0129 .792 .0575 + +#Cname Cgain Xhinge HingeVec SgnDup +CONTROL +elevator 1.0 0.001 0.0 1.0 0.0 1.0 +#------------------------------------------------------------- +SECTION +#Xle Yle Zle Chord Ainc Nspanwise Sspace +0.004564 0.2025 0.0 0.073 0. 0 0 + +CLAF +0.938569 + +CDCL +-.56 .0202 .528 .0129 .792 .0575 + +#Cname Cgain Xhinge HingeVec SgnDup +CONTROL +elevator 1.0 0.001 0.0 1.0 0.0 1.0 +# +#==================================================================== +SURFACE +V-stab +#Nchordwise Cspace Nspanwise Sspace +6 1.0 5 1.0 +TRANSLATE +0.7885 0.0 0.01 +#------------------------------------------------------------- +SECTION +#Xle Yle Zle Chord Ainc Nspanwise Sspace +0.0 0. 0.0 0.1141 0. 0 0 + +#------------------------------------------------------------- +SECTION +#Xle Yle Zle Chord Ainc Nspanwise Sspace +0.03227 0.0 .205 0.0912 0. 0 0 + +#------------------------------------------------------------- +#==================================================================== +SURFACE +Fuselage +#Nchordwise Cspace Nspanwise Sspace +2 1.0 2 1.0 +TRANSLATE +0. 0.0 0.0 +#------------------------------------------------------------- +SECTION +#Xle Yle Zle Chord Ainc Nspanwise Sspace +0.0 0. -0.01 1 0. 0 0 + +#------------------------------------------------------------- +SECTION +#Xle Yle Zle Chord Ainc Nspanwise Sspace +0.0 0.0 0.01 1 0 0 0 + +#------------------------------------------------------------- diff --git a/src/pyfme/aircrafts/E205.txt b/src/pyfme/aircrafts/E205.txt new file mode 100644 index 0000000..0651fbe --- /dev/null +++ b/src/pyfme/aircrafts/E205.txt @@ -0,0 +1,54 @@ +1.00000 0.00000 +0.99974 0.00085 +0.99392 0.00159 +0.98578 0.00307 +0.97290 0.00499 +0.94617 0.00876 +0.91866 0.01274 +0.88020 0.01864 +0.83393 0.02611 +0.79263 0.03228 +0.73829 0.04008 +0.68535 0.04742 +0.63333 0.05440 +0.58021 0.06127 +0.53232 0.06738 +0.48264 0.07291 +0.44197 0.07676 +0.38814 0.08039 +0.32774 0.08186 +0.26612 0.08023 +0.21066 0.07548 +0.14521 0.06478 +0.09684 0.05300 +0.06230 0.04164 +0.04043 0.03241 +0.02021 0.02210 +0.01003 0.01499 +0.00152 0.00614 +0.00000 0.00000 +0.00089 -.00334 +0.00310 -.00596 +0.00816 -.00968 +0.01807 -.01343 +0.03718 -.01680 +0.07273 -.02114 +0.13766 -.02413 +0.20297 -.02449 +0.26877 -.02305 +0.34581 -.02057 +0.42989 -.01762 +0.49449 -.01526 +0.56883 -.01258 +0.63816 -.01012 +0.69937 -.00831 +0.75692 -.00681 +0.82133 -.00505 +0.87969 -.00361 +0.92076 -.00233 +0.96116 -.00099 +0.98546 -.00048 +0.98991 -.00068 +0.99485 -.00044 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.cessna_310 import Cessna310 from .cessna_172 import Cessna172, SimplifiedCessna172 from .boeing_linear import LinearB747 +from .uav import MeterSpanUAV + diff --git a/src/pyfme/aircrafts/aircraft.py b/src/pyfme/aircrafts/aircraft.py index 1f10875..c961c58 100644 --- a/src/pyfme/aircrafts/aircraft.py +++ b/src/pyfme/aircrafts/aircraft.py @@ -130,8 +130,63 @@ def _calculate_aerodynamics_2(self, TAS, alpha, beta, environment): self.Mach = self.TAS / environment.a self.q_inf = 0.5 * environment.rho * self.TAS ** 2 + @abstractmethod def calculate_forces_and_moments(self, state, environment, controls): self._set_current_controls(controls) self._calculate_aerodynamics(state, environment) + + + def calculate_derivatives(self, state, environment, controls, eps=1e-3): + """ + Calculate dimensional derivatives of the forces at the vicinity of the state. + The output consists in 2 dictionaries, one for force one for moment + key: type of variables derivatives are taken for + val : 3x3 np array with X,Y,Z and L,M,N as columns, and the variable we differentiate against in lines + (u,v,w ; phi,theta,psi ; p,q,r ; x,y,z) + """ + names = {'velocity': ['u', 'v', 'w'], + 'angular_vel': ['p', 'q', 'r'], + 'acceleration': ['w_dot']} + Fnames = ['X', 'Y', 'Z'] + Mnames = ['L', 'M', 'N'] + + # F, M = self.calculate_forces_and_moments(state, environment, controls) + + # Rotation for stability derivatives in stability axis + V = np.sqrt(state.velocity.u**2 + state.velocity.v**2 + state.velocity.w**2) + alpha = np.arctan2(state.velocity.w, state.velocity.u) + beta = np.arcsin(state.velocity.v / V) + + + derivatives = {} + for keyword in names.keys(): + for i in range(len(names[keyword])): + eps_v0 = np.zeros(3) + + # plus perturb + eps_v0[i] = eps/2 + eps_vec = wind2body(eps_v0, alpha, beta) + state.perturbate(eps_vec, keyword) + forces_p, moments_p = self.calculate_forces_and_moments(state, environment, controls) + forces_p = body2wind(forces_p, alpha, beta) + moments_p = body2wind(moments_p, alpha, beta) + state.cancel_perturbation() + + # minus perturb + eps_v0[i] = - eps/2 + eps_vec = wind2body(eps_v0, alpha, beta) + state.perturbate(eps_vec, keyword) + forces_m, moments_m = self.calculate_forces_and_moments(state, environment, controls) + forces_m = body2wind(forces_m, alpha, beta) + moments_m = body2wind(moments_m, alpha, beta) + state.cancel_perturbation() + + k = names[keyword][i] + for j in range(3): + # print(Fnames[j] + k, forces[j]) + derivatives[Fnames[j] + k] = (forces_p[j] - forces_m[j]) / eps + derivatives[Mnames[j] + k] = (moments_p[j] - moments_m[j]) / eps + + return derivatives diff --git a/src/pyfme/aircrafts/cessna_172.py b/src/pyfme/aircrafts/cessna_172.py index 67c8ddb..397359f 100644 --- a/src/pyfme/aircrafts/cessna_172.py +++ b/src/pyfme/aircrafts/cessna_172.py @@ -417,14 +417,6 @@ def calculate_derivatives(self, state, environment, controls, eps=1e-3): return derivatives - def build_linear_system(self, state, environment, controls): - """ - Building linear system as described in Etkin. For full linearized equations see page 113. The variables are - delta_u, w, q and delta_theta for the long. system,. and v,p,r and psi for the lateral one. - /!\ Important notice: Ixz is defined as done in Roskam - """ - ## TODO : Verify definitions for Izx - class SimplifiedCessna172(Cessna172): def __init__(self): diff --git a/src/pyfme/aircrafts/uav.py b/src/pyfme/aircrafts/uav.py new file mode 100644 index 0000000..7bdc087 --- /dev/null +++ b/src/pyfme/aircrafts/uav.py @@ -0,0 +1,201 @@ +# -*- coding: utf-8 -*- +""" +Python Flight Mechanics Engine (PyFME). +Copyright (c) AeroPython Development Team. +Distributed under the terms of the MIT License. +---------- +Hypothetical Fixed Wing UAV - AVL is ran to get forces and moments +---------- +""" + +import numpy as np +nl = np.linalg +import pdb +from scipy.interpolate import RectBivariateSpline +from scipy.stats import linregress + +from pyfme.aircrafts.aircraft import Aircraft +from pyfme.models.constants import slugft2_2_kgm2, lbs2kg +from pyfme.utils.coordinates import wind2body, body2wind +from copy import deepcopy as cp +from pyfme.aero.avl import avl_run +import pandas as pd +import matplotlib.pyplot as plt + + +class MeterSpanUAV(Aircraft): + """ + """ + + def __init__(self, avl_file): + + # AVL stuff + # self.avl = avl_run(avl_geometry_file, ) + self.data = pd.read_pickle(avl_file) + self._build_aero_model() + + # Mass & inertia + self.mass = .50 + self.inertia = np.diag((.01, 0.02, 0.01)) + self.cg = [.3, 0, 0] + + # Reference values + self.Sw = .9**2/6 # m2 + self.span = .9 # m + self.chord = self.Sw/ self.span # m + self.propeller_radius = 0 # m + + # CONTROLS + self.controls = {'delta_elevator': 0, + 'delta_aileron': 0, + 'delta_rudder': 0, + 'delta_t': 0} + + self.control_limits = {'delta_elevator': (np.deg2rad(-26), + np.deg2rad(28)), # rad + 'delta_aileron': (np.deg2rad(-15), + np.deg2rad(20)), # rad + 'delta_rudder': (np.deg2rad(-16), + np.deg2rad(16)), # rad + 'delta_t': (0, 1)} # non-dimensional + + # Aerodynamic Coefficients + self.CL, self.CD, self.Cm = 0, 0, 0 + self.CY, self.Cl, self.Cn = 0, 0, 0 + + # Thrust Coefficient + self.Ct = 0 + + self.total_forces = np.zeros(3) + self.total_moments = np.zeros(3) + + # Velocities + self.TAS = 0 # True Air Speed. + self.CAS = 0 # Calibrated Air Speed. + self.EAS = 0 # Equivalent Air Speed. + self.Mach = 0 # Mach number + self.q_inf = 0 # Dynamic pressure at infinity (Pa) + + # Angles + self.alpha = 0 # rad + self.beta = 0 # rad + self.alpha_dot = 0 # rad/s + + def _build_aero_model(self): + self.CL_0 = 0.148 + self.CM_0 = 0.0075 + self.CL_alpha = 5.440E+00 + self.CL_q = np.mean(self.data.CLq) + self.CL_delta_elev = np.sum(self.data.de*self.data.CLd1)/np.sum(self.data.de**2) + + self.CM_alpha2, self.CM_alpha, self.CM_0 = np.polyfit(self.data.alpha, self.data.Cm, 2) + self.CM_q = 2*np.mean(self.data.Cmq) + self.CM_delta_elev = np.sum(self.data.de*self.data.Cmd1)/np.sum(self.data.de**2) + + # pre-stall drag model + ICL_max = self.data.CL.idxmax() + cl = self.data.CL[:ICL_max-2] + cd = self.data.CD[:ICL_max-2] + al = self.data.alpha[: ICL_max] + self.CD_K1, self.CD_0, r_value, p_value, std_err = linregress(cl ** 2, cd) + self.CL_MAX = self.data.CL[ICL_max] + + self.CY_beta = np.mean(self.data.CYb) + self.CY_p = np.mean(self.data.CYp) + self.CY_r = np.mean(self.data.CYr) + self.CY_delta_rud = np.mean(self.data.dr) + + self.Cl_beta = np.mean(self.data.Clb) + self.Cl_p = np.mean(self.data.Clp) + self.Cl_r_cl = np.sum(self.data.CL*self.data.Clr)/np.sum(self.data.CL**2) + self.Cl_delta_rud = np.mean(self.data.Cld2) + self.Cl_delta_aile = np.sum(self.data.da*self.data.Cld2)/np.sum(self.data.da**2) + + self.CN_beta = np.mean(self.data.Cnb) + self.CN_p_al = np.sum(self.data.alpha*self.data.Cnp)/np.sum(self.data.alpha**2) + self.CN_r_cl, self.CN_r_0, _, _,_ = linregress(self.data.CL**2,self.data.Cnr) + self.CN_delta_rud = np.mean(self.data.Cnd3) + # x = np.reshape(self.data.CL, (1, 12)) * np.reshape(self.data.da, (9, 1)) + # self.CN_delta_aile_cl = np.sum(self.data.Cnd2*x) / np.sum(x**2) + + @property + def delta_elevator(self): + return self.controls['delta_elevator'] + + @property + def delta_rudder(self): + return self.controls['delta_rudder'] + + @property + def delta_aileron(self): + return self.controls['delta_aileron'] + + @property + def delta_t(self): + return self.controls['delta_t'] + + def calculate_aero_coeffs(self, state, controls): + # Compute features + V = nl.norm(state.velocity.vel_body) + p = state.angular_vel.p * self.span / (2*V) + q = state.angular_vel.q * self.chord / (2*V) + r = state.angular_vel.r * self.span / (2*V) + alpha = np.arctan2(state.velocity.w, state.velocity.u) + beta = np.arcsin(state.velocity.v, V) + + # Run AVL + avl_state = np.array([alpha, beta, p, q, r]) + avl_controls = np.array([self.delta_elevator, self.delta_aileron, self.delta_rudder]) + data = self.avl.run(avl_state, avl_controls) + + # set values for non-dimensional coefficients. + for attr in data.columns: + setattr(self, attr, data[attr][0]) + + def _calculate_aero_forces_moments(self, state): + q = self.q_inf + Sw = self.Sw + c = self.chord + b = self.span + + self.calculate_aero_coeffs(state) + + L = q * Sw * self.CL + D = q * Sw * self.CD + Y = q * Sw * self.CY + l = q * Sw * b * self.Cl + m = q * Sw * c * self.Cm + n = q * Sw * b * self.Cn + + return L, D, Y, l, m, n + + def _calculate_thrust_forces_moments(self, environment): + return np.array([1, 0, 0]), np.array([0, 0, 0]) + + def calculate_forces_and_moments(self, state, environment, controls): + # Update controls and aerodynamics + super().calculate_forces_and_moments(state, environment, controls) + + Ft, Mt = self._calculate_thrust_forces_moments(environment) + L, D, Y, l, m, n = self._calculate_aero_forces_moments(state) + Fg = environment.gravity_vector * self.mass + + Fa_wind = np.array([-D, Y, -L]) + Fa_body = wind2body(Fa_wind, self.alpha, self.beta) + Fa = Fa_body + + self.total_forces = Ft + Fg + Fa + self.total_moments = np.array([l, m, n]) + + self.Fa_wind = Fa_wind + + # return state.velocity._vel_body, state.angular_vel._vel_ang_body + return self.total_forces, self.total_moments + + + +if __name__=='__main__': + a = MeterSpanUAV('MeterSpanUAV.pkl') + plt.plot(a.data.CL, a.data.alpha) + plt.show() + From 9c48167380547d617730503c44f35e5d787384ec Mon Sep 17 00:00:00 2001 From: jdebecdelievre Date: Sat, 9 Jun 2018 12:47:26 -0700 Subject: [PATCH 5/5] finished validation against simulaing withh off-diag inertia terms --- src/pyfme/aircrafts/cessna_172.py | 9 +- src/pyfme/models/euler_flat_earth.py | 34 +- src/pyfme/simulator.py | 21 +- src/pyfme/utils/coordinates.py | 12 +- .../PyFME vs Simulink - batch of cases.ipynb | 624 ++++++++++++++++++ validation/PyFME vs Simulink.ipynb | 86 ++- 6 files changed, 720 insertions(+), 66 deletions(-) create mode 100644 validation/PyFME vs Simulink - batch of cases.ipynb diff --git a/src/pyfme/aircrafts/cessna_172.py b/src/pyfme/aircrafts/cessna_172.py index 397359f..b03d29f 100644 --- a/src/pyfme/aircrafts/cessna_172.py +++ b/src/pyfme/aircrafts/cessna_172.py @@ -95,8 +95,13 @@ def __init__(self): # Mass & Inertia self.mass = 2300 * lbs2kg # kg self.inertia = np.diag([948, 1346, 1967]) * slugft2_2_kgm2 # kg·m² - self.inertia[0, 2] = - 100*slugft2_2_kgm2 - self.inertia[2, 0] = - 100*slugft2_2_kgm2 + self.inertia[0, 2] = - 10000*slugft2_2_kgm2 + self.inertia[2, 0] = - 10000*slugft2_2_kgm2 + self.inertia[1, 0] = - 20000*slugft2_2_kgm2 + self.inertia[0, 1] = - 20000*slugft2_2_kgm2 + self.inertia[1, 2] = - 10000*slugft2_2_kgm2 + self.inertia[2, 1] = - 10000*slugft2_2_kgm2 + self.inertia_inverse = np.linalg.inv(self.inertia) # Geometry self.Sw = 16.2 # m2 diff --git a/src/pyfme/models/euler_flat_earth.py b/src/pyfme/models/euler_flat_earth.py index 680979d..bcce3c4 100644 --- a/src/pyfme/models/euler_flat_earth.py +++ b/src/pyfme/models/euler_flat_earth.py @@ -24,6 +24,7 @@ ) from pyfme.utils.coordinates import body2wind, wind2body import math +from numba import jit _FLOAT_EPS_4 = np.finfo(float).eps * 4.0 @@ -45,10 +46,11 @@ def fun(self, t, x=None): mass = updated_simulation.aircraft.mass inertia = updated_simulation.aircraft.inertia + inertia_inverse = updated_simulation.aircraft.inertia_inverse forces = updated_simulation.aircraft.total_forces moments = updated_simulation.aircraft.total_moments - rv = _system_equations(t, x, mass, inertia, forces, moments) + rv = _system_equations(t, x, mass, inertia, inertia_inverse, forces, moments) return rv @@ -63,13 +65,14 @@ def right_hand_side(self, full_state, environment, aircraft, mass = aircraft.mass inertia = aircraft.inertia + inertia_inverse = aircraft.inertia_inverse forces = aircraft.total_forces moments = aircraft.total_moments t0 = 0 x0 = self._get_state_vector_from_full_state(full_state) - return _system_equations(t0, x0, mass, inertia, forces, moments) + return _system_equations(t0, x0, mass, inertia, inertia_inverse, forces, moments) def steady_state_trim_fun(self, full_state, environment, aircraft, controls): @@ -174,6 +177,8 @@ def linearized_model(self, state, aircraft, environment, controls=None, method=" Iy = I[1, 1] Iz = I[2, 2] Ixz = - I[0, 2] + assert abs(I[1,0]) < 1e-10 and abs(I[2,0]) < 1e-10, "This method is only valid for symmetrical aircrafts" + Ixprime = (Ix*Iz - Ixz**2)/Iz Izprime = (Ix*Iz - Ixz**2)/Ix Ixzprime = Ixz/(Ix*Iz - Ixz**2) @@ -371,8 +376,9 @@ def body2wind4attitude(eps_v0, alpha, beta): eps_vec = body2wind(eps_vec, alpha, beta) return np.array([eps_vec[1], eps_vec[0], eps_vec[2]]) -# TODO: numba jit -def _system_equations(time, state_vector, mass, inertia, forces, moments): + +@jit +def _system_equations(time, state_vector, mass, inertia, inertia_inverse, forces, moments): """Euler flat earth equations: linear momentum equations, angular momentum equations, angular kinematic equations, linear kinematic equations. @@ -423,6 +429,8 @@ def _system_equations(time, state_vector, mass, inertia, forces, moments): """ # Note definition of total_moments of inertia p.21 Gomez Tierno, et al # Mecánica de vuelo + I = inertia + invI = inertia_inverse Ix = inertia[0, 0] Iy = inertia[1, 1] Iz = inertia[2, 2] @@ -432,6 +440,7 @@ def _system_equations(time, state_vector, mass, inertia, forces, moments): L, M, N = moments u, v, w = state_vector[0:3] + omega = state_vector[3:6] p, q, r = state_vector[3:6] theta, phi, psi = state_vector[6:9] @@ -441,13 +450,14 @@ def _system_equations(time, state_vector, mass, inertia, forces, moments): dw_dt = Fz / mass + q * u - p * v # Angular momentum equations - dp_dt = (L * Iz + N * Jxz - q * r * (Iz ** 2 - Iz * Iy + Jxz ** 2) + - p * q * Jxz * (Ix + Iz - Iy)) / (Ix * Iz - Jxz ** 2) - dq_dt = (M + (Iz - Ix) * p * r - Jxz * (p ** 2 - r ** 2)) / Iy - dr_dt = (L * Jxz + N * Ix + p * q * (Ix ** 2 - Ix * Iy + Jxz ** 2) - - q * r * Jxz * (Iz + Ix - Iy)) / (Ix * Iz - Jxz ** 2) - - # Angular Kinematic equations + dp_dt, dq_dt, dr_dt = invI @ (moments - np.cross(omega, (I @ omega))) + # dp_dt = (L * Iz + N * Jxz - q * r * (Iz ** 2 - Iz * Iy + Jxz ** 2) + + # p * q * Jxz * (Ix + Iz - Iy)) / (Ix * Iz - Jxz ** 2) + # dq_dt = (M + (Iz - Ix) * p * r - Jxz * (p ** 2 - r ** 2)) / Iy + # dr_dt = (L * Jxz + N * Ix + p * q * (Ix ** 2 - Ix * Iy + Jxz ** 2) - + # q * r * Jxz * (Iz + Ix - Iy)) / (Ix * Iz - Jxz ** 2) + + # Angular Kinematic equations (min and max to prevent blow up) dtheta_dt = q * cos(phi) - r * sin(phi) dphi_dt = p + (q * sin(phi) + r * cos(phi)) * np.tan(theta) dpsi_dt = (q * sin(phi) + r * cos(phi)) / cos(theta) @@ -463,4 +473,4 @@ def _system_equations(time, state_vector, mass, inertia, forces, moments): phi) * cos(theta) return np.array([du_dt, dv_dt, dw_dt, dp_dt, dq_dt, dr_dt, dtheta_dt, - dphi_dt, dpsi_dt, dx_dt, dy_dt, dz_dt]) + dphi_dt, dpsi_dt, dx_dt, dy_dt, dz_dt]) \ No newline at end of file diff --git a/src/pyfme/simulator.py b/src/pyfme/simulator.py index bb08d1e..b2ed055 100644 --- a/src/pyfme/simulator.py +++ b/src/pyfme/simulator.py @@ -14,6 +14,7 @@ import pandas as pd import tqdm +from pyfme.utils.coordinates import AlphaBetaRangeError class Simulation: @@ -91,13 +92,13 @@ class Simulation: } def __init__(self, aircraft, system, environment, controls, dt=0.01, - save_vars=None): + save_vars=None, verbose=True): """ Simulation object Parameters ---------- - aircraft : Aircraft + aircraft : Aircraft Aircraft model system : System System model @@ -117,6 +118,7 @@ def __init__(self, aircraft, system, environment, controls, dt=0.01, self.controls = controls self.dt = dt + self.verbose = verbose if not save_vars: self._save_vars = self._default_save_vars @@ -156,7 +158,8 @@ def propagate(self, time): dt = self.dt half_dt = self.dt/2 - bar = tqdm.tqdm(total=time, desc='time', initial=self.system.time) + if self.verbose: + bar = tqdm.tqdm(total=time, desc='time', initial=self.system.time) # To deal with floating point issues we cannot check equality to # final time to finish propagation @@ -168,11 +171,17 @@ def propagate(self, time): self.aircraft.calculate_forces_and_moments(self.system.full_state, self.environment, controls) - self.system.time_step(dt) + try: + self.system.time_step(dt) + except AlphaBetaRangeError: + break self._save_time_step() - bar.update(dt) - bar.close() + if self.verbose: + bar.update(dt) + + if self.verbose: + bar.close() results = pd.DataFrame(self.results) results.set_index('time', inplace=True) diff --git a/src/pyfme/utils/coordinates.py b/src/pyfme/utils/coordinates.py index 8f48750..ab2daeb 100644 --- a/src/pyfme/utils/coordinates.py +++ b/src/pyfme/utils/coordinates.py @@ -309,6 +309,14 @@ def hor2wind(hor_coords, gamma, mu, chi): return wind_coords +class AlphaBetaRangeError(Exception): + """Exception raised if alpha and beta get too big + """ + + def __init__(self, message): + self.message = message + + def check_alpha_beta_range(alpha, beta): """Check alpha, beta values are inside the defined range. This comprobation can also detect if the value of the angle is in degrees in @@ -319,9 +327,9 @@ def check_alpha_beta_range(alpha, beta): beta_min, beta_max = (-np.pi, np.pi) if not (alpha_min <= alpha <= alpha_max): - raise ValueError('Alpha value is not inside correct range') + raise AlphaBetaRangeError('Alpha value is not inside correct range') elif not (beta_min <= beta <= beta_max): - raise ValueError('Beta value is not inside correct range') + raise AlphaBetaRangeError('Beta value is not inside correct range') def body2wind(body_coords, alpha, beta): diff --git a/validation/PyFME vs Simulink - batch of cases.ipynb b/validation/PyFME vs Simulink - batch of cases.ipynb new file mode 100644 index 0000000..97b1ffb --- /dev/null +++ b/validation/PyFME vs Simulink - batch of cases.ipynb @@ -0,0 +1,624 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# PyFME Validation: comparing response versus Matlab model" + ] + }, + { + "cell_type": "code", + "execution_count": 238, + "metadata": {}, + "outputs": [], + "source": [ + "from pyfme.aircrafts import LinearB747, Cessna172, SimplifiedCessna172\n", + "from pyfme.models import EulerFlatEarth\n", + "from pyfme.models.state import AircraftState\n", + "import numpy as np\n", + "# nl = np.linalg\n", + "import matplotlib.pyplot as plt\n", + "from pyfme.environment.atmosphere import SeaLevel\n", + "from pyfme.environment.wind import NoWind\n", + "from pyfme.environment.gravity import VerticalConstant\n", + "from pyfme.environment import Environment\n", + "from pyfme.utils.trimmer import steady_state_trim\n", + "from pyfme.models.state.position import EarthPosition\n", + "from pyfme.simulator import Simulation\n", + "from pyfme.utils.export import results2matlab\n", + "from scipy.io import savemat, loadmat\n", + "from pyfme.utils.coordinates import wind2body, body2wind\n", + "from pyfme.utils.input_generator import Constant, Doublet, Ramp\n", + "from json import load as jload\n", + "from copy import deepcopy as cp\n", + "plt.style.use('ggplot')\n", + "from scipy.interpolate import interp1d as itp\n", + "import pickle" + ] + }, + { + "cell_type": "code", + "execution_count": 218, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The autoreload extension is already loaded. To reload it, use:\n", + " %reload_ext autoreload\n" + ] + } + ], + "source": [ + "%load_ext autoreload\n", + "%autoreload 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Running a PyFME simulation and save it to a MATLAB readable file" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We start by defining the airplane and the environment." + ] + }, + { + "cell_type": "code", + "execution_count": 128, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "aircraft = SimplifiedCessna172()" + ] + }, + { + "cell_type": "code", + "execution_count": 129, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "atmosphere = SeaLevel()\n", + "gravity = VerticalConstant()\n", + "wind = NoWind()\n", + "environment = Environment(atmosphere, gravity, wind)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate a serie of states on which to test" + ] + }, + { + "cell_type": "code", + "execution_count": 130, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "pos = EarthPosition(x=0, y=0, height=1000)\n", + "psi = 0.5 # rad\n", + "TAS = 45 # m/s\n", + "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}\n", + "tstate, cont = steady_state_trim(\n", + " aircraft,\n", + " environment,\n", + " pos,\n", + " psi,\n", + " TAS,\n", + " controls0\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 131, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "N = 100;\n", + "omega = np.random.normal(loc=1,scale=.5,size=(N,3)) * np.random.choice([-1,1],(N,3), replace=True)\n", + "euler = 60*np.pi/180*np.random.normal(loc=1,scale=.5,size=(N,3)) * np.random.choice([-1,1],(N,3), replace=True)\n", + "velocity = np.random.normal(loc=[50, 5, 5],scale=.5,size=(N,3)) * np.random.choice([-1,1],(N,3), replace=True)\n", + "velocity[:,0] *= np.sign(velocity[:,0])\n", + "states = []\n", + "for case_id in range(N):\n", + " state = cp(tstate)\n", + " state.velocity._vel_body = velocity[case_id, :]\n", + " state.angular_vel._euler_ang_rate = omega[case_id, :]\n", + " state.attitude._euler_angles = euler[case_id, :]\n", + " states.append(state)\n", + " state.save_to_json(f'{case_id}.json')" + ] + }, + { + "cell_type": "code", + "execution_count": 228, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Bd/R2bCIislq9u6H2Ao4BnjGzPyVl5wAXAW5mE4lvCJxQp/hERDK5/aGzuj/g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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(omega[:,:]*180/np.pi,40,stacked=True)\n", + "plt.xlabel('rotation rates in deg/s')\n", + "plt.ylabel('number of occurences')\n", + "plt.title('distribution of initial roll rates')\n", + "plt.legend(('roll','pitch','yaw'))\n", + "plt.show()\n", + "\n", + "plt.hist(euler[:,:]*180/np.pi,40,stacked=True)\n", + "plt.xlabel('euler angles in degrees')\n", + "plt.ylabel('number of occurences')\n", + "plt.title('distribution of initial attitudes')\n", + "plt.legend(('roll','pitch','yaw'))\n", + "plt.show()\n", + "\n", + "vel = velocity*1.0\n", + "vel[:,0]/=10\n", + "plt.hist(vel,40,stacked=True)\n", + "plt.xlabel('velocities in m/s')\n", + "plt.ylabel('number of occurences')\n", + "plt.title('distribution of velocities')\n", + "plt.legend(('u / 10','v','w'))\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "We finally pick a particular time serie of controls and run the simulation." + ] + }, + { + "cell_type": "code", + "execution_count": 132, + "metadata": {}, + "outputs": [], + "source": [ + "controls = {\n", + " 'delta_elevator': Doublet(t_init=2, T=1, A=0.1, offset=cont['delta_elevator']),\n", + " 'delta_aileron': Ramp(t_init=1,T=2, A=.2, offset=cont['delta_aileron']),\n", + " 'delta_rudder': Constant(cont['delta_rudder']),\n", + " 'delta_t': Constant(cont['delta_t'])\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 133, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "T = 3 # seconds" + ] + }, + { + "cell_type": "code", + "execution_count": 134, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Aircraft State \n", + "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n", + "theta: -1.018 rad, phi: -1.910 rad, psi: -1.009 rad \n", + "u: 50.52 m/s, v: -3.92 m/s, w: -5.04 m/s \n", + "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n", + "u_dot: -0.00 m/s², v_dot: -0.00 m/s², w_dot: -0.00 m/s² \n", + "P_dot: 0.00 rad/s², Q_dot: 0.00 rad/s², R_dot: -0.00 rad/s² " + ] + }, + "execution_count": 134, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "state" + ] + }, + { + "cell_type": "code", + "execution_count": 141, + "metadata": {}, + "outputs": [], + "source": [ + "results = {}\n", + "for case_id in range(N):\n", + " state = states[case_id]\n", + " environment.update(state)\n", + " system = EulerFlatEarth(t0=0, full_state=state)\n", + " sim = Simulation(aircraft, system, environment, controls, verbose=False)\n", + " results[case_id] = sim.propagate(T)" + ] + }, + { + "cell_type": "code", + "execution_count": 242, + "metadata": {}, + "outputs": [], + "source": [ + "with open('batch_results.pkl','wb') as f:\n", + " pickle.dump(file=f,obj=results)\n", + "# r = pickle.load(open('batch_results.pkl','rb'))" + ] + }, + { + "cell_type": "code", + "execution_count": 136, + "metadata": {}, + "outputs": [], + "source": [ + "nT = int(T/sim.dt)\n", + "t= np.arange(nT)*sim.dt\n", + "controls4matlab = np.ones((nT,4));\n", + "for it in range(nT):\n", + " controls4matlab[it,0] = controls['delta_aileron']._fun(t[it])\n", + " controls4matlab[it,1] = controls['delta_elevator']._fun(t[it])\n", + " controls4matlab[it,2] = controls['delta_rudder']._fun(t[it])\n", + " controls4matlab[it,3] = controls['delta_t']._fun(t[it])\n", + "savemat('controls.mat',{'c': controls4matlab, 'dt':sim.dt})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We save the controls in a Matlab file" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Run the same simulation in Simulink" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The simulink bloc diagram used for comparison uses exactly the same model to compute forces and moments (the method aircraft.compute_forces_and_moments() was translated directly to Matlab). The entire equations of motion integration is done with the %6DOF (Quaternion) % Simulink bloc from the aerospace blocset. Verifying against this tool allows to make sure that there are no mistake in the way the EulerFlatEarth equations of motion are written, and in the way they are integrated.\n", + "\n", + "We run the Simulink model and load the results:" + ] + }, + { + "cell_type": "code", + "execution_count": 143, + "metadata": {}, + "outputs": [], + "source": [ + "matlab_rslt = {}\n", + "for case_id in range(N):\n", + " with open('../../matlab_comparison/results' + str(case_id) + '.json','r') as f:\n", + " mat_states = jload(f)\n", + " mat_states = {k:np.array(el) for k,el in mat_states.items()}\n", + " matlab_rslt[case_id] = mat_states" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Compare outputs" + ] + }, + { + "cell_type": "code", + "execution_count": 256, + "metadata": {}, + "outputs": [], + "source": [ + "getname={'Euler':['phi','theta','psi'], 'Omega_body':['p','q','r'], 'V_body':['u', 'v', 'w']}\n", + "unit = {'Euler':'deg', 'Omega_body':'deg/s', 'V_body':'m/s'} \n", + "legend = {'Euler':('roll','pitch','yaw'), 'Omega_body':('roll','pitch','yaw'), 'V_body':('u','v','w')} \n", + "factor = {'Euler':180/np.pi, 'Omega_body':180/np.pi, 'V_body':1}\n", + "name = {'Euler':'euler angles', 'Omega_body':'rotation rates', 'V_body':'velocities'} \n", + "def getMSE(keyword, idx):\n", + " name = getname[keyword][idx]\n", + " error = np.zeros(N)\n", + " for case_id in range(N):\n", + " nc = len(results[case_id].u)\n", + " matlab_calc = itp(matlab_rslt[case_id]['t'], matlab_rslt[case_id][keyword][:,idx])\n", + " error[case_id] = np.sum(abs(results[case_id][name] - matlab_calc(results[case_id].index)))/nc\n", + " return error*factor[keyword]" + ] + }, + { + "cell_type": "code", + "execution_count": 257, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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XokvoC54IU0Df56lknQerqufgKgrzlU1VzZednQ1DQ0M9JNJW3DngipadnV1o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\nlT8W4FIQOjzOsrh+imovb2XJV+DWrVv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XEmvQoAG2b9+OmTNnol69ehg9erR0CWPgyXUhwsLC0KxZMyxfvhxTpkzB4MGD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\nuLu7w8LCAu3bt0d8fLyxYxERUQ1X4w9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isLAQp06dwttvv4233noLFy5cUDoKEVGN06lTJ6xcuRIdO3ZEx44dsXHjRrRs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\nZMT/B5eBJgGPJrUyAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for keyword in getname.keys():\n", + " err = (getMSE(keyword,i) for i in range(3))\n", + " error = np.vstack(err)\n", + " plt.hist(error.T, 30, stacked=True);\n", + " plt.title('Distribution of absolute errors on ' + name[keyword] + ' for all trajectories')\n", + " plt.ylabel('number of occurences')\n", + " plt.xlabel('Error in ' + unit[keyword])\n", + " plt.legend(legend[keyword])\n", + " plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Show examples" + ] + }, + { + "cell_type": "code", + "execution_count": 147, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "case_id=19" + ] + }, + { + "cell_type": "code", + "execution_count": 148, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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1E20LfcQyZ+vaWC3Cf7ztseLlEdt8AIbMz2112vDQ4FcqTLL682+V5XzkGIxd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\nfp8KtM+lzM1AmjHmT2PMX0Aa0PIsXvO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LciCQI+I02Ivh+W9+YZDtGzxYTHTfAGhrXamiGtUrFhCecA1ikzmf8Y6x1Jcd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\nh+rVq2uohzkRoXr16sX6Zhb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LHtcjB1UySiIYMoD6+e5HAbuKaiMiDqAG8Gcxty0R0xLjad8sApddaFTnLD65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\nlAoZSd1aUM1l50NvR360GvK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ckgDXUpVHGgBKBYnsxeQ+c5rxt6wRREsa74Y9RW32kpaeqRPGVInTAFAqiGx7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\nqQrq/wGr+IN1ud+3WwAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Longitudinal values\n", + "plt.plot(matlab_rslt[case_id]['t'], matlab_rslt[case_id]['V_body'][:,0], '.', label='Simulink output')\n", + "plt.plot(results[case_id].u, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Horizontal velocity\")\n", + "plt.show()\n", + "\n", + "plt.plot(matlab_rslt[case_id]['t'], matlab_rslt[case_id]['V_body'][:,2], '.', label='Simulink output')\n", + "plt.plot(results[case_id].w, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Vertical velocity\")\n", + "plt.show()\n", + "\n", + "plt.plot(matlab_rslt[case_id]['t'], matlab_rslt[case_id]['Omega_body'][:,1], '.', label='Simulink output')\n", + "plt.plot(results[case_id].q, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Pitch rate\")\n", + "plt.show()\n", + "\n", + "plt.plot(matlab_rslt[case_id]['t'], matlab_rslt[case_id]['Euler'][:,1], '.', label='Simulink output')\n", + "plt.plot(results[case_id].theta, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Pitch angle\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 149, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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W6B00aBBXX301TZs2ZfTo0bz66qt07NiRrl27snv3buDYpX937txJQkLCcedauHAh3bp1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\nvQBoGV+rStbOwWr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6rVnrtmKDNieDkJxlbaoOU1lYMBhTiIKm48iWOyjinW/o4mwjUvxtz6iXjRrN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\nrYRlG2NM2ZkwsjMnqcEMXw+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JmLkqsBVVQU3DX6kQlN0ZXN5ucZDq3Jk1ifnuBEbZl/Cu8xmu5BfSMk7RbOKy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\nsjt/13mvYbHnJu61fUodORx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UdbqqZqtqdkpKSi1OyRhjGsaNQ7uylxZ8rp042/MZEF3jAN6aCqjqiBCP9RLw\nNnB/JcfYEfy7SUTmAf2AjaGHaYwxjc+ATq1J8AifuJlM8syhCUc4dCQp0mGFLNyrgLqXezkOWFdJ\nmdYikhh83hYYAqwJp15jjGkskhM8LHAz8Imfgc46/C5RMw4Q7hjAtGB30CrgPOB2ABHJFpFngmV6\nArkishL4LzBNVS0BGGNiwoSBaSx1T6dQEzjLCXQDPfHf9RGOKjQ1dgFVR1UvruL9XOD64POFQGY4\n9RhjTGM1ZUxP/vrxJha7PRjmrOQ3XMU3B45EOqyQ2ExgY4wJU2KChw/dfnRzdtBJvomabiBLAMYY\nE6aMDi34wO0HwLnOCiA6uoEsARhjTJgmj+7JNm3Hl25HfuAsB+C7g43/clBLAMYYE6YBnVrj8wgf\nuv3JcdbRjHyK/cqyrXsjHVq1LAEYY0wdOLl5Ih/4+5Egfs4OXg007Z21EY6qepYAjDGmDtw8vDvL\ntTv7tCkjPMsA+Pzr/RGOqnqWAIwxpg5MyEkD8fC+O4AfOsvxUUxBsRvpsKplCcAYY+pI00Qvb/lz\naCH5nOV8hgLT5jTebiBLAMYYU0cmDEzjEzeT/dqE8z2fAvDCoi0Rjak6lgCMMaaOTBnTk2K8vOs/\ngx86y/BRTH4j7gayBGCMMXWoqc/D2+4gWkgBZzurgMbbDRTWWkCRUFxczPbt2zlyJDrW2jC1k5SU\nRGpqKgkJCZEOxZgTctWgTjwzv5B92pQLPIv4wB3A859sZsqYnpEO7ThRlwC2b99O8+bNSU9PR0Qi\nHY6pB6rKnj172L59O507d450OMackCljevL0/E287R/Ejzwf05x8DvqbsGzrXgZ0ah3p8I4RdV1A\nR44coU2bNvblH8NEhDZt2lgrz0Stpj4P//IPJVmKygaDG+OksKhLAIB9+ccB+4xNNLtqUCfytCvr\n3Y5c6vkIgOWNcFmIqEwAxhjTmE0Z0xNB+Jf/HAY46+kqX+PXxrdEtCWAWnjooYfo3bs3ffr0ISsr\ni8WLFwNw/fXXs2ZN3dzsLD09nd27dwMwePDgEypfV2bNmhXW+ezbt48nn3yyDiMyJnqkNPcx0382\nJepwqWc+AH+Y+0WEozpWXCSAZVv38sR/N9TJynyLFi3irbfeYvny5axatYr333+fU089FYBnnnmG\nXr16hV1HRQsXLqzzY4bCEoAxtXfHiNPZRSv+6/bjEs9HJFLE7kNFkQ7rGDGfAJZt3cvEZz7l0fe+\nYOIzn4adBHbu3Enbtm1JTEwEoG3btnTo0AGAYcOGkZubC0CzZs2YPHkyAwYMYMSIESxZsoRhw4bR\npUsXZs+eDcCMGTO49dZby46xwfWtAAAQfUlEQVQ9duxY5s2bd1ydzZo1A2DevHkMGzaMSy65hB49\nejBx4kRU9ZiyBQUFjBo1ir/+9a/HHefll18mMzOTjIwMJk+efNzxAV577TWuvfZaFi5cyOzZs/nF\nL35BVlYWGzduZNiwYdxxxx0MHjyYjIwMlixZAsADDzzAI488UnaMjIwMtmzZwpQpU9i4cSNZWVn8\n4he/CP0f2ZgYMCEnDY/ADP95tJUDjHUCg8F3vLIiwpEdFfMJ4NNNeygqcXEViktcPt20J6zjnXfe\neWzbto3TTjuNm2++mY8++qjScocPH2bYsGEsW7aM5s2bM3XqVObOncvMmTO57777al3/ihUreOyx\nx1izZg2bNm3ik08+Kdt26NAhLrjgAiZMmMBPfvKTY/bbsWMHkydP5sMPPyQvL4+lS5cya9asKusZ\nPHgw48aN4+GHHyYvL4+uXbuWndfChQt58sknmTRpUrWxTps2ja5du5KXl8fDDz9c63M2Jlpd0LcD\nn7gZrHc7co33XUCZlbcj0mGVifkEMKhLG3xeB49AgtdhUJc2YR2vWbNmLFu2jOnTp5OSksLll1/O\njBkzjivn8/kYNWoUAJmZmQwdOpSEhAQyMzPZsmVLresfOHAgqampOI5DVlbWMccaP348P/7xj7n6\n6quP22/p0qUMGzaMlJQUvF4vEydOZP78+Sdc/5VXXgnAOeecw4EDB9i3b1+tz8WYWPfYFf0A4W/+\n8+jjbKa/BG4T2VhaATGfAAZ0as2L1w/iZ+edzovXD6qTiRgej4dhw4bxq1/9iscff5zXX3/9uDIJ\nCQlllzI6jlPWZeQ4DiUlJQB4vV5c9+g6IaFc9156nNI4So8FMGTIEN55553juoWASt8rVf6Sy5pi\nqHh5pojU6jyMiRe92jfnDf/ZHNAmTPL+B4B/N5JWQMwnAAgkgVuGd6uTL/8vvviC9euP3uw5Ly+P\nTp061epY6enp5OXl4bou27ZtK+tTr60HH3yQNm3acPPNNx+3LScnh48++ojdu3fj9/t5+eWXGTp0\nKADt2rVj7dq1uK7LzJkzy/Zp3rw5Bw8ePOY4r776KgALFiygZcuWtGzZkvT0dJYvD9wHdfny5Wze\nvLnK/Y2JN7++MJN8knjJ/wNGO4tJl52NZpnouEgAdenQoUNcc8019OrViz59+rBmzRoeeOCBWh1r\nyJAhdO7cmczMTO6880769+8fdnyPPfYYR44c4Ze//OUx77dv357f/e53DB8+nL59+9K/f3/Gjx8P\nBPrqx44dyw9+8APat29fts8VV1zBww8/TL9+/di4cSMArVu3ZvDgwdx00008++yzAFx88cV8//33\nZGVl8dRTT3HaaacB0KZNG4YMGUJGRoYNApu4NaBTa1o1SeDZkjEU4+WnnjcBmD5/U4QjA6muayDS\nsrOztfSqmlJr166lZ8/Gt6hSPBg2bBiPPPII2dnZDVKffdYmVry0+CvunvkZD3hnMNHzAcMK/8DX\npHDTOV3qfJE4EVmmqiH9T2otAGOMqWcTctJokuAwvWQsCtzofQuIfCvAEoAJ2bx58xrs178xsWbq\n2N7soC2v+YdyhedDTpVvcYnsWIAlAGOMaQClrYDHSi7Gj4c7vf8C4C8RbAVYAjDGmAYydWxvvqM1\nz/pHM96zkN6yGSVy8wLqLAGIyJ0ioiLStort14jI+uDjmrqq1xhjokVpK+AvJRfwvTbjbu9LRHJ2\ncJ0kABE5FfghUOlapyJyEnA/kAMMBO4XkcZ1axxjjGkAU8f25iBN+EPJpQzxfF62RtCFjy9o8Fjq\nqgXwv8AvgaquKR0JzFXV71V1LzAXGFVHdTc4j8dDVlYWGRkZXHrppeTn51dZdsuWLSQnJ5OVlVX2\nKCoqYsaMGYgIH3zwQVnZmTNnIiK89tprQOCyy9NPP71sv0suuSSk+Hbs2BFy2ZrMmzePsWPHVlsm\nLy+POXPmlL2ePXs206ZNq5P6jYk1E3LSaNM0gZf85/KZm87UhH/QlALytu+vkxWLT0TYCUBExgFf\nq+rKaop1BLaVe709+F5lx7tBRHJFJHfXrl3hhlcvkpOTycvLY/Xq1fh8Pp5++ulqy5cuiFb68Pl8\nQGCNoJdffrms3CuvvELfvn2P2ffFF18s2680MdSkQ4cOIZetCxUTwLhx45gyZUqD1W9MtJl+9Rm4\nOEwtnsTJ7OP/eQP/v172dMMu/R7STeFF5H3glEo23QPcDZxX0yEqea/S1oKqTgemQ2AiWLVHfWcK\nfPNZDVWfoFMyYXTov17PPvtsVq1axb333kvbtm25/fbbAbjnnnto164d48aNq3bfjz/+mOLiYgoL\nC9mwYQNZWVknFO5HH31UVqeIMH/+fPbs2cPYsWNZvXo1M2bMYNasWfj9flavXs3Pf/5zioqK+Pvf\n/05iYiJz5szhpJNOOmaS1+7du8nOzj5u0bolS5Zwxx13UFBQQHJyMs8//zydO3fmvvvuo6CggAUL\nFnDXXXdRUFBAbm4ujz/+OFu3bmXSpEns2rWLlJQUnn/+edLS0rj22mtp0aIFubm5fPPNN/z+97+v\ns1aLMY3dgE6tyUptSd72brzk/wE/9vyHt/2DWKHd+eGj85j782ENEkdILQBVHaGqGRUfwCagM7BS\nRLYAqcByEamYLLYDp5Z7nQo0jtWQwlBSUsI777xDZmYm1113HX/7298AcF2XV155hYkTJwKUrYmf\nlZXFLbfcUra/iDBixAjeffdd/v3vf1eaLCZOnFi2b2XLKTzyyCM88cQT5OXl8fHHH5OcnHxcmdWr\nV/PSSy+xZMkS7rnnHpo0acKKFSs488wzeeGFF0I+3x49ejB//nxWrFjBgw8+yN13343P5+PBBx/k\n8ssvJy8vj8svv/yYfW699VauvvpqVq1axcSJE7ntttvKtu3cuZMFCxbw1ltvWYvBxJ1Zt56F1xGm\nlVzJTtrwSMLTJFHI+l2HG+zWkSG1AKqiqp8BJ5e+DiaBbFWteG/Cd4Hflhv4PQ+4K5y6gRP6pV6X\nCgoKyn6pn3322Vx33XX4fD7atGnDihUr+Pbbb+nXrx9t2rTh4MGDZV1Albniiiv405/+xP79+3n0\n0Uf57W9/e8z2F198sdrJV0OGDOFnP/sZEydO5Ec/+hGpqanHlRk+fDjNmzenefPmtGzZkgsuuAAI\ndEGtWrUq5PPev38/11xzDevXr0dEKC4urnGfRYsW8cYbbwBw1VVXHbNG0YUXXojjOPTq1Ytvv/02\n5DiMiRWv3ngmFz+1kF8U38jLvof4pfdVHiy5mrtnfsaEnLR6r7/e5gGISLaIPAOgqt8DvwaWBh8P\nBt+LSqVjAHl5efz5z38u69O//vrrmTFjBs8//3yNN0spNXDgQFavXs3u3bvLFlE7EVOmTOGZZ56h\noKCAQYMGsW7duuPKlF9COpSlqatazvnee+9l+PDhrF69mjfffLNWyz6XX066fFyNeU0qY+pLaVfQ\nIrc3M0rOY5L3Pwx3AnMCzvjN3Hqvv04TgKqml/76V9VcVb2+3LbnVLVb8PF8XdbbWFx00UX85z//\nYenSpYwcOTLk/X73u98d98s/VBs3biQzM5PJkyeTnZ1daQIIRXp6OsuWLQOocgB5//79dOwYGLsv\nfxOc6pZ9Hjx4MK+88goQaM2cddZZtYrPmFhV2hX0u5IJrHE78YeEp2jPHnYdKqr3ZSJsJnAd8vl8\nDB8+nMsuuwyPxxPyfqNHj2b48OGVbis/BjBixIjjtj/22GNkZGTQt29fkpOTGT16dK1iv/POO3nq\nqacYPHgwu3dX7MEL+OUvf8ldd93FkCFD8Pv9Ze8PHz6cNWvWkJWVVXa/gFJ/+tOfeP755+nTpw9/\n//vf+eMf/1ir+IyJZa/eeCaF+Lil+DYSKOHPvj/jpYQXFm2p13ptOeg65Lou/fv351//+hfdu3eP\ndDhRrzF/1sbUtaufXcz89bsZ5ywkx1nLgyVXgTeJL35zYj/qbDnoCFizZg3dunXj3HPPtS9/Y8wJ\ne+G6HFJbJTHbHcw9JddRiI/RGZVdfV93wroKyBzVq1cvNm2K/B1+jDHRa8GUc7njlRXM+3IXw05L\nCd5Uvv5EZQJQ1eNuTm5iS2PumjSmPtX3l355UdcFlJSUxJ49e+wLIoapKnv27CEpKSnSoRgT06Ku\nBZCamsr27dtprOsEmbqRlJRU6aQ2Y0zdiboEkJCQQOfOnSMdhjHGRL2o6wIyxhhTNywBGGNMnLIE\nYIwxcapRzwQWkV3A1lru3haofE2D6BMr5xIr5wF2Lo1RrJwHhHcunVQ1JZSCjToBhENEckOdDt3Y\nxcq5xMp5gJ1LYxQr5wENdy7WBWSMMXHKEoAxxsSpWE4A0yMdQB2KlXOJlfMAO5fGKFbOAxroXGJ2\nDMAYY0z1YrkFYIwxphqWAIwxJk5FfQIQkVEi8oWIbBCRKZVsTxSRV4PbF4tIesNHWbMQzuNaEdkl\nInnBx/WVHSfSROQ5EflORFZXsV1E5E/B81wlIv0bOsZQhXAuw0Rkf7nP5L6GjjFUInKqiPxXRNaK\nyOcicnslZRr9ZxPieUTF5yIiSSKyRERWBs/lV5WUqd/vL1WN2gfgATYCXQAfsBLoVaHMzcDTwedX\nAK9GOu5anse1wOORjjWEczkH6A+srmL7GOAdQIBBwOJIxxzGuQwD3op0nCGeS3ugf/B5c+DLSv4b\na/SfTYjnERWfS/DfuVnweQKwGBhUoUy9fn9FewtgILBBVTepahHwCjC+QpnxwN+Cz18DzpXGdzeZ\nUM4jKqjqfOD7aoqMB17QgE+BViLSvmGiOzEhnEvUUNWdqro8+PwgsBboWKFYo/9sQjyPqBD8dz4U\nfJkQfFS8Kqdev7+iPQF0BLaVe72d4/9jKCujqiXAfqBNg0QXulDOA+DiYNP8NRE5tWFCq3Ohnmu0\nODPYhH9HRHpHOphQBLsR+hH4xVleVH021ZwHRMnnIiIeEckDvgPmqmqVn0l9fH9FewKoLBNWzKCh\nlIm0UGJ8E0hX1T7A+xz9VRBtouHzCNVyAuuu9AX+DMyKcDw1EpFmwOvAHap6oOLmSnZplJ9NDecR\nNZ+LqvpVNQtIBQaKSEaFIvX6mUR7AtgOlP8lnArsqKqMiHiBljS+Zn2N56Gqe1S1MPjyr8CABoqt\nroXymUUFVT1Q2oRX1TlAgoi0jXBYVRKRBAJfmi+q6huVFImKz6am84i2zwVAVfcB84BRFTbV6/dX\ntCeApUB3EeksIj4CgySzK5SZDVwTfH4J8KEGR1QakRrPo0Jf7DgCfZ/RaDZwdfCKk0HAflXdGemg\nakNETintjxWRgQT+f9oT2agqF4zzWWCtqv6himKN/rMJ5Tyi5XMRkRQRaRV8ngyMANZVKFav319R\nd0vI8lS1RERuBd4lcCXNc6r6uYg8COSq6mwC/7H8XUQ2EMicV0Qu4sqFeB63icg4oITAeVwbsYCr\nISIvE7gKo62IbAfuJzC4hao+DcwhcLXJBiAf+HFkIq1ZCOdyCfBTESkBCoArGuGPi1JDgKuAz4J9\nzgB3A2kQVZ9NKOcRLZ9Le+BvIuIhkKT+qapvNeT3ly0FYYwxcSrau4CMMcbUkiUAY4yJU5YAjDEm\nTlkCMMaYOGUJwBhj4pQlAGOMiVOWAIwxJk79f4dHL9GUQZMqAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Lateral case\n", + "plt.plot(matlab_rslt[case_id]['t'], matlab_rslt[case_id]['V_body'][:,1], '.', label='Simulink output')\n", + "plt.plot(results[case_id].v, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Lateral velocity\")\n", + "plt.show()\n", + "\n", + "plt.plot(matlab_rslt[case_id]['t'], matlab_rslt[case_id]['Omega_body'][:,0], '.', label='Simulink output')\n", + "plt.plot(results[case_id].p, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Roll rate\")\n", + "plt.show()\n", + "\n", + "plt.plot(matlab_rslt[case_id]['t'], matlab_rslt[case_id]['Omega_body'][:,2], '.', label='Simulink output')\n", + "plt.plot(results[case_id].r, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Yaw rate\")\n", + "plt.show()\n", + "\n", + "plt.plot(matlab_rslt[case_id]['t'], matlab_rslt[case_id]['Euler'][:,0], '.', label='Simulink output')\n", + "plt.plot(results[case_id].phi, label='PyFME simulation')\n", + "plt.legend()\n", + "plt.title(\"Heading angle\")\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/validation/PyFME vs Simulink.ipynb b/validation/PyFME vs Simulink.ipynb index 61293f0..2aa4feb 100644 --- a/validation/PyFME vs Simulink.ipynb +++ b/validation/PyFME vs Simulink.ipynb @@ -9,7 +9,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 116, "metadata": { "collapsed": true }, @@ -36,7 +36,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 117, "metadata": {}, "outputs": [ { @@ -69,7 +69,7 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 118, "metadata": {}, "outputs": [], "source": [ @@ -78,8 +78,10 @@ }, { "cell_type": "code", - "execution_count": 38, - "metadata": {}, + "execution_count": 119, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "atmosphere = SeaLevel()\n", @@ -97,7 +99,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 120, "metadata": { "collapsed": true }, @@ -120,7 +122,7 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 121, "metadata": { "collapsed": true }, @@ -140,8 +142,10 @@ }, { "cell_type": "code", - "execution_count": 41, - "metadata": {}, + "execution_count": 122, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "controls = {\n", @@ -154,7 +158,7 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 126, "metadata": { "collapsed": true }, @@ -162,12 +166,12 @@ "source": [ "environment.update(trimmed_state)\n", "system = EulerFlatEarth(t0=0, full_state=trimmed_state)\n", - "sim = Simulation(aircraft, system, environment, controls)" + "sim = Simulation(aircraft, system, environment, controls,verbose=False)" ] }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 127, "metadata": { "collapsed": true }, @@ -178,17 +182,9 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 128, "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "time: 100%|████████████████████████████████████████████████████████████▉| 9.999999999999831/10 [00:06<00:00, 1.60it/s]\n" - ] - } - ], + "outputs": [], "source": [ "results = sim.propagate(T)" ] @@ -202,8 +198,10 @@ }, { "cell_type": "code", - "execution_count": 45, - "metadata": {}, + "execution_count": 129, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "N = int(T/sim.dt)\n", @@ -235,7 +233,7 @@ }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 130, "metadata": {}, "outputs": [ { @@ -247,7 +245,7 @@ } ], "source": [ - "with open('../matlab_comparison/matlab_results.json','r') as f:\n", + "with open('../../matlab_comparison/matlab_results.json','r') as f:\n", " mat_states = jload(f)\n", "mat_states = {k:np.array(el) for k,el in mat_states.items()}\n", "print(f\"{mat_states.keys()}\")" @@ -262,14 +260,14 @@ }, { "cell_type": "code", - "execution_count": 51, + "execution_count": 131, "metadata": {}, "outputs": [ { "data": { - "image/png": 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6KU2sa+jr7cbP5mIABtxeL5alqQhFGuiNjTENgdbA4yLSBBgL1ARSgB3AkIJ2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\nhAa6UkrFCQ10pZSKE/8PNaT/AxJG1AAAAAAASUVORK5CYII=\n", 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pmMc2DXSl4pzT5eY89jPDMZVWls3M9SXxqK9/tnvL9cJnfNBAVyqOOV1uLpVN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\n+6FV3gB65L61KslsFthmqrM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TmeavKaKdFLDeNAsNgzyzk76fKxVLnJVtICJTgGwgXUTygUcBF4Ax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\nyhtvvEGbNm244YYbaNiwIYsWLWLz5s3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M1FgwmDp5cfEW2msBQLgpKTmhcf8b5WhvznRyCE7uLa16ptWqI26d0KRtPvzk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\n", 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3A/nE7fG5mnbVm+zPxO8dx7WeKXTIe5HfSGBAWhOeuaxdrEMzpkQ2yMuUSmmn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\n6wBioKZ955r2fcG+c01R7t+52rb5G2O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ksfA3xhwj2AHsohqDcx7iV63JePfTtJWfAOsAIoWFvzHmBMEOIIvq3JDzMDu1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\nxkQtt1PYQU0+8bVnkPMzzuA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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -335,14 +333,14 @@ }, { "cell_type": "code", - "execution_count": 52, + "execution_count": 132, "metadata": {}, "outputs": [ { "data": { - "image/png": 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LAl2ljugHvB/4/n2gfyjOpSJTYf2+wNgsds4HYrNe+O5N7Vltkthjzgj2+1cq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\neybg7zUfCQaPWUBL2cSF1gY+8F2CCaQ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hDLX4DYid0osqnVmzZlXo6Ly0NKGriNN8xFQEl6cS3mIPp/Nowa0E55iXdSlk06h+HCKR\nBwr+QA3yeDZhLMHW/u2fml6mx1KqvGlCVxEnL9/hans2ba11PFtwA3vwVvWV11L9Z4a04HtTj3/6\nr6aPvZjLLO88T07eSfc8VyriaEJXEeWC9Axqspd034dkuo0Z73YFIKlqYrkd84aO9fBZMNbpyxq3\nHk8kvMNpeHV0Lb2oaKIJXUWMpZt3Y4A/+iZQg32MKLiFYKll8fDe5Xrs9c/0w4+PRwtu5Rz5lft9\nhxfOfJC55STPVCpyaEJXEePKV+dzLjkMs2fwsdOdtcZbwn93t/oVcvzBqeewzDTiA39PbrWn0EB+\nAuCRCSsr5PiRzLZtUlNTad68OVdffTX79+8/4WM3bdpElSpVSE1NDV3y8/N5++23ERFmzpwZeuyE\nCRMQET755BPAmyZ40UUXhZ531VVXnegwR9i2bVuRH3sqs2bNon///id9TFZWFpMnTw5dnzRpEqNG\njSqT45eGJnQVEYKjYG9kLPzbPzR0X/oVFTMH+4XrvH1cnvNfw34qke77MHTfTWMzKySGSFWlShWy\nsrJYtWoViYmJvPbaayd9fLBBVfCSmOiVzFq0aMGHHx7+uY4bN45WrVod8dz3338/9Lxgoj+Vc845\np8iPLQtHJ/SBAweSnp5eYcc/EU3oKiI8MmElF0o2Q+25vOv05me8/iMV3bN806h+7KY6r/oH0dte\nRifL2+xgzrqy3UghmnXt2pX169fz2GOP8e9//zt0+6OPPsqLL754yucuWrSIgoIC8vLyWL9+Pamp\nqcU6/uzZs0Mj+NatW7N37142bdpE8+bNAa9F7+DBgxkwYAAXXHABL730Ev/85z9p3bo1nTp14tdf\nfwWObP27c+dOUlJSjjnWokWLSEtLo3Xr1qSlpbF27Vry8/MZMWIEH330EampqXz00UdHtAXevHkz\nvXr1omXLlvTq1YstW7zByi233MIf//hH0tLSqF+/frn8AtINLlTYBUfn9/k+5QCVeMU/EABfmIYb\nibbwltOH/+ebziO+9xmU/zcMFr1Hz2L6g93DE1TQlHT4uYxLQGe3gL5FKxf4/X6mTJlCnz596Nu3\nL0OHDuW+++7DdV3GjRvHokWL2Lt3b6gnOHjL/V9++WXAa2x16aWXMm3aNPbs2cPAgQNDfVCChg0b\nRpUqVQDo3bv3MW1on3/+eV5++WU6d+5MXl4elSsfuzZh1apVLF++nIMHD3LhhRfy97//neXLl/PA\nAw/w7rvvcv/99xfp/TZu3Jg5c+bg8/mYMWMGjzzyCOPHj2fkyJEsWbKEl156CeCI7pP33nsvN910\nEzfffDNvvfUWf/zjH0Nte7dv3868efP4/vvvGThwYJmViYI0oauwe2TCSs6Xn7nCyuQNpz+7qQ4c\nXvhT0X54+gpS0jN4vuAa/pX4Kn2sxUxxO7IuZ19Y4okEBw4cCCXorl27ctttt5GYmEjt2rVZvnw5\nO3bsoHXr1tSuXZu9e/eGSi7Hc9111/Hiiy+yZ88eRo8ezTPPPHPE/e+///5JF/N07tyZP/3pTwwb\nNoyhQ4eSnJx8zGN69OhBtWrVqFatGjVq1GDAgAGAV/JZsWJFkd/3nj17uPnmm1m3bh0iQkFBwSmf\ns2DBAj799FMAbrzxxiN6zAwePBjLsmjatCk7duwochxFpQldRYS77C/w42Os3+unHa7ReVDNKj4+\nO9CZe92J/NH3KVPz22Ow6DJqZnj7vBRxJF3WgjX0o91+++28/fbb/Pzzz6fc/CGoQ4cOrFq1iipV\nqoSaWhVHeno6/fr1Y/LkyXTq1IkZM2YcM0ov3HK3KK18T9T+9rHHHqNHjx5MmDCBTZs20b1792LH\nW7j9buG4yqOPltbQVVhd+EgGZ7KbK+05fOJ0IwevO2C4RudBWY9fjovFi/4hNLG2hhYbaZ+XIw0Z\nMoSpU6eyePFiLr/88iI/79lnnz1mZF5UGzZsoEWLFjz88MO0a9eO77//vkSvk5KSwtKlSwFOWM/e\ns2cP557r9RAqXFY5WZvctLQ0xo0bB3h/bXTp0qVE8ZWEJnQVVn4XbvVNwYfD687Jp4pVtOSalfnc\nTWODW5f7fZ8igRa7wQ03lLdLUY8ePbjmmmuwbbvIz+vbty89evQ47n3Dhg0LnfS89NJLj7n/hRde\noHnz5rRq1YoqVarQt2/fEsX+5z//mVdffZW0tDR27jz+Se+//OUv/PWvf6Vz5844jhO6vUePHqxe\nvTp0UrSwF198kf/85z+0bNmS995774gTx+VN2+eqsGn/1HT25u0ls9IfmOu24N6C+wAY//u0Munj\nXRZS0jMYYs3lX4mvclf+A0xz2wMVO/smktvnuq5LmzZt+O9//0vDhg3DHU5MKNf2uSJynoh8LSJr\nROQ7EbkvcPsTIvKTiGQFLleU+B2ouJSTl89g+xtqyH7e8R/+cz1Skjl4LQcmuWn86J7F732fEWzc\nFe/z0gFWr17NhRdeSK9evTSZR4iinBT1Aw8aY5aJSDVgqYgE29D9yxjzfPmFp2LV/eOWA4ab7S9Z\n7Z7PYnMRAN0a1glvYEdZPLw3KekZvOn04+mEt+gg37PINNF56UDTpk3ZuHFjuMNQhZxyhG6M2W6M\nWRb4fi+wBji3vANTsW1i1jbay1qaWFt4x7mMYM+Wd2/rGN7AjqNqos14pyu7TDXu8B1u1rV08+4K\ni6EiS6MqfEr771ysk6IikgK0BoJ/b94rIitE5C0ROe7fySJyp4gsEZElOTk5pQpWxZabfdPINafz\nmZMGeFMFI9GqkX04SCX+z+lNb3sZ9WUb4PWeqQiVK1dm165dmtRjnDGGXbt2HXehVFEV+X+QiFQF\nxgP3G2N+E5FXgb/hFRX/BowGjpmIaowZA4wB76RoiSNVMaP5iKkksZs+1mLecvpyEG9ubtbjRZ/2\nVtESbeFdf2/utj/ndnsyj/hvr7BjJycnk52djQ6IYl/lypWPu1CqqIqU0EUkAS+Zv2+M+RTAGLOj\n0P1vAF+UOAoVV/LyHYbZ8/CJywdOz3CHUyTB1aPjna5cac/lef81/Ep1mo+YyqqRfcr12AkJCVxw\nwQXlegwVG4oyy0WAscAaY8w/C91et9DDhgCryj48FWuCJ0OvsWexyL2ITcb7GD0zpEV4Ayui/zh9\nqCQFXG3PBrxfTkpFiqLU0DsDNwI9j5qi+A8RWSkiK4AewAPlGaiKDROzttFG1tHA2s5/nUtCt9/Q\nsV4Yoyqau7vVZ51JZqHbhGH2DKzAQiOdwqgiRVFmucwzxogxpqUxJjVwmWyMudEY0yJw+0BjzPaK\nCFhFv2vsWewzlchwOgHlu71cWQr2ZX/P35t6Vg7drG8Bba2rIocu/VcVpsuomVThIP3thWQ4ndiP\ndza/vLeXK0vJNSszzW3HL6YmN9nTT/0EpSqQJnRVYbJzD3KFtYiqcpCPC5Vbosm89F748fGh05Pu\n1recJ97cgCbDp4Q5MqU0oasKdrVvNhvds1kSWBk6OPWcMEdUfLbAB/6euAjDbG9/zAN+N8xRKaUJ\nXVWQ1CenUZdddLLWMMHpQnBlaHAfz2jy8d1p7OAMprttucqeQwJef+3BL80Lc2Qq3mlCVxUi94Cf\n/vYCACa53srQaP3wBZuHfeT0oI78Rk9rOQBZ2XvCGZZSUft/SkWhgfZ8vnXrs9mcDcBTUTL3/Hga\nJp3OHLclP5taXG3PCnc4SgGa0FUFaD5iKhfIdlpYm5jkXBy6PRrmnp/I9Ae742Ix3ulKDyuLM/Ea\ndTUfMTXMkal4pgldlbu8fIcB1gJcI3wRSOhVE4u+u02ksgX+61yCLYah9lxAV46q8NKErsqV12LW\nMNCezyLTmB2cAVDu/U8qwsd3p7HJ1CXTbRxoBeD1nhs1eU14A1NxSxO6KlfD3lhIU9nMhdY2Pi9U\nbokFwZOj/3UuoYG1nbbyAwCvzdFNH1R4aEJX5eqg32WAvQC/sZjsdABio9wSlFQ1kclOR/JMZa7V\nk6MqzDShq3Jm6GMtYr7bjN1UB2Kj3BK0eHhv9lOZDKcTV9iZVOYQoHPSVXhoQlflpvmIqVwkW7nA\n2sFUt0O4wylXE93OVJWDXGotA3ROugoPTeiq3OTlO/SxFuMaYbrTFoitcktQanINFrpN2G7OYLCt\nI3MVPprQVbnqYy9miWlEDjWB2Cq3BE28twsGi0nOxVxiraAWvwFed0mlKpImdFUu2j81nfPlZ5pY\nW5jmtA93OOVOgIlOFxLEoZ/tbXiRnXswvEGpuKMJXZWLnLx8LrcWAzDN9RJ6Qgx/2u7qVp81ph5r\n3WQG2d+EOxwVp2L4v5gKtz72Yla6KWSbJADG3ZUW5ojKj7ebkfCZ05n21g8kyy+A12VSqQ8yt3Dj\n2Ew+yNxSrsfxleurq7jUZdRMzuJX2ljrea7gmtDtwYU4scoW+MxJ4y8JHzHIms/LzmByD/jDHZYK\ns5T0DHz48eNjbmC7wvLqY6QjdFXmsnMPcpm9BICpgXJLPHzQ/ja4BT+RxCL3Igbb3xBsBaDiV0p6\nBvVkB3Mr3c/F1ncATFlVftsvx8P/MxUGva2lbHDrssGcC0R3q9yiCo66JjpdaGj9RFPZDGgHxngV\nXFz2qO99qrOPDa63O1ff5nXL7Zia0FWZumlsJqdzgE7Wama4bUK3R3Or3OKo4rOY4rTHbyz62QsB\n7cAYr7Ky99DZWsnl9hJe9g/mF7ySY3n+X9CErsrUnHU76WKtJFEcvnLanPoJMWbNU33ZTXXmu83o\nZ2USLLt4XSdVvGj06GQSKeAJ37tscZMY6/QFINGWcj2uJnRV5npZy9ljTmOpaQhAt4Z1whxRxctw\nO5Fi7aBZoOxy3evzwxyRqkj5juEPvs9oaP3ECP/vOEQiAD88fUW5HveUCV1EzhORr0VkjYh8JyL3\nBW4/Q0Smi8i6wNfYnsKgTmnp5t0ILj3s5cx2W+EPTKJ697aOYY6sYtWs4mOa0+6IskuBG+agVIVJ\nSc+gkWzl9/ZnTHA6M8tNBbxtC8tbUUbofuBBY0wToBPwBxFpCqQDM40xDYGZgesqjg17YyEtZSNJ\n8hszndbhDidssh6/nFyqBcouC9GyS/xo/9R0LFz+nvAGeVThbwU3hu6b/mD3cj/+KRO6MWa7MWZZ\n4Pu9wBrgXGAQ8E7gYe8Ag8srSBUdDvpdetrLcYyERiXJNSuHOarw+cLtxPnWLzSTTYCWXeJBTl4+\nN9rTaW2t58mCm/g10DJ606h+FXL8YtXQRSQFaA1kAmcZY7aDl/SBM0/wnDtFZImILMnJySldtCri\nXWotY4m5iD1UBWBeeq8wRxQeNav4+NJpR4Gx6a9ll7iQkp7BOezkL75xzHJa8ZnbGfBmPlWUIh9J\nRKoC44H7jTG/FfV5xpgxxph2xph2SUlJJYlRRYHeo2dxNrtoZm3mqzgutwQVLrtcUWi2i4pNXmdN\nw1MJbwHwaMGteC3bvJlPFaVICV1EEvCS+fvGmE8DN+8QkbqB++sCv5RPiCoarMvZR087C4CZrpfQ\ny3eCVnQIll2ay4+ALjKKVdm5BxloLaCnncXz/mv4CW/wene3+hUaR1FmuQgwFlhjjPlnobsmATcH\nvr8Z+Kzsw1PRpKe1jC1uEusDq0PvquAPc6Q5suzitdTVRUaxJyU9g1r8xuMJ75DlNuAd53LAG9B4\nTdsqTlFG6J2BG4GeIpIVuFwBjAJ6i8g6oHfguopDH2RuoTKH6GKtYqbbhuDYvKI/zJEm6/HL2UNV\nvnGbc0Wh2S4qdgQ3MRme8D7V2c/DBXfgBtLqjxV0IrSwosxymWeMEWNMS2NMauAy2RizyxjTyxjT\nMPD114oIWEWeEZ+topO1mspSwNeB2S3qsCluB+pZOTQRr3WqttSNHdm5B+lqreBKey6vOgNYa7xl\n/YNTzwlLPLpSVJWa3zVcYq3ggEkk0/VG5RWxiCIaVPZZzHDa4Bjhctvb8ENb6saGlPQMKnOIp31j\n2eDW5WX/4ZnbL1wXnokBmtBVmehmrWCh2yS0xLkiFlFEg/fv6MQuarDEXMTl1pJwh6PKyE1jvXMi\n9/k+pZ6Vw6P+20Kf/Yqac348mtBVqQx+aR7J8gsNrO3McVuGO5yIE9zU40unHU2sLdSTHYC3olBF\nrznrdtJYtnCHncHH/ktY6DYFwldqCdKErkolK3sPl1grAEIJXacrHslnSWhf1eA+qzl5+eEMSZVC\no0cnY+HybMKb7OF0nvHfELoW2WaBAAAgAElEQVQvXKWWIE3oqtS6WSvINnXYYLzRSbxPVzzayEHN\nyTZJrHJTuNzWsku0y3cMw+wZtLbW87eCG8mlGhDeUkuQJnRVYh9kbsGHnzTrO+Y4LdHpiscX3NBg\nmtOONrKOJLwmXb1HzwpjVKokUtIzOIPfeMj3MXOd5kwMLO+PlEkAmtBViT0+aRVtZB3V5ACztX5+\nUgJMc9tjieEyeyngra5V0SO4pdyffR9ThUM84b+Z4CAmUiYBaEJXJVbgGLrZK/Abi/lucyByRiqR\nZlDqOfxgktnonh2qo6vokpW9h6ayievsr3nXuSy0X24klFqCNKGrUrnE+pZlpiF7OQ2InJFKpPFO\nlglfuu252FpNdbzReXD6m4ps3mIww+MJ77KbqvzbPxQo/y3liksTuiqRm8ZmUps9tLA2Bernqiim\nOe1IEIce1nLAm/6mIl/uAT9XWJl0tL7nef81/Ib3l2h5bylXXJrQVYkEN4MGmO22CnM00SE1uQZZ\npgE/m1r0sbXsEi0ufCQDH34e8n3EGvc8PnJ6AJG5eYsmdFVil9gr2GWqscqkAOFfVBHpJt7bBYPF\nl047LrFWUAlvLvqoyWvCHJk6Gb8LV9uzucDawXP+a0PNtyJx8xZN6KpEBJeu1grmuS0wgY9RuBdV\nRItpbjtOk0N0CyzIem3OxjBHpE6kwV8zqEQ+9/k+ZYnbiK8Cvf4jdfCiCV0VW5dRM2kqW0iS35it\n9fNiaZh0OpluE/aY0+htLQ13OOoUHAM32V9ytuzmuYJrCU5TjNTBiyZ0VWzZuQe5xPoWgLmB+een\nJehHqSimP9gdPz6+dlPpaS/HwttodOnm3WGOTB2tfnoGVdnPPb5JzHZakmm8BXPPDGkR5shOTP8X\nqhLpbK1ijXseOdQE4L3bO4U5ougyw2lLHfmNVFkPwA1jFoQ5InU0F7jJnk4tyeM5/zWh24MrfyOR\nJnRVLEs376YS+bSzfuCbwGIiONxVUJ1aUtVEZrutKDA2vQOrRg85uptRJGnwV6/X+a2+KXzttGKV\n8foTjf99WpgjOzlN6KpYbhqbSTtrLZWk4IiEropu8fDe7OU0FrpNuNRaFu5w1HE4Bq61Z1FHfuNl\n/6DQ7ZE+cNGEroplX75DZ+s7CozNIrcxoMv9S2qG25aG1k+kyHbg8P6UKrwaPTqZBPzc6fuCTLcx\nS4z3OY/00TloQlclkGatIss0YB9VAF3uXxI+SwIbahMapWfnHgxnSCog3zEMtudxruzilSganYMm\ndFUMoyavoTp5tJQftdxSSsEe6WvceqE6ugq/9k9NR3C52/6cVW5KqIvo3VHS418TuiqyMXM3crG1\nBksM3zia0EsjOFPiS7ct7WQtNdkLaLOucMvJy6eHlUUDazuv+QcQbT3+NaGrInONV27ZbyqRZS4E\noFvDOmGOKrrNcNpii6GHlQVos65wCv4y/Z09le3mDKYGtg2Mps+4JnRVLF2sVWS6jSnAB8C7t3UM\nc0TRq1vDOqwyKfxsanGpll3Cbs66nTSUbLraq3jP3xt/FH7GT5nQReQtEflFRFYVuu0JEflJRLIC\nl8jqIanK3E1jMzmbXTSwtmv9vIy8e1tHDBYznTZcYq0gkQLA29pPVazgz/x39lQOmgQ+cHoC3pqB\naFKUEfrbQJ/j3P4vY0xq4DK5bMNSkWbOup10tr4DCCX0yGrtH72mu22oKge52FoNwGMTV4Y5ovjz\n6ISV1CCPIfY8JjhdQhs/Lx7eO8yRFc8pE7oxZg7wawXEoiJcmr2KXaYa35vzALgrSs78R7LkmpVZ\n4DZjv6nEpYFmXbpotOIZ4Hr7K6pIPm87lwNQxRd9FenSRHyviKwIlGROOEFTRO4UkSUisiQnJ6cU\nh1PhZehsfccCt1moXW60nPmPZPPSe3GIROa4LbnUXoaXWlRFSn1yGoLL//PNYL7TlLXGm4G05qm+\nYY6s+Eqa0F8FGgCpwHZg9IkeaIwZY4xpZ4xpl5SUVMLDqXDqPXoWDWQbZ8tu5mn9vFxMd9pSV36l\nmWwCvPnQqmLkHvDT1VpJsuzkAyfyNq0ojhIldGPMDmOMY4xxgTeADmUblook63L20dnyzol/4zYD\nIAr/Go1YlX0WX7upOEa4LDDbJScvP8xRxYfgblHX2V+zy1TjS7cdELkbWJxKif5bikjdQleHAKtO\n9FgVG7pYq9jiJrHVnAXAyEGR2xM62rx/Ryd+pTpLTaNQHV1VjNfmbCSJXHpbS/nE6UY+CUDkbmBx\nKkWZtvghsAC4SESyReQ24B8islJEVgA9gAfKOU4VRjYOnaw1R0xXjOSe0NEm2CNkhtOGZtZmzsFb\nXKSrRivGVfYcEsQJbf5cs4ovzBGVXFFmuVxvjKlrjEkwxiQbY8YaY240xrQwxrQ0xgw0xmyviGBV\nxWv/1HSay49Ul/3MD5RbVNkTvO6LAL1sr1mXrhotX11GzURwudb+moVuEzYar8yS9fjlYY6s5LQS\nqk4qJy8/VD8PJvTkmpXDGVJMGpR6DhvNOWxw6+peoxUkO9eb+59i7eADf89wh1MmNKGrU+psfcca\ntx67qAF4U+1U2QrWbGe4behkraYa+4HDJ+1U2Qru4Xq9/RW7TVWmBfq2ROvJ0CBN6OqEPsjcEtpu\nTqcrVowZTlsSxQltwv3anI1hjig2Xfv6AqqTx2XWUiY6nTmEt8Q/Wk+GBmlCVyf05OffFdpuTuvn\n5a1h0uksNY341VTVZl3lzO8a+tmZVJICxjtdgehcGXq06H8Hqtwc8ruFtpvzVoXqdnPlZ/qD3XGx\n+MptQw8rCx/+cIcUk+4ftxyAofZcfnDPZZW5AIjOlaFH04SuTqqztYrl5kL2450I1e3myt90py01\nZD/trbWAtzRdlZ2JWduoJztob/3Ap05XYqnNnCZ0dVzB7eZayI86XbEC1aziY47bgkMmITTbJfeA\njtTL2lB7Lq4RJjqdgdiZuaUJXR3XG/N+5GJrNZYY5ul2cxUm6/HLOUBl5rnNAwldm3WVpS6jZgKG\nodZcvnGb8TO1gdiZuaUJXR2X43rdFfeZSnwb2G4uNblGmKOKH9Pdtpxn5dBYtgJegzRVetm5B2kn\na6ln5QTKLbFFE7o6oc7WKhYV2m5u4r1dwhxRfLAEZjptAEK9Xdbl7AtnSDFlqD2XfaZSzMw9L0wT\nujrG/eOWh7ab0/nnFe/OrvXJoSbL3QvprdMXy0zqk9OoRD797Uymuh1CJ/qjfe55YZrQ1TE++3Zb\naLu5+ZrQK1xw45DpTltaWRs5K7BhWHC6nSqZ3AN+ulvfUl32h06G2rEzwQXQhK6Owxhvu7mdpnpo\nu7luDeuEOar482WgWdelgWZdE7O2hTOcmNDPXsguUy00c+vju9PCHFHZ0oSujsPQxVrFArdpaLu5\nd2/rGOaY4ktqcg3Wm3PZ5J6lzbrKQJPhU6jMIXpZy5jqdMDBBg63Lo4VmtDVEW4am0kD2cZZkntE\n/3NVsbwT0MJ0ty0XW99xOgeAw02lVPEc8Lv0sLI4XQ7xhdsJgKqJdpijKnua0NUR5qzbSZdAu1w9\nIRp+0522VBI/3awVANwwZkGYI4o+wV+C/eyF5JjqLHIbA7BqZJ9whlUuNKGrY3QObDeXbc4EYmta\nVzRJqprIUtOI3aZqaLbLIUcXGhXXta8voAoH6WUtZ4rTMVRuiUWa0NURgtvNFR6dx9K0rmiyeHhv\nHGy+clvT01qOjRPukKKS3zX0spZTRfLJcLxySzRvM3cymtBVyOCX5tEitN2cllsixZdOW2rKvlCz\nLm/5uiqKDzK3AF655RdTk8XmIiC6t5k7GU3oKiQrew9drJW4RkLTumKgRXRU81nCXLflEc26snMP\nhjmq6PHYxJWczgF6WFlkOB1xYzzlxfa7U8XW1V7Jd+Z8fqU6ACMHtQhzRPFt5KDm7Kcy37jN6G0t\nQZt1FY9joJe1jMpSQIbjTb1NqpoY5qjKjyZ0FXI6B2gj65jrtgzddkPHemGMSAV//tPdttSzcmgk\n2YA3vVSdXLDc0t9eyHZzBktNI8A7NxGrNKErwKvLdrJWkyAOc10dlUeaYLOuYNllzrqd4QwnKjw2\ncSVV2c8l1rdMdjqGFsnFsth/h6pIsnMP0tVayX5TiaWuN5KpVil2p3dFk24N6/ALtchyG2izrmJw\njPcLsJL446LcAkVI6CLyloj8IiKrCt12hohMF5F1ga+xtX42TnW1VrLQbUI+CQC8fasu948EwbYL\nXzptSbU2cCbeQhlt1nVihWe3/GRqszzQ0z+Wyy1QtBH628DRS6rSgZnGmIbAzMB1FaXuH7ecc8mh\ngbX9iHJLrPW5iHYzAs26emmzrlN6bOJKqrOPbtYKMpxOcVFugSIkdGPMHAj07zxsEPBO4Pt3gMFl\nHJeqQJ9lbaOL7f0BpvXzyJSaXIMfTDKb3TO1WVcROAYus5eQKE7clFug5DX0s4wx2wECX8880QNF\n5E4RWSIiS3Jyckp4OFWeDNDN+pbt5gzWm3MB3W4u0hRu1tXZ+o7T8OaiB0sL6rBRk9cA0M9ayFY3\niW9NAyD2yy1QASdFjTFjjDHtjDHtkpKSyvtwqgQS8NPVWskspxXgdfzX7eYi0wy3LZWkgK6BZl2P\nTVwZ5ogiz+tzNlKDPLpYq8hwOxH8TMeDkib0HSJSFyDw9ZeyC0lVpC6jZtLe+p7qcoCZbptwh6NO\nIqlqIovdi9htqnKZvQTwSgvqSAa43F5Mgjh8ESi3JNesHN6gKkhJE/ok4ObA9zcDn5VNOKqiZed6\nXegOmQS+CSz3rxRr+3LFiGCzrpluG3pby0jAH+6QIk6w3NLfWshm90xWmQsAmJfeK5xhVZiiTFv8\nEFgAXCQi2SJyGzAK6C0i64DegesqKhl6WcuY7zblQGDT3A/uvDjMMamTmeK0p7rsJy2w72vqk9PC\nHFHkGDN3I7X4jTTru8BGFvE1ODllD0ljzPUnuCs+fuXFsODuRCnWDt4suCJ0u05XjFxVE23m5bcg\nz1Smj7WI2W4rcg/oSD3INdDHXoxP3FCr3Hgpt4CuFI1rc9btpKflLU75ytGe59Fg1cg+HCKRr9zW\nXGYv0R7phYQWE1kL2eiezWpzPhA/5RbQhB73LrWXscatxzbqAN4ycxX5pjgdqC176WB9D0D7p6aH\nOaLwe2ziSmqzh4ut1XFZbgFN6HHrg8wt1CCPtvIDMwrNbgkuM1eRy2cJs9xWHDCJ9LEWAZCTlx/m\nqMLPMdDXXoQtJlRuiYfFRIVpQo9Tj01cSW97KT5xmeHodMVoMnJQcw5QmdluK/rYixHccIcUdofL\nLZmsd89hrTkPiI/FRIVpQo9TjoG+1iKyTZ3QSrp4OnkUzYI90qc47TlLcmkt64H43prusYkrSSKX\njtaauC23gCb0uLR0826qs4+u1gqmOB0Ifvjj6eRRtBPgK7cN+camr+2VXeJ5azqv3JKJFcflFtCE\nHpeuH7OAXtYyEsVhsqM182h0V7f67OU05rktAgk9fpeMHm6Vm8laN5l1JhmIv3ILaEKPS/mO4Qp7\nEdvMGWQFyi01q5xySYKKIOlXNAFgituBZNlJc/kRgN6jZ4UxqvAY8dkqzuJX2stavgiMzuOVJvQ4\ns3Tzbqqyn27WCqYU2pYr6/HLwxyZKonpTlv8xgqVXdbl7AtzRBXP7xquCJRbJrvx0yr3eDShx5nr\nxyygp7WcSlLAZKdDuMNRpTA49RxyqcZCtwl9rMXEY9ll6WZv96b+9kLWuPXYEGj/HI/lFtCEHnfy\nHcMAewE/m1osMw0BLbdEqxeu81b3TnU70MDaTmPZCsTXbJfrxyzgXHJoa63jc0d7EGlCjyOjJq/h\nDH6ju/UtE53OWm6JAQJMdTrgGKG/vQCIr9ku+Y6hn70QgM9dr34ezwMUTehx5PU5GxlgLyBBHCY4\nuoFFLLirW312UoNv3OYMsBYQT2WX4OyW/vZCvnXrs9WcBcT3AEUTehwxwBB7Lt+557PWeItT4vXk\nUawIznb53L2Y861faCUbgPgouzw2cSXny8+0tH7UckuAJvQ40Xv0LBrIT6RaG/m00Og8Xk8exRIB\npjntOWR8DIyjsotjvM6KQGgxUTyXW0ATetxYl7OPIfY8HCNMctLCHY4qQ3d1q89vnM5stxX97QVY\ncdDbJbgz0QB7AUvcRmynNhDf5RbQhB43bByusucwx21JDt4GFtoqNzYEyy6TnDTOkty4aKn7+pyN\nNJCfaGJt1XJLIZrQ40CT4VPoaS3nbNnNh07P0O3aKjd2WAIz3dbsN5UCJ0dju6WuwRudu0ZC6ym0\nuZwm9LhwwO9ygz2Tn00tZgZ6n+s+0LHlqcEtOEBlprtt6Wtn4ovhDaTvH7ccMAywFpDpNgn9xanN\n5TShx7zBL80jWXK4xFrBR053HGwAPr5b6+ixJNhS93PnYs6QPLpYqwBoPmJqOMMqFxOzttFEttDA\n2s7nrpZbCtOEHuOysvdwrf01BvjI3yN0u24EHXsSbWGO25I95jQG2PMByMuPzT1H+9sL8BuLKU57\nABomnR7miCKDJvQYtnTzbhIp4Dr7a2a5qaF9Q/XDH5s+vPNi8klgstORy60lVMGbuhjsdxILbhqb\nieAy0FrAN25zdlMdgOkPdg9vYBFCE3oMu/q1+QyyvyFJ9vCW0yd0u374Y1Pwr65Pna5UlYOBhl1w\nzWvzwxlWmZqzbift5AfOs3J0tfNxaEKPYa4x3GZPYY1bj2/c5oD3Z7mKXTWr+FhsLmKzeyZX2XMA\nbwFOLBliz2WfqcQ0tx0Aqck1whxR5ChVQheRTSKyUkSyRGRJWQWlSq/J8Cl0tVbS2NrKm/4rCG4z\n98PTV4Q3MFWuvIU1wninGxdbqzmXHCA4MyS6dRk1k0rk09/OZJrbngN40xQn3qsj9aCyGKH3MMak\nGmPalcFrqTJywO9yh53BDlOTSa7OaIk3n7pdscQwxJ4HeDNDol127kF6WFlUl/1abjkBLbnEoNQn\np9FCNtLNXsk7/sspwOtvcXe3+mGOTFWE5JqVyTZJLHCaMtSeSyx1YBxqz+UXUzNUQhycek6YI4os\npU3oBvhSRJaKyJ3He4CI3CkiS0RkSU5OTikPp4oi94Cf+3zj2W2q8q5zuPlWcIm4im3BBTbj3a7U\nt36mjawDorsVQOqT06jJXrpbWXzmpOEGUldwkw/lKW1C72yMaQP0Bf4gIt2OfoAxZowxpp0xpl1S\nUlIpD6dOJTg6v9Rezhv+K8jjNED7tsSjyU5H9plKXGXPBqK7FUDuAT/97YUkFurlr6f3j1WqhG6M\n2Rb4+gswAdBNKsPsyNH5ZaHbtW9LfBmceg77qcxUtwP97YVUwkvmwU0hokkw5iH2PNa6yaw25wPw\n9JAW4QwrIpU4oYvI6SJSLfg9cBmwqqwCU8XX6NHJtJEfjhmd67Su+BMsRXzidKO6HOAKKxOARyas\nDGdYJTJ84kpSZDttrXWB0bk3Ng+2O1CHlWaEfhYwT0S+BRYBGcaY2GscEUXyHZfhCf/Hz6YW/ym0\nkEindcWnqok2C9ymbHDrMswXvTsYuQautWfhNxbjna6AbmRxIiVO6MaYjcaYVoFLM2PM02UZmCqe\nlPQM+lsLaWOtZ7T/6tAcXZ0FEL9WjewDCB86PWln/cBF4pUuoml7ut6jZ+HDz1X2HL5yW4c6K8b7\nRhYnotMWY8CoyWuoRD4P+8axxq3HeOfwuWmdBaDGO105ZBK4wfYSeTRtT7cuZx89reUkyR7GOT1O\n/YQ4pwk9Brw2ZyO/s6dynpXDU/5hoSldz+hJo7jXrWEddlOdyW4HhtjzQg27ounk6LX2LH42tZjt\ntgL0nNDJaEKPcu2fmk6y5HCf71O+dNryjXs4ietJIxWc3fS+vxfV5QADAptIR8PJ0UaPTuZsdtHd\nyuK/ziWhXv56TujENKFHuZy8Q4z0/QcX4fGCW0K3bxrVL3xBqYhSxWexxFzED+65DLNnEi0rR/Md\nw1X2HGwxfOxcAmhzuVPRhB7FUtIz6GstoqedxT/9V4d2Pq+aaIc5MhVJ1jzVFxDec3rTytoYWjma\n+uS08AZ2Er1Hz8LC5Trf18xzmrHVnAVoc7lT0YQepXqPnkUN8ngi4R1WuSm87Rw+6+/NblDqSOOd\nbuwxp3GbbzLgLUKLVOty9nGptZRk2cl7hdpXqJPThB6l1uXk8UzCm9RiLw8X3BmqL2oDLnU8wZWj\nHzi96GMtJll+8W5/aV6YIztW8ITtzfaX/GRqM8NtC+jJ0KLQhB6FUtIzGGrNpZ+9iH/5r+Y7kxK6\nTxtwqeMJTl99x38ZLha32F65JSt7TzjDOq5HJ6ykoWTT2f6O//P31pOhxaAJPcrUT88gWX7hyYR3\nyHQb87rTP3SfnghVJ5NcszI/U5sMtyPX2rOoyn7AW8cQSQxwsz2NQyaBcU53wDuxq05Nf0pR5P5x\ny0kgn1cTXsAgPFjw+9Ccc10Rqk4l2FZ3rP8KqskBrrVnAd46hkjRZPgUqrOPofY8JjkXhzaB9k7s\nqlPRhB5FJmb9xNMJb9HC2sT9BfeQbbx2xBa6IlQVTRWfxUpTn0y3Mbf7JpNIAQBLN+8Oc2SeA36X\nG+yZnCaHeNvRk/vFpQk9SqSkZ3CjPZ2r7Dm84B/KV26b0H0btdSiiig40n3RP4S68mtoI+krX50f\nzrAAb5FcJfK51TeVOU6L0LkhPdFfdJrQo0BKegY9rOU87nuXGU5r/u0fGrpP6+aquGyBb9zmLHMv\n5B7fZyTgTV8M9yg9Jy+fofZczpRcXnUGhm7XE/1Fpwk9wqWkZ9BK1vNywousNufzx4L/wWivFlUK\nG57tBwgv+oeSLDsZYs8FwjtKDy4kutP+giy3PgvcpoBOVSwuTegRLCU9gwbyE28lPkeOqcGt+X9h\nf6Atbs0qPu3VokrMFpjltuJbtz732hPxBUbp4WratS5nH1dYmVxg7eBV/0CCm1joVMXi0YQeoVLS\nM2go2YxL/BsONjcXPMxODo9WtB+0Ko3gKP3f/qHUs3K4zv4aCE/Trt6jZ2Hj8IDvE9a6yUx32wGQ\nVDWxwmOJdprQI1BKegaNZQvjEv+Gi8V1+cPZZOqG7te6uSoLtsBXbmsy3cbc5xvP6RwAvOmxFWld\nzj6G2nNpYG3nn/6rQ1NxFw/XJf/FpQk9wqSkZ5BmreLjxJHkk8C1+Y+x0RyeY67JXJWV4Cj9mYIb\nSJLfuNOXAcDErG0VFkPqk9NIpID7fJ/yrVufaTo6LxVN6BGiy6iZpKR/wXX2V7yT8He2mdpcdehx\nHZmrcuWz4FtzIV84nbjDzuBMvJku7Z+aXiHHzz3g53r7K5JlJ6P9VxOsnevovGQ0oUeAlPQMfs3N\nZXTCq4xKeJMFblOuzn+cn0gKPUaTuSoP65/xPld/91+LjctjCe8B3hTC8tbgrxnUZC8P+D5hvtOU\nOW5LABomnV7ux45VmtDD6MJHMkhJz+Bi6zu+SHyEwdY3/LPgKm4peJi9nBZ6nCZzVZ5qVvGx1ZzF\nS/5BDLAX0s36FvAGGuVl6ebdOAYe9P2XqhzgSf9NBEfn0x/sXm7HjXWa0MOg0aOTSUnPoJa7m9EJ\nr/Jh4tPYuNyQP5wXnaGhk0I+S5O5Kn/BGVOvOwPY4NZlpO9tKuGN0MvrBOmVr86nqWziBnsm7zm9\nWWu8KbjdGtYpl+PFC03oFSgl3RuR13B2M9z3HnMr3c8Aaz7/6x/MZfn/INMcXhF3d7f6oT+HlSpv\n3RrWIZ8EhvtvJcXawZ99HwPlc4I09clp+PDzj4Qx/Eo1/uW/MnRfcA9UVTK+cAcQyz7I3BKa1yu4\ndJS1DPPNoI+1CBuXT52u/K8zhC2B7bWCdFSuKtq7t3UkJT2DBW4z3vNfyh2+yXztpjLfbU5KekaZ\nfiZzD/j5H3sSza1N3JX/AL9RFdDPfVkQY0q+YayI9AH+DdjAm8aYUSd7fLt27cySJUtKfLxIdrx6\n4xn8RlvrB3pYy7nUXs6ZkssecxqfOl15x7nsiBks4E3V0rP7KpxS0jOozCEyEh/hNDnEFYeeYTfV\n8VmUyV+MKekZtJCNjE98nKluB/5Y8D+Atw+ubp14YiKy1BjT7lSPK/EIXURs4GWgN5ANLBaRScaY\n1SV9zRNpPmIqeflOWb9sMXi/9ASDBL4CJOCnJnmcIXtJs/I4V3ZyvuwgRX6mmWziAmsHAHmmMrPc\nVnzptONLtx0HqXTMEXR0oiJBanINsrL38MeCe/k08QleTniRmwrS8bs+7h+3vFRtmlPSvVktrya+\nwC/UYkTBLaH7NJmXjdKUXDoA640xGwFEZBwwCCjThN58xFRa+Ffwv5X+N5BQTeBcOKHr3vfASe47\n/mOPvP/w88CSkv3l4jcWW00SP5jzGFfQk+XuhWSZC8kn4biP10SuIsnEe7uQkp7Bd+YC/lpwG/9M\nfI3h5v94wn8zE7O2lTihp6RnYOPwr4RXSCKXq/MfJ5dqgP4fKEulSejnAlsLXc8GjjmjISJ3AncC\n1KtX/GZSefkOOVKDKU4H4HAaNsekcELp3hx13fue0Pj6yOuHvz/pY82RvwYMgoPNbqqy21Ql11Tj\nZ2rxk6mD/xQ/1tTkGtp0SEWsTaP6kZKewaduNxr7t3KnL4NfTXVedIaWqJ7ulSMNT/vG0sP+lr8W\n3MYK0wDQFaFlrTQJXY5z2zHDWmPMGGAMeDX04h6kaqLN+vxkHvPfWvwII4iOQlQ0CSb1Z/3XU4u9\n/CnhExwsXnYGkZKeQXLNyqEt7U4mJT0DwWWE7z2u883i3/4hfOgcfp6eMypbpUno2cB5ha4nA2U+\nx2nVyD4RUEMvuru71deG/ComjP99Gle+Op+H/XfiE4eHEj4mWXIY4f8d2bkHTzpaHzV5Da/N2UgV\nDvL3hDcYaC/gTX9f/uW/KvQYHeSUvRLPchERH/AD0Av4CVgM3GCM+e5Ez4nlWS5KxaJgYhZc/uT7\nhP/xTWSNW4+HCu5klYLvSx8AAATDSURBVDm8NVxwlkrh2V6tZD2jE16jvmznH/5rec0ZQPAPe03m\nxVPUWS6lnbZ4BfAC3rTFt4wxT5/s8ZrQlYo+hddT9LKW8mzCWM6UXKY47fnI6cF8t1nopH8iBaRZ\n33Gt/TV97cXsMDV5oOAe5rvNQ6+nybz4KiShF5cmdKWiV3D0XZ08bvNN5Xf2VKrLfvzG4mfOAOAs\ndpMgDnvMabzt9GGMvx/7qBJ6DU3mJaMJXSlV5gqXVCqRz8XWd7Sx1nGu7ATgZ3MGy9yGzHVbHjFV\n15Zg/3VVEprQlVLlYvBL88jK3lPkx+uovPTKfaWoUio+FV5DcaIWu2XVKkAVjyZ0pVSJ6eg7smj7\nXKWUihGa0JVSKkZoQldKqRihCV0ppWKEJnSllIoRmtCVUipGVOjCIhHJATaX8Ol1gJ1lGE400Pcc\nH/Q9x4fSvOfzjTFJp3pQhSb00hCRJUVZKRVL9D3HB33P8aEi3rOWXJRSKkZoQldKqRgRTQl9TLgD\nCAN9z/FB33N8KPf3HDU1dKWUUicXTSN0pZRSJ6EJXSmlYkRUJHQR6SMia0VkvYikhzue8iYi54nI\n1yKyRkS+E/n/7d1PiFVlHMbx74OT+CfERJSaCWYCyQZBRkSmhBB1kRSOm6CgkGhZOooQ6aZtiwhd\nRBuzBIeJmAYaRCoZF+5E/ANZBobFzM2xEUINN+Pg0+Ic4TK0aHHf88498/tszjnv4r7P4Zz7u+d9\nz7n3ajB3pipIWiTpiqTTubNUQdJKSSOSfi2P9Yu5M6Um6WB5Tl+TNCxpSe5MrSbphKRpSdea2lZJ\nOivpRrl8KkXf876gS1oEfAbsAnqBNyX15k2V3CxwyPYLQD/w3gLYZ4BB4HruEBU6Bnxvez2wkZrv\nu6ROYD+w2fYGij+XfyNvqiS+Al6Z0/YhMG57HTBebrfcvC/owBbgN9s3bc8AXwMDmTMlZXvK9uVy\n/R+KN3pn3lRpSeoCXgWO585SBUkrgJeBLwBsz9i+mzdVJTqApZI6gGXArcx5Ws72eeDvOc0DwMly\n/SSwJ0Xf7VDQO4HJpu0GNS9uzSR1A33AhbxJkjsKfAA8yh2kIs8Bd4Avy2mm45KW5w6Vku0/gU+A\nCWAKuGf7x7ypKrPW9hQUF2zAmhSdtENB13+0LYhnLSU9CXwLHLB9P3eeVCS9BkzbvpQ7S4U6gE3A\n57b7gAckGobPF+W88QDQAzwDLJf0Vt5U9dIOBb0BPNu03UUNh2lzSXqCopgP2R7NnSexrcBuSX9Q\nTKltl3Qqb6TkGkDD9uOR1whFga+zncDvtu/YfgiMAi9lzlSVvyQ9DVAup1N00g4F/SKwTlKPpMUU\nN1HGMmdKSpIo5lav2/40d57UbB+23WW7m+L4nrNd6ys327eBSUnPl007gF8yRqrCBNAvaVl5ju+g\n5jeCm4wBe8v1vcB3KTrpSPGirWR7VtL7wA8Ud8VP2P45c6zUtgJvAz9Julq2HbF9JmOm0Hr7gKHy\nQuUm8E7mPEnZviBpBLhM8STXFWr4EwCShoFtwGpJDeAj4GPgG0nvUnywvZ6k7/jqfwgh1EM7TLmE\nEEL4H6KghxBCTURBDyGEmoiCHkIINREFPYQQaiIKeggh1EQU9BBCqIl/AUtHpz4HK2EdAAAAAElF\nTkSuQmCC\n", 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iW6XD3xjjBUYCM4DVwAfGmJUi8riIDAosNgPYKSKrgG+Ae40xOyu77US3tGA3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\nV0qpBPT/n0uDJvyXo3cAAAAASUVORK5CYII=\n", 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q2cHnmwks8p4Y5n6NOWah/v+tNOTy/DupxUGmuh+jHnlk5+5j+pc/RbhCYypP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\nNYllhQZ+o3mRRwt/Y4wBfhg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ernXMcrqFukqqHNEZvqpSeHvpD3SxNgKw3KkccwyTbmyFweILO56eVqrO9lWn\n0OCvKoWCfP+Ppm6lyfcXWOi0p7Yco4N4u9p0tq8CDf6q0ijI97eiYHRyOOf7C5yc7eumt0tn+6qT\nNPirsJc8J40msptoORz24/tPN3NMd45SjZVOK13qQZ1Cg78Ke958v298fyUL/gUWOu1pYu0h1jfb\nV/f2VRr8VdjzruezkT3mYnaYS4HKk+8H72zfz532wMnZvrq3r9LgryoBQ0drM6ucllSmfH+B1Gdu\nINNEs8lpQG9LR/oor6CM81eqvFq74yAxso/L5CBrnOahrk5Ife4kcJ8rhVoc5TA1uOPdlZXqQ7C8\niRs/j5w8+6znM5IHlGr5GvxVWLvrvVX0Eu+GJmucFiGuTegIsMhO4EH3LK6xvifF6cKSrftCXa1K\nKTYpBYAIPHSQ7TSxdlObo9i42GWi2eDEspt6xCallOoHgAZ/FdYO53pIdG/hsKnGZuNdfzBc9uu9\nEEPiL2dWqsMBE0Vv1zekOF1CXaVKpyDot5Sd3OOaww2u1dSS40Veu8xuzW3540r1A0CDvwp7idYW\nUp2mOGG2X++FmDQ8gZmpu/nCiec6KxULBweLtTsO0uHKi0JdvbAXm5RCXQ7xZMRHDHMt4Zipwv/s\nq/ncSWCjacgBU4sIPMTKXjpYW8qkThr8VVirxVFayC7m2p1CXZVy4XO7Pbe4lpIgW1lrWnDblOVs\nfv7GUFcrbE1duZOnZnxPV2s9r0ZMpjZHedMziLc8gzhE1BnXp5qapNpNy6RuGvxV2Bo6eSkJ1jYs\nMawxlbuzFyA6KpIlOe3INy76uL5hracFJ2zd4rG03PHuSpZs3cfdrrk87f4X6eZybssfx1YTc8a1\nBamdjhMXnDIMV3P+SpVAauYhfuPejMdYpDre1lTNKq4Q1yp0Vo/rS2xSCqucllxnreOPjAh1lcJW\n8pw0lmzN4lH3pzzi/g9z7Y78Nv/XHKOq/5oHejQm6cZTJx2uHte3zOqo4/xVWEuULWw0V/r/6N6/\nW4c2fu4k0MLKJEZ+BnSDl9Lw1pJ0f+Cf7unJQ/mP+H8HBW+L/vTAX9Y0+Kuw5cZDgrWNtYXG91f2\nzk1LYJGTAMB1vglfusFLcMUmpTDStdAf+JM89/oHGzzQozE/lPL4/eLS4K/CUvKcNFrLDqpJXqUe\n33+60dc0JsPUZ7tTnz660FvQxSal0MP6lgnu91hoJ/CU5x6ML8yWh9Z+YUEJ/iLST0Q2i8g2EUkq\n4vxvRGSjiHwnIotE5MpglKvU2by99AcSfUPmKvvM3sIKgs8ipz2drTRq4B1nPnXlzlBWKyzEJqUQ\nI1m8GvE6W0wD/i///7Dx9jEe/6m4AAAgAElEQVSV9mzdkgg4+IuIC3gd6A+0BkaIyOlbJa0DEo0x\n7YBPgD8FWq5S52I7hg7WZjJNPfZyMQBD4y8Pca3Kj8+dBKqIh+7WegB+P/P7ENeoYhs6eSlVyOON\niEm4sHkgfyzHfTn+8vp7F4yWfydgmzEm3RiTB0wDhhS+wBjzhTHmmO/pCuDMsU5KBZWho7WF1YVS\nPpOGJ4SwPuVHs+garHGac9hU96/yqSM+A5OaeYjH3B/TzvqBx/IfYIe5DAC3VX5/74IR/K8AdhV6\nnuk7djb3AHOLOiEio0VkjYisycrKCkLVVGXVQH7mEsk+pbNXeS34bU88uFnsXEUv1zoEJ9RVqtBi\nk1LoKJu4xzWXf3l685nT0X9u2wvlL91TIBjBX4o4VmQ7QkR+BSQCLxV13hgzxRiTaIxJjI6ODkLV\nVGXUPXkRiVKQ79fO3rNZZCcQLYdpJ+mA999NXZjuyYuoRi4vRfyNTFOPFzwj/efKY56/sGAE/0yg\nQaHnMcAZO0SLSB/gaWCwMeZEEMpVqkiZ2bkkWt7F3Lb4ZlNWxsXcziXCJXzpXIVthOtc3iGfmdm5\nIa5VxZOZncvj7unEWnv5Xf4D/rH8D/RoHOKanV8wgv9qoJmINBKRSGA4MKvwBSKSAPwNb+D/OQhl\nKnVO7XUxt3N6bnAc2dRkjWmhQz5LKDYphThJZ5TrM973XM9K4x1JJVCuhnSeTcDB3xjjAcYA84E0\n4GNjzAYRmSAig32XvQREAf8WkVQRmXWW2ykVsBocp7lk8o1pFuqqlFu3dW4IwOd2Am2sHVzGfsC7\nHo06v6krdyI4TIx4j/3U4mXPL/znysskrvMJyto+xpg5wJzTjo0v9LhPMMpR6nzGTltHOysdlxj/\nej7q7BY5CTzJR1znSmWq3Vs3eCmmp2Z8zy9dXxJvbWds3oMcoTpQsfaG1hm+KqzM+nY38bIdgFSn\nCaC/5GfTo1k9tpkr2OFc4h/yqc6v78uLqU0OT7g/YqXTkplON/+5irQtpv5dqLDiGEiwtpLuXEY2\nNQEYXQE630LBG6iEz50EulnrqYp3HMbaHQdDW7FybmvWUca4Z1KbozyTfycFAx7L++ie02nwV2HG\nkGBtY505mfKpCJ1vobTIaU9VyaertQGA26YsD3GNyq+48fOIkSzucH3Gp3YPNhlv30k1d8ULpRWv\nxkqdwxXsI1oOsc7Rzt7iiKlTlVVOS3JMVXr7VvnUDV7OLifP5jfuf2MQXvEM8x9Pm9g/hLUqGQ3+\nKmz0fXkxCdY24GS+X53b0qTe5BHBEqedb7y/Bv6zaf70HFpLBkOtr3nP7sdP1AUq7hwSDf4qbGzN\nOkq8tY1cE+H/Ol5R/zDL2udOAvXlAG1kB6CzfYuSZxuS3B9xiBq86RnsP15R55Bo8FdhJcHaxvem\nER7fKOaK+odZltyW8IUdj2OE63yjfnS276maPJnC1dYGeri+Z7JnKIfxNioq0tDO02nwV2EjAg9x\nkqH5/gs0YUgc+6lNqmlCb5cO+SyKbQxj3Z+yx1zMv+yT05Yq0tDO02nwV2Fh7LR1tJIdVJF81unk\nrgtSMNt3kd2eeCudaLIBne1bwNvq30hnaxNvegZxgkgAXripbYhrFhgN/ioszPp2d6HOXm/w11/u\nC/O5b2/fnq5UAJ3t62MbGOv+lJ/MRUy3e/mPF3xoVlT696HCgmMg3trGT+Yi9vh27tLJXcXXo1k9\n0kxDfjR1/UM+FTR9KoUu/lb/4LBp9YMGfxVGEmSbr9XvnXGpk7uKzz/b107gGus7qpAH6N6+Hsfb\n6t9r6jAtjFr9oMFfhYmLOUystVfz/QFa4HSghpygu+Xd07cy7+3b/Ok5dLE20sVKC7tWP2jwV2Fg\n6OSlXGV5F3PT4F9yMXWqstxpw2FTnX7WaqBy7+2bZxvGuGbws6nDR/Z1/uPh0OoHDf4qDKRmHiLB\n2orHWHxvGgFwcfWIENeq4lma1Jt83Cx02tPH9Q0u7FBXKWTixs8jTtLp7trAu57+/lZ/Rdihq7g0\n+KuwEC/b2WwacNy3jd7bozqe5xXqbObbiVwkOXSyNgEQ/9z8ENeo7OXk2Tzgns1hU42pdm//8XDq\nR9Lgryo8wSHe2nbK5i0drrwohDWquOpUc7PEacdxE0k/axUA2cc9Ia5V2eo4cQENZS/9rZV8aPep\nkBu1FEdQgr+I9BORzSKyTUSSijjfQ0S+ERGPiAwr6h5KlcTUlTtpIrupJcdPWcZZlUzqMzdwnKp8\n6VzF9a61CE6oq1TmsnLyGO2ajQcXf/f08x+vyLN5ixJw8BcRF/A60B9oDYwQkdanXbYTuBOYGmh5\nShU2cfYG/+Qu7ewNnvl2IvXlAFdJOuBtDVcGfV9eTD0OcatrCf+xryEL7zfIcFwgMBgt/07ANmNM\nujEmD5gGDCl8gTEmwxjzHVTCZoQqVcfyHRJkG4dNddJNfSD8vp6XNbclLHISyDcu+rm8o36ycvJC\nXKuysTXrKKPc84nAwxR7oP94OC4QGIzgfwWwq9DzTN+xCyYio0VkjYisycrKCkLVVGUQb20n1WmC\n8f06h9vX87I2YUgch4liudOaG6xVVJY1/sdOW0d1crnD9RnznUR+8DUmYupUDXHNSkcwgr8UcaxE\nvy3GmCnGmERjTGJ0dHSA1VKVQXVyaSE7WWd0Jc9gKRjHPt/pSCNrL80lEwj/1M/M1N2McH1ObTnG\n3zyD/MeXJvU+x6sqrmAE/0ygQaHnMcDuINxXqXMaO20dbeUHXGJYpzt3BZVL4DO7A44R+vtG/YRz\n6mftjoNE4OEe9xxWOK1I9Q0eiIp0hbhmpScYwX810ExEGolIJDAcmBWE+yp1Tt6VPLcCJ1fydBX1\nPVRdsD8MbUsWF7HGNKe/a1Woq1Pqhr25jEHWMi6XA7xVqNW/fkK/c7yqYgs4+BtjPMAYYD6QBnxs\njNkgIhNEZDCAiHQUkUzgVuBvIrIh0HKVcox3564fnEvJpiYA910TPjMwQ6kg9TPb7kJLaxfNxdut\nF77bOzrc755NmtOAxc5VALjDfBZUUN6eMWaOMaa5MaaJMeZ537HxxphZvserjTExxpgaxpi6xpg2\nwShXVXaGBGvbKfn+cJqBGWoCzLU7YxthoGs5EJ7bOzZ/eg69rFRaWJm+XL/36+O2FwaEtmKlLMw/\n21Q4u5z9XCLZOr6/lNzfozFZ1GG505qB1grCddRPnm243z2bTFOP2U6XUFenzGjwVxXS0MlLiT9t\n5y4VXAXfomY7V9PY+ok2kgGEV+on/rn5tJctdLY28Y7nRjy4gfBZtvlcNPirCsm7kuc2ck0Em4w3\nP60reQafAPPsjuQbF4PCMPWTfdzD/e7ZHDRRTLd7+o+Hy7LN56LBX1VYCdY21ptG5Ptaa7qSZ/Dd\n36Mx2dTkK6ctA13hlfrp+/JimsiP9LXW8oF9vX9F2MoyQ1yDv6qQIvAQJz+cku/XlTyDryD18z/7\namJkH+3FO7Q2HJZ53pp1lPtcKeTh5h+e6/3HK8sMcQ3+qsJZu+MgLWUnVSVfO3vLgEu82zueMBH+\n1E9FX+Z57LR1XMJBbnIt5WO7JweoBYTvUg5F0eCvKpzRH6zWzt4y9IehbcmhOoucBAa5luOmYgd+\n8C7lcJd7Hm5s3rFv9B8P16UciqLBX1U4+4/mk2BtY6+pw27qAhAfUzvEtQpfBZ2f/7GvoZ4c5lrr\nWwBajZsbymqV2NSVO4niGCNdC5nrdGanuRQI76UciqLBX1VICbLV1+r3TsiZOaZ7aCsU5qq5LRY7\nV7HP1OIW11cAHPdUzBXan5rxPSNcn1NLjvOW5+SyzeG8lENR3KGugPJuFp2TV7zNsjOSw3vWYXHU\n4QiNrL1Mz+8V6qpUGmkT+xOblMIsuysjXQupTQ6HiCJ5TlqFm1UdST73uOey1G7DeuNdDiSyEi4K\npcE/hGKTUgCoTQ7DXGvpJJtobe0gWrKxMBw21fnBXMY3TnO+cOJJMw39rxkafzmThieEsvohkTwn\n7WS+X7dtLHOf2j242z2PQa7l/Mvuy1tL0itU8G/6VAo3ub7mMjnI7+z7/ce3PH/jOV4VnjT4h0DT\np1LwONBMMnnIPZP+1mqqSD4HTBTfOU1Y78TiYFFbcmgqu+kTsY7Hmc4G50ret29ght2dmam7mZm6\nu9J9E3h36Q+MsbZhG+Fbx9tqq3xtttCIjopkQ86VpDkNGOZawr/svqGu0gWzHYfRkSlsdK7kKyf8\nZ/Geiwb/MhablEItjjLO/S+GuZZwlKpMta/jE7sHG82V/t2oCovmINe71vIr1wJeipjCr12zSPaM\n4DOnI7FJKbit0lmEquBbBkAUx6hKPgeJwubUjrE61dykPnND0MsvSr5jSHBtY7Np6J+UMyT+8jIp\nu7JbPa4vsUkpfGr3YFzEhzSRH9lurqDvy4srxDaHrcbNpbe1jmbWjzyc9xAFzYZPf901tBULEQ3+\nZaTjxAVk5eTRSdJ4JfJNLuUg79g38oZnsH854rPJ4iI+tPvwod2bXlYqT7qnMiXyL8y2OzM+/y4O\nOLWITUoJ2reAxkkpOEAbyeB212dc6/qO+nIAANsIGeYy1jgtWG1asMJpTebx6KCWfy6CQ7y1nf/Z\nV/uPVcb0Vyj91+5GkvsjbnV9SbLnNrZmHQ11lYrluMdmTORMdjnRzHFOTuSqrJMDNfiXgdikFNx4\neMz9KQ+6ZrHDXMKw/Gf4toicdVEBtHvyIt96KsIXTgJL8tpxnyuFR92f0KVKGo/kP8TXTltvq+zX\nXQP6ZY5NSqEmx3jSPZXhri84TiSLnPZscGI5TiT15BCtZBfXu9bwS1kMwHueG3jOM6pMPgAayx5q\nyTHWab4/JHo0q8eSrd5JX7e6vuQVz63kEcHaHQfLdRCNf24+11jfE29t56n8e/wLuD3Qo/Lu/6DB\nv5TFJqUQK3uYFPE68VY60zw9meC5g2OcnEl4vrRJ4YknsUkp2Lh4yx7MIqc9kyNe44OIZF7y/JK3\n7EHc8uYyYupULdFkldikFKI5yAeRf6SZZPKu3Z/XPDdzhOpnXCs4NJMfeTXiddpaP1xwWSXR9+XF\ntPft3KUze0Pjg3s6E5uUwod2H/q7VtPPWs0spyu3vrmM9HLc/5R9PJ//i5zBbnMxn9g9/McrUmd1\nsAVlnL+I9BORzSKyTUSSijhfRUSm+86vFJHYYJRbnjV9KoXYpNnc6lpMSuRTxMpeHsgbS5Jn9CmB\nPyN5wAXlyzOSB/hbK1tNDDflTWCu05mkiGm8HvEq1cglMzv3lHx9cRR8SH0a+SwNZS935j/B855f\nFRn4AQwWW0wDdphLieL4BZVVUluzjpIg2zhkqpNu6gPQLLpGmZStTqrmtvjaaUOGcykj3QsBKM8j\n/jtOXEAXK41O1mbe8gwiD+/qr5VlAbezCTj4i4gLeB3oD7QGRohI69Muuwc4aIxpCvwF+GOg5ZZX\nsUkpxCalUM/Zz3sRf+KliCmkOk3pdyKZeU4n/3UP9Ghc4hRJ0o2t/K89RlXG5P8fz+ffRj9rNZ9E\nPsfl7PPXpbh1biM/8Enkc9SQXEbkjWNpoZEQL9zUlozkAWf8AORQjZpyDPCOBiltCdY2Up2m/o7x\nitDRGG7SJvbHYPGRfR2drU00lUyg/K7zn5WTxxjXDH42dZhun5wbUlkWcDubYKR9OgHbjDHpACIy\nDRgCbCx0zRDgWd/jT4DJIiLGmFJZH7bvk3+jBrmIb/lZKWIZ2tPPyWnHTzkmxb9PT8vDtdZ3DHd9\ngUF4Jn8UH9h9TxnFE6y8eEbyAPq+vJitWUd52x7IVhPDaxF/ZVaVcYzJf5gVTmtik1KIinQVOXux\noC/hamsDUyJe4RA1uCMviXRz+SllnE2ry2pyZF81avpa/vWiqgTlfZ1NdXJpLrv4zEks1XJU8fzb\nvpbfuj9mpGsRz3lGlct1/jtOXEB72UJ31wb+kD+SE3gbKPqNMTjB/wpgV6HnmcDpH6n+a4wxHhE5\nBNQFXxM1iGKTUvhP5BTa+yYChUK+cTHL6cokz83s8q0bAt7VEbe/GNy8aEHLNzYphcVOPDflTWBK\nxCtMjXief9jX85Lnl+TkVfV/C8hIHuB/bOFwn2sOj7uns91czqi8J9jLxb5znDeHezg3nyNUI4rj\nCA6Hc/OD+t4Km7pyJ+2sdFxiNN9fDhR0/M5xOnOLawkve24lh+rlbsZvVk4eL0XMYL+pyVT7ZD+Y\nfmMMTvAvao7N6U3k4lyDiIwGRgM0bFjynXQm5v+KWr5UhPEVXVCYKVSVs50zRVTXf86c+prT72MQ\ntpgGZ+TKX7ipbanuDlQQ1LebKxiY9zxPuKdxl3s+Q1xf8w/PDcx2upBu6hOblEJtcuhtfcN97hRa\nWbuYa3fkifzRHMbbGop0SfFmPIpwxFTHEkN1ToCUXmtq4uwNjJKClTyblFo5qngKOn7/7unP0CrL\n+KVrMe/aN5arGb8dJy4gUTbR0/UtL+aP8M8LqUzLNp9LMIJ/JtCg0PMYYPdZrskUETdQGzhw+o2M\nMVOAKQCJiYklTgl9Y5qXqw2HymoWbsEHwHGq8qznTmbY3XnE/R8ejfiUR/mUXBNBHm5qiTdNk+5c\nxkN5D5PidKbg8/lsKaKi1KriJodqANTkGLanTqm8L4Bj+Q4JEVvZ7tT3z4uo7B12oRYV6eK7vCas\ndFpyl3se79s3nDEBMJSyck7weuR09po6/MM+uVlLZVq2+VyCMdpnNdBMRBqJSCQwHJh12jWzgFG+\nx8OAz0sr319eljsYGn/5KR2jZSUjeYC/4/Vb05S78x/n6ty/8nj+ffzDvp5P7R68kD+Cm088y3V5\nL5PidKEg8PdoVu+CVjaMdFscMd5vOFFynJ+OnGDqyp1Bf09extvZW2h8f2XvsAu1gt+Vdzw3EiP7\n6G+tArwj3UItbvw8elrf0snazF89N5GLtz9KW/0nBdzy9+XwxwDzARfwd2PMBhGZAKwxxswC3gX+\nKSLb8Lb4hwda7rmUlw+AUFk9zrvmSkFufw91+dg+9wqYJfk3+2XHhsz/rzf418KbZvv70vRSSW/F\nyD6i5ZDm+8sZARY67Ul3LuNedwqz87rgcUK/2tLRvHx+FzmdHc4lp4zw0Vb/SUEZ52+MmWOMaW6M\naWKMed53bLwv8GOMyTXG3GqMaWqM6VQwMkiVroJvHmcb2eC2COjbyW2dGyJVogBvyx9KZ433O95d\nSYLo5K7y6JNfd8Vg8Xe7P/FWOp1lExDajV6aPz2HAdZK2lg7+ItnGPm+Nq5u+HMqneFbCZTmyIYq\nURfBEfzDPWtVCf6v1Fdb9/F79zaOm0g2G2/3UlW37kNUHhQs6fBv+1oeds9grPtTRuSPC+lGL2Kf\n4InIaaQ5DZjlnFy0TTf8OZX+BamA/Jzn7V8oaPmXxnBPA8Rb2/jONPavyTJ+UJugl6NKZmj85Zwg\nkjc9g7jatZEulneKT9z4eWVel9ikFO5xzaWBlcUfPLfj+ELcUF359Qwa/FVADtjeDrSavpz/CTv4\nLb5I8mkjGaekfEpz2Ky6MAWrqk61e7PX1OFR9yeAKfbudMGSPCeNSzjIQ+6ZfGZ3YJkTd0Yd1Uka\n/FVAjlEVx4h/iYdgW7vjIK1lB1XEo/n+cqxHs3qcIJI3PEPobG2iq7UBKNvc/1tL0nk8YjpubJ73\njPQfr6zr9Z+PBn8VECMWOVT15/yDbfQHq0nwr+TZrFTKUIErGHY7ze5FpqnHOPeHWDhllvuPf24+\nHWUTw1xLeM/uzw5zGeAdjVSel5oOJQ3+KmA5VPOnfYJt/9F8Eqxt7DYX8zPeP2IdtVE+FbT+k/NH\n0NrawS9ci4HiLzAYiOPHj5Ec8Ta7nGhe9dzkP/5DJR/2fS4a/FXAjpjq/g7f0tDe2npKykdHbZRP\nBa3/2U4XVjkteMz9sb9RkDwnrdTKjU1K4UH3f2li7eFpz93+ZRzqVNPBjOeiwV8FrDRb/pdygBjZ\nx1qnRancXwXXCze1BYQJ+bdzMUd8nb/efHxp6J68iDaSwYOuWfzH7s4S5yr/ubLaV7qi0uCvAlZa\nLf873l1JorUFgDVO86DfXwVfwSis9aYx/7L7cKdrPu3F+/+w+dNzgl7e/uxsXov4K/upxYT82/3H\nK/P2jMWlwV8F7AjVSqXD96ut+0i0NnPcRLLRXAl4l8VW5VvBjPFkzwh2U5eXIv5GFfLIsw1rdxwM\nWjmxSSk84/6ARvITj+Y/6F/wT6jc2zMWlwZ/FbAjpho1S6Hlb4AO1ha+NU38k7vuu0ZbdBVBdFQk\nx6jK4/mjaWLt4ffufwJwy5vLgnL/2KQUbrK+Yrh7MW/ag1junJz0p528xaPBXwXsMDWoxdGg37c6\nubSWHaekfLRFVzEULC64zInjLc8gfuV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ACc8i200dVtsNWW3OZ6WdzDLTjDxTj9KGiir79zX4a5skO7nbMZXrHXP5jWq8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\n", 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GKihNAEqFuaReTfPMJfSs+y/c4XrIP730aHrY1gLaJVQRaQJQSgF57wNY6m1F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\nUkqFqf8HmUlTeQiWl6EAAAAASUVORK5CYII=\n", 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