5.2-LongitudinalAircraftExample.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1b7c62f7-b9b3-460a-87d2-cc7a761b8756",
   "metadata": {},
   "source": [
    "This notebooks shows how to derive transfer functions for analysis of longitudinal aircraft dynamics.\n",
    "\n",
    "# Translational Equations of Motion\n",
    "\n",
    "$\\frac{^ed}{dt} m V = F$\n",
    "\n",
    "Mechanized in inertial frame:\n",
    "$\\frac{^ed}{dt} m V_e = F_e$\n",
    "\n",
    "$\\frac{^ed}{dt} m V_e = F_e$\n",
    "\n",
    "If m is constants, back to F= mA\n",
    "\n",
    "$m \\dot{V_e} = F_e$\n",
    "\n",
    "$m A_e = F_e$\n",
    "\n",
    "\n",
    "Mechanized in body frame:\n",
    "$\\frac{^bd}{dt} m V_b + \\omega^{eb}_b \\times (m V_b) = F_b$\n",
    "\n",
    "If taking derivative of a vector with respect to frame it is expressed in, \n",
    "it becomes the vector dot, time derivative of components.\n",
    "\n",
    "$m \\dot{V_b} + \\omega^{eb}_b \\times (m V_b) = F_b$\n",
    "\n",
    "\n",
    "# Rotational Equations of Motion\n",
    "\n",
    "$\\frac{^ed}{dt} J \\omega^{eb} = M$\n",
    "\n",
    "$\\frac{^bd}{dt} J \\omega^{eb}_b + \\omega^{eb}_b \\times J \\omega^{eb}_b  = M_b$\n",
    "\n",
    "If J is constant (rotational inertial in body frame about cm):\n",
    "\n",
    "$J \\dot{\\omega^{eb}_b} + \\omega^{eb}_b \\times J \\omega^{eb}_b  = M_b$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ac608997-521a-4848-aaa6-146cfed2eddf",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy\n",
    "import sympy.physics.mechanics as me\n",
    "import scipy.optimize\n",
    "import scipy.integrate\n",
    "import matplotlib.pyplot as plt\n",
    "import control\n",
    "import numpy as np\n",
    "\n",
    "m, J_y, g, t = sympy.symbols('m, J_y, g, t')\n",
    "gamma, alpha, V, Q = me.dynamicsymbols('gamma, alpha, V, Q') # functions of time\n",
    "frame_e = me.ReferenceFrame('e')\n",
    "frame_w = frame_e.orientnew('w', 'Axis', (gamma, frame_e.y))\n",
    "frame_b = frame_w.orientnew('b', 'Axis', (-alpha, frame_w.y))\n",
    "J = me.inertia(frame_b, 0, J_y, 0)\n",
    "\n",
    "# control inputs\n",
    "th, elv = sympy.symbols('th, elv')  # thrust, elevator\n",
    "\n",
    "T = th \n",
    "\n",
    "# gravitational force\n",
    "W = m*g"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2fcc778-1f25-4355-bd3e-b6a576f0b876",
   "metadata": {},
   "source": [
    "## Aerodynamics Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "33be04d9-cd37-4d3d-9117-dca7bcc57a2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "C_La, C_L0, k_CLCD, C_D0, C_M0, C_Me, C_MQ, C_Ma, rho, S, alpha_s = \\\n",
    "    sympy.symbols('C_La, C_L0, k_CLCD, C_D0, C_M0, C_Me, C_MQ, C_Ma, rho, S, alpha_s')\n",
    "\n",
    "# aero coefficients, neglecting stall\n",
    "C_L = C_L0 + C_La*alpha\n",
    "C_D = C_D0 + k_CLCD*C_L**2\n",
    "C_M = C_M0 + C_Ma*alpha + C_Me*elv + C_MQ*Q\n",
    "\n",
    "# aero forces/moments\n",
    "q = rho*V**2/2\n",
    "D = C_D*q*S\n",
    "L = C_L*q*S\n",
    "M = C_M*q*S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "eff6edd6-9b65-4543-89aa-b39e94d1cae6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle C_{L0} + C_{La} \\alpha{\\left(t \\right)}$"
      ],
      "text/plain": [
       "C_L0 + C_La*alpha(t)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a56bedc1-2a9e-48ea-a0b9-dd8ef01f7fd0",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RbADAmD7tRE5zezZX7GRSCUZGtQXAOe2IiIjo1o5nX8fFgjI42MkwLNJP7Di3ZXPFDgBGRplOx+6/UIica+UipyEiIiJztfaIaRDo4e5+cFHaiZzm9myy2LXzdET/Dp4QBN5EQURERA0rqdRjy8k8AOZ/08QNNlnsAGBszXny9ccuo9pgFDkNERERmZstJ/NQoTegvbcTege5ix2nUWy22MV39YG7ox3U2krsPlcgdhwiIiIyMzfmrhvTOxASiUTkNI1js8VOIZfV3kRx424XIiIiIgA4py5BSk4x5FIJnujVVuw4jWazxQ7447bl38/mQ62pFDkNERERmYsbo3UPhreBt4tC5DSNZ9PFrkMbZ/QN9oCRN1EQERFRDV21ARuTTevKj7WAuev+zKaLHQCM7Wu6y2Xt0RwYjYLIaYiIiEhsCalXUVyuh6+rEvd28hY7zh2x+WL3UIQfXJVy5BZXYN+FQrHjEBERkchunIYd1bstZFLLuGniBpsvdko7We1FkWuP8CYKIiIiW5ZzrRz7awZ6RkVZxtx1f2bzxQ7443RsQupVFJToRE5DREREYvk+6TIEAejfwRPtPB3FjnPHWOwAhPm6okegG6qNAjYcvyx2HCIiIhKBwSjgh5qbKUf3trzROoDFrta4GzdRHMmGIPAmCiIiIluz93wBrmgqoXKww+CuvmLHaRIWuxqPdPeHs0KOrKJyJGYUiR2HiP5i8eLFCAkJgVKpRFRUFPbt23fTffPy8jB+/Hh07twZUqkU06dPr7fPfffdB4lEUu/x8MMP1+4zb968el/39bXMb/ZEdHvfHb4EABjRqy2UdjKR0zQNi10NJ4Ucj/bwBwCsPcI57YjMybp16zB9+nTMnTsXycnJiIuLw9ChQ5Gd3fANTzqdDt7e3pg7dy4iIyMb3Gfjxo3Iy8urfZw+fRoymQyjRo2qs1/Xrl3r7Hfq1Klmf39EJL4rxRX4/Ww+AGB8tGWehgVY7OoYVzMJ4fbTalwvqxI5DRHd8NFHH2HKlCmYOnUqwsPDsWjRIgQGBmLJkiUN7h8cHIyPP/4YkyZNgkqlanAfDw8P+Pr61j4SEhLg6OhYr9jJ5fI6+3l7W9acVkTUOOuO5sAoANEhHujQxkXsOE3GYvcnEW1V6OrviiqDkTdREJmJqqoqJCUlIT4+vs72+Ph4HDx4sNmOs3z5cowdOxZOTk51tqenp8Pf3x8hISEYO3YsMjIybvk6Op0OWq22zoOIzFu1wVg7d934aMtaaeKvWOz+Ymxf0we69mgOb6IgMgOFhYUwGAzw8fGps93HxwdqtbpZjnHkyBGcPn0aU6dOrbM9Ojoaq1atwo4dO7Bs2TKo1WrExsaiqOjm1+EuWLAAKpWq9hEYaLmndIhsxa5zBVBrK+HhZI8h3Sz7OloWu794rIc/HOxkuJBfiqRL18WOQ0Q1JJK6s78LglBvW1MtX74c3bp1Q9++fetsHzp0KEaMGIGIiAgMHDgQW7duBQB8/fXXN32tOXPmQKPR1D5ycnjNLpG5W11z08TIqLZQyC3zpokbWOz+wlVph0e6+wEA1vAmCiLReXl5QSaT1Rudy8/PrzeK1xTl5eVYu3ZtvdG6hjg5OSEiIgLp6ek33UehUMDV1bXOg4jMV861cuw+XwAAGNfXsk/DAix2DbpxOnbrqSvQVOhFTkNk2+zt7REVFYWEhIQ62xMSEhAbG3vXr79+/XrodDpMmDDhtvvqdDqkpaXBz8/vro9LROZh3dEcCAIQG+qJEC+n2z/BzLHYNaBXOzd08nFGpd6IH1NyxY5DZPNmzpyJL7/8EitWrEBaWhpmzJiB7OxsTJs2DYDp9OekSZPqPCclJQUpKSkoLS1FQUEBUlJSkJqaWu+1ly9fjuHDh8PT07Pe12bNmoU9e/YgMzMThw8fxsiRI6HVajF58uSWeaNE1Kr0BiPW1aw08WR0kMhpmodc7ADmSCKRYGyfdpi/JRWrD2djYr+gZruWh4ju3JgxY1BUVIT58+cjLy8P3bp1w7Zt2xAUZPpGnJeXV29Ou549e9b+OikpCatXr0ZQUBCysrJqt58/fx779+/Hzp07Gzzu5cuXMW7cOBQWFsLb2xv9+vXDoUOHao9LRJbttzTTGvFezvYY1OXuL+0wBxKBt342SFOuR993foWu2ogNL8QiKshd7EhEZIG0Wi1UKhU0Gg2vtyMyMxOXH8a+9EK8cF8oXhkSJnacZsFTsTehcrTDsEjTShTfHbokchoiIiJqTtlF5diXXgjgjwUKrAGL3S08WTNJ4ZZTeVyJgoiIyIqsPmK6fCOuoxfaeTqKnKb5sNjdQo9AN9NKFNVG/JDElSiIiIisgenf9Rs3TVjPaB3AYndLEokEE/qZLpL+7vAlGI28HJGIiMjS7UxVo7C0Cm1cFHgw3DpumriBxe42Ho30h7NCjqyichy4WCh2HCIiIrpLqw+bTsOO6RMIO5l1VSHrejctwEkhxxO9AgAA3x3Kvs3eREREZM4yCkpx8GIRJBJTsbM2LHaNcGPSwoS0q1BrKkVOQ0RERE21puamifs6eaOtu/XcNHEDi10jdPZ1QZ9gdxiMAtYe5agdERGRJarUG2pvhhxvJStN/BWLXSPduIli7ZEcVBuMIqchIiKiO7XjjBrXy/XwdVXi/s7eYsdpESx2jTSkmy88nOyh1lbit7P5YschIiKiO/Tdn26akFvZTRM3WOe7agEKuQyjercFAHzLlSiIiIgsSvrVEhzJvAapBBjb1/pumriBxe4OPNk3CBIJsC+9EJeKysSOQ0RERI30Tc2gzIPhPvBTOYicpuWw2N2Bdp6OuLej6Zz8jTlwiIiIyLyV6qqx8XguAGBSjHXeNHEDi90durH0yPpjOajUG0ROQ0RERLezKTkXpbpqtPdyQv9QL7HjtCgWuzv0QFgb+KmUuF6ux/bTarHjEBER0S0IgoBvErMAmGa4kEol4gZqYSx2d0guk2JcX9OoHW+iICIiMm+HM6/h/NVSONjJMCKqrdhxWhyLXROM6RMImVSCY5eu46xaK3YcIiIiuolvEk2DMMN7+kPlYCdympbHYtcEPq5KxHfxAcBROyIiInN1VVuJHWdMl01N7BcsbphWwmLXRDdWoth0PBcllXqR0xAREdFfrTmSjWqjgN5B7uji7yp2nFbBYtdEsaGeaO/thLIqQ+0t1ERERGQe9AZj7dRkE618ipM/Y7FrIolEgskxwQCArxOzIAiCuIGIiIio1s4zV5FfooOXswJDu/mJHafVsNjdhSd6BcDJXoaMgjIcuFAkdhwiIiKqsapmipNxfQNhL7edumM777QFuCjtam+d/rrmDxARERGJ65y6BIczr0EmlWB8zcICtoLF7i7dWJrkt7SryLlWLnIaIiIi+uZQFgBgYHgbq14XtiEsdnepQxsX9O/gCaMAfMf1Y4mIiERVUqnHptp1YYPFDSMCFrtmcOMPzrqj2Vw/loiISESbknNRVmVAqLcTYkM9xY7T6ljsmsGDYW0Q4OaA6+V6/HziithxiIiIbJIgCFhVs9LExH5BkEise13YhrDYNQO5TFo7YTGnPiEiIhJHYkYRLuSXwtFehidsYF3YhrDYNZMxfUy3U5/O1SI5p1jsOERERDbnxrqwj/cMgKvS+teFbQiLXTPxcLLHo5H+AIBVB7PEDUNERGRj8jQV2Jl6FYBtrTTxVyx2zejGShRbT+WhoEQnbhgiIiIbsuZwNgxGAX2DPRDmaxvrwjaExa4ZRbRVoWc7N+gNAtYe4dQnRERErUFXbcDqI7a3LmxDWOya2Y1Ru+8OZ0NvMIobhoiIyAb8fCIPhaVV8HVVYkg3X7HjiIrFrpkNjfCFl7M91NpKJNSc6yciIqKWIQgCvjqQCcA0Wmcns+1qY9vvvgUo5DKM62tal+5r3kRBRETUoo5mXceZK1oo5FKM72tb68I2hMWuBYyPbgeZVILDmddwVq0VOw4REZHVujFa93jPALg72YucRnwsdi3AT+WAwV19AHDUjoiIqKVcvl6OHWfUAICn+4eInMY8sNi1kBt/wDYez8W1siqR0xAREVmfbxIvwSgA/Tt4orOvi9hxzAKLXQvpHeSObgGu0FUbsYZTnxARETWr8qrq2n9fn47laN0NLHYtRCKR4JmaUbtvEi9x6hMiIqJmtPF4LrSV1QjydMQDYW3EjmM2WOxa0MPd/eDlrIBaW4lfTqvFjkNERGQVBEHAyppr2CfHBEMqlYgbyIyw2LUghVyGif1MM2Cv2J8pchoiy7Z48WKEhIRAqVQiKioK+/btu+m+eXl5GD9+PDp37gypVIrp06fX22flypWQSCT1HpWVlU0+LhG1jn3phbiQXwpnhRyjercVO45ZYbFrYeOj28FeJkVKTjGOZ18XOw6RRVq3bh2mT5+OuXPnIjk5GXFxcRg6dCiysxu+flWn08Hb2xtz585FZGTkTV/X1dUVeXl5dR5KpbLJxyWi1nFjipORUW3horQTOY15YbFrYd4uCgyL9AcAfHUgS9wwRBbqo48+wpQpUzB16lSEh4dj0aJFCAwMxJIlSxrcPzg4GB9//DEmTZoElUp109eVSCTw9fWt87ib4xJRy8soKMWucwWQSICnYoPFjmN2WOxawdP9gwEAv5zKQ56mQtwwRBamqqoKSUlJiI+Pr7M9Pj4eBw8evKvXLi0tRVBQENq2bYtHHnkEycnJd31cnU4HrVZb50FEzefG/LAPdG6DYC8nccOYIRa7VtAtQIW+IR6oNgr4JvGS2HGILEphYSEMBgN8fHzqbPfx8YFa3fSbksLCwrBy5Ur89NNPWLNmDZRKJfr374/09PS7Ou6CBQugUqlqH4GBgU3OSER1aSr0+D7pMgDgmXs4xUlDWOxayY2pT9YcyUZFlUHkNESWRyKpe9ebIAj1tt2Jfv36YcKECYiMjERcXBzWr1+PTp064X//+99dHXfOnDnQaDS1j5ycnCZnJKK6vj+Wg/IqAzr7uCA21FPsOGaJxa6VDOrig7buDrhersfmlFyx4xBZDC8vL8hksnqjZPn5+fVG0+6GVCpFnz59akfsmnpchUIBV1fXOg8iunsG4x9TnDzVP/iufrCzZix2rUQmldRe5PnVgUwIgiBuICILYW9vj6ioKCQkJNTZnpCQgNjY2GY7jiAISElJgZ+fX6sel4ga59e0q7h8vQJujnYY3iNA7DhmSy52AFsyqncgPko4j/NXS3HgQhHu6egldiQiizBz5kxMnDgRvXv3RkxMDL744gtkZ2dj2rRpAEynP3Nzc7Fq1ara56SkpAAw3SBRUFCAlJQU2Nvbo0uXLgCAt956C/369UPHjh2h1WrxySefICUlBZ999lmjj0tErefGFCfj+raDg71M5DTmi8WuFakc7DAqqi2+TryErw5kstgRNdKYMWNQVFSE+fPnIy8vD926dcO2bdsQFGSaADwvL6/e3HI9e/as/XVSUhJWr16NoKAgZGVlAQCKi4vx3HPPQa1WQ6VSoWfPnti7dy/69u3b6OMSUetIy9PiUMY1yKSS2on/qWESgecEW1VGQSke+HAPAGDXrPsQwlu1iayaVquFSqWCRqPh9XZETfTvH05g/bHLeLi7Hz4b30vsOGaN19i1svbezrWLFa88wGXGiIiIbqWoVIfNKVcAAM/UzAtLN8diJ4IbExZ/n3QZmnK9uGGIiIjM2Joj2aiqNqJ7WxV6tXMXO47ZY7ETwT0dvBDm64LyKgNWH+Gak0RERA3RVRuwqmZi/6c5xUmjsNiJQCKRYErNjNkrD2aiqtoociIiIiLz81PKFeSX6ODrqsTDEf5ix7EILHYiebSHP9q4KHBVq8OWk1fEjkNERGRWBEHAsn0ZAEyjdfZyVpbG4P8lkSjkMkyumbB42T5OWExERPRne84X4PzVUjgr5BgX3U7sOBaDxU5ET0a3g4OdDGl5Why8WCR2HCIiIrNxY7RubJ9AuCrtRE5jOVjsROTmaI/RvdsC+OMPMBERka07navBgQtFkEkleLrmmnRqHBY7kT1zTwgkEmD3uQKkXy0ROw4REZHovqwZ7Hikux8C3BxETmNZWOxEFuTphMFdfAEAX+7jhMVERGTbrhRX4OeTeQCAZ+Pai5zG8rDYmYFn7zUNM29KzkVBiU7kNEREROL56kAmDEYBsaGe6BagEjuOxWGxMwNRQR7o2c4NVQYjvknMEjsOERGRKLSVeqw5kgMAePZejtY1BYudmbgx3PzNoUuoqDKInIaIiKj1rT2SjVJdNTq2ccZ9nbzFjmORWOzMxOCuvgj0cMD1cj02HL8sdhwiIqJWVVVtxIr9WQBMgx1cPqxpWOzMhEwqwTP9TdfardifCaORExYTEZHt2HrqCtTaSng5K/BYTy4f1lQsdmZkdO9AuCrlyCgsw29n88WOQ0RE1CoEQcAXe00zQzzdPxgKuUzkRJaLxc6MOCnkGB8dBAD4Yu9FkdMQERG1jgMXipCWp4WDnQxPcvmwu8JiZ2ae7h8MO5kER7OuI+nSdbHjEBERtbgvaiYkHtMnEG6O9iKnsWwsdmbGx1WJx3sGAAA+38NROyIism5peVrsPV8AqQS115pT07HYmaHn7g2FRAIkpF3FhfxSseMQERG1mBurLg3t5od2no4ip7F8LHZmqEMbZwwK94Eg8Fo7IiKyXmpNJX46kQsAmBrH0brmwGJnpp4fEArAtMzYVW2lyGmIiIia38qDWdAbBPQN9kDPdu5ix7EKLHZmKirIHX2DPaA3CFixP1PsOERERM2qVFeN1YcvAeDyYc2Jxc6MTbvP9Af9u8PZ0FToRU5DRETUfNYdzYG2shrtvZzwYFgbseNYDRY7M3Zfpzbo5OOMUl01vqv5qYaIiMjSVVUb8WXNFCdT49pDKuXyYc2Fxc6MSaUSPH+v6Vq7rw5koVJvEDkRERHR3ducnIs8TSXauCgwIipA7DhWhcXOzD3awx/+KiUKSnTYlJwrdhwiIqK7YjAKWFozT+vUuBAuH9bMWOzMnJ1MimfuMd0C/sXeDBiMgsiJiIiImm7HGTUyCsugcrCrXUaTmg+LnQUY17cdVA52yCwsQ0KqWuw4RERETSIIAhbvvgAAmBwTBGeFXORE1ofFzgI4KeSYFGP6qWbJngwIAkftiIjI8uy/UIjTuVoo7aR4isuHtQgWOwsxOTYYCrkUJ3KKcSjjmthxiIiI7tjiXaZr68b2aQcPJ3uR01gnFjsL4eWswKjebQGg9qJTIiIiS5GcfR2JGUWQSyWckLgFsdhZkOfiQiGVAHvOF+B0rkbsOERERI22eLdpUGJ4zwAEuDmInMZ6sdhZkHaejnikuz8AYMlujtoREZFlOH+1BAmpVyGRANNq1kKnlsFiZ2H+fn8HAMC203m4kF8qchoiIqLbW1ozGDG4iy86tHEWOY11Y7GzMJ19XTCoiw8EgaN2RERk/nKulePHE1cAAC/cx9G6lsZiZ4FujNptTslFzrVykdMQERHd3Jf7TJPr9+/gichAN7HjWD0WOwvUI9AN93TwgsEo4Iu9GWLHISIialBhqQ5rj+YAAP52XweR09gGFjsLdWPUbt2xHORrK0VOQ0REVN9XBzKhqzYisq0KsaGeYsexCSx2Fqpfew9EBbmjqtqIL/dnih2HiIiojpJKPVYlXgIAvHBfB0gkEpET2QYWOwslkUjw9/tNF6F+e+gSisurRE5ERET0h28PZaOkshqh3k6I7+IjdhybwWJnwe7v3AZd/FxRXmXAVweyxI5D1KIWL16MkJAQKJVKREVFYd++fTfdNy8vD+PHj0fnzp0hlUoxffr0evssW7YMcXFxcHd3h7u7OwYOHIgjR47U2WfevHmQSCR1Hr6+vs391oisTkWVActrziZNGxAKqZSjda2Fxc6CmUbtTNfarTyYhVJdtciJiFrGunXrMH36dMydOxfJycmIi4vD0KFDkZ2d3eD+Op0O3t7emDt3LiIjIxvcZ/fu3Rg3bhx27dqFxMREtGvXDvHx8cjNza2zX9euXZGXl1f7OHXqVLO/PyJrs+ZINgpLdQhwc8DwngFix7EpLHYWbkg3X7T3doKmQo9vD10SOw5Ri/joo48wZcoUTJ06FeHh4Vi0aBECAwOxZMmSBvcPDg7Gxx9/jEmTJkGlUjW4z3fffYe//e1v6NGjB8LCwrBs2TIYjUb89ttvdfaTy+Xw9fWtfXh7ezf7+yOyJpV6Q+2a5n+/vwPsZKwarYn/ty2cTCrBCzXLs3y5LxOVeoPIiYiaV1VVFZKSkhAfH19ne3x8PA4ePNhsxykvL4der4eHh0ed7enp6fD390dISAjGjh2LjIxbTzGk0+mg1WrrPIhsyfpjOcgv0cFfpcSIKI7WtTYWOytwY0HlwlId1h/LETsOUbMqLCyEwWCAj0/di699fHygVqub7TizZ89GQEAABg4cWLstOjoaq1atwo4dO7Bs2TKo1WrExsaiqKjopq+zYMECqFSq2kdgYGCzZSQyd7pqQ+2qSC/cFwqFXCZyItvDYmcF7GRSTBvQHgDw+Z4MVFUbRU5E1Pz+OlWCIAjNNn3C+++/jzVr1mDjxo1QKpW124cOHYoRI0YgIiICAwcOxNatWwEAX3/99U1fa86cOdBoNLWPnBz+sEW2Y0NSLvI0lWjjosCo3vyhRgwsdlZiVO9AeLsokFtcgY3HL4sdh6jZeHl5QSaT1Rudy8/PrzeK1xQLFy7EO++8g507d6J79+633NfJyQkRERFIT0+/6T4KhQKurq51HkS2QG8w4rNdFwCY7oRV2nG0TgwsdlZCaSfD8/eaRu0+3XUBegNH7cg62NvbIyoqCgkJCXW2JyQkIDY29q5e+4MPPsB//vMfbN++Hb17977t/jqdDmlpafDz87ur4xJZo03Hc5FbXAEvZwXG9W0ndhybxWJnRZ6MDoKXswKXr1dg0/Hc2z+ByELMnDkTX375JVasWIG0tDTMmDED2dnZmDZtGgDT6c9JkybVeU5KSgpSUlJQWlqKgoICpKSkIDU1tfbr77//Pl577TWsWLECwcHBUKvVUKvVKC0trd1n1qxZ2LNnDzIzM3H48GGMHDkSWq0WkydPbp03TmQhqg1GfFozWvf8ve3hYM/ROrHIxQ5AzcfB3jRq93/b0vDprgt4vFcAbzMnqzBmzBgUFRVh/vz5yMvLQ7du3bBt2zYEBQUBME1I/Nc57Xr27Fn766SkJKxevRpBQUHIysoCYJrwuKqqCiNHjqzzvDfffBPz5s0DAFy+fBnjxo1DYWEhvL290a9fPxw6dKj2uERk8mPKFWRfK4eHkz2e7MfROjFJBEEQxA5Bzae8qhpx7+1CUVkVPhjZnRevEolMq9VCpVJBo9HwejuySgajgEEf7UFGYRleGRKGF+4LFTuSTeNwjpVxtJfj+QF/XGtXzWvtiIioBW05eQUZhWVwc7TDxBiOZouNxc4KTegXBE8ne1wqKsfmlCtixyGq4/r161i1apXYMYioGRiNAv73u+nauqn3hMBZwSu8xMZiZ4Uc7eV49sYdsr+nc9SOzEp2djaefvppsWMQUTP45bQaF/JL4aqUY1JssNhxCCx2VmtivyB4ONkjq6gcP53gqB0RETUv02idaU7HZ+4JgavSTuREBLDYWS0nhRxT40IAAJ/+fgEGI++RISKi5rMz9SrOqkvgrJDj6dgQseNQDRY7KzYpJhhujnbIKCzDzxy1IyKiZiIIf4zWPRUbDJUjR+vMRaOuchQEASUlJS2dhVrAhF7e+OS3C/hoWwoGhDhDJm2etTWJbmbp0qW3/PqVK1cgCAK0Wm0rJRLXjfdpK++XbMPuc/k4lamGg70Uo7p78s93K3FxcbntGtmNmsfuxjxMRERERCSOxsyH2ahixxG7lqfVahEYGIicnJxmn8T08z0X8b/fLyDEyxGb/34PR+3MQEt+3mRecnNz0aVLF6SmpiIgIEDsONSCbOXv9W9pV/Hy2hQ42Eux/eV74emsEDtSqxPrs27MiF2jTsVKJBKr/kNqTlxdXZv9//W0Qd3w7fECXCrRY9+lMjwa6d+sr09N1xKft9h+//13vPjiizh06FC996bRaBAbG4ulS5ciLi5OpISt68YpKhcXF6v7rKlh1vj3+gajUcDniSmQKhwx9f5QhPh7ix1JVOb4WfPmCRvgorTDlHtMdyx98ls675ClFrVo0SI8++yzDX6zU6lUeP755/HRRx+JkIyI7tbWU3k4qy6Bi1KO5+K4dJg5YrGzEU/1D4bKwQ4X8kvx04lcseOQFTtx4gSGDBly06/Hx8cjKSmpFRMRUXOoNhjx34TzAIDn4trzTlgzxWJnJhQKBd58800oFC1zrYKr0q52Ddn/JqRDz9UoRNXSn7eYrl69Cju7m3/Dl8vlKCgoaMVE4rrxGVvjZ011WfPfawDYlJyLjMIyuDva4el7bHveOnP+rBt18wRZh/Kqatz7/i4UllZhwRMRGNe3ndiRyAqFhoZi4cKFePzxxxv8+saNGzFr1ixkZGS0cjJx3JhVoDF3sxGZq6pqIx74cDcuX6/Aqw+F4bl7eRrWXHHEzoY42svxt/s6ADBda1epN4iciKzRQw89hDfeeAOVlZX1vlZRUYE333wTjzzyiAjJiKip1h/LweXrFfB2UWBiv2Cx49AtcMTOxlTqDbh/4W7kaSrxxiNd8IyND6dT87t69Sp69eoFmUyGF198EZ07d4ZEIkFaWho+++wzGAwGHD9+HD4+PmJHbRUcsSNLV6k3YMAHu3BVq8Nbj3bF5NhgsSPRLTRquhOyHko7GV56sCPmbDyFxbsvYGzfQDja848BNR8fHx8cPHgQL7zwAubMmYMbPztKJBIMHjwYixcvtplSR2QNvjucjataHfxVSoztGyh2HLoN/otug0ZGtcXSPRdxqagcKw9m1Z6eJWouQUFB2LZtG65fv44LFy5AEAR07NgR7u7uYkcjojtQpqvGkt0XAAAvPdgRCrlM5ER0O7zGzgbZyaSYPrAjAODzPRnQVOhFTkTWyt3dHX369EHfvn1Z6ogs0NeJWSgsrUKQpyNGRLUVOw41AoudiK5fv46JEydCpVJBpVJh4sSJKC4ubvTzn3/+eUgkEixatOiOj/1oZAA6tnGGpkKP5fsz7/j5dGfu9LPW6/V45ZVXEBERAScnJ/j7+2PSpEm4cuVK64WmRlu8eDFCQkKgVCoRFRWFffv23XL/PXv2ICoqCkqlEu3bt8fSpUtbKSndrTv5rDdu3IhBgwbB29sbrq6uiImJwY4dO1ox7d3RVOjx+R7T3evTB3aEncy2KsOd/r2+4cCBA5DL5ejRo0fLBrwJ2/qUzMz48eORkpKC7du3Y/v27UhJScHEiRMb9dzNmzfj8OHD8Pdv2vJgMqkEMwd1AgAs35eBa2VVTXodapw7/azLy8tx/PhxvP766zh+/Dg2btyI8+fP49FHH23F1NQY69atw/Tp0zF37lwkJycjLi4OQ4cORXZ2doP7Z2Zm4qGHHkJcXBySk5Px6quv4qWXXsKGDRtaOTndqTv9rPfu3YtBgwZh27ZtSEpKwv33349hw4YhOTm5lZM3zfL9mdBU6NGhjTMejbStdY7v9LO+QaPRYNKkSXjwwQdbKWkDBBJFamqqAEA4dOhQ7bbExEQBgHD27NlbPvfy5ctCQECAcPr0aSEoKEj473//26QMRqNReOjjvULQK1uE/9ua2qTXoNu7m8/6z44cOSIAEC5dutQSMamJ+vbtK0ybNq3OtrCwMGH27NmCIAiCRqMRAAgajUYQBEH497//LYSFhdXZ//nnnxf69evXOoGpyW73WTdGly5dhLfeequ5ozW7olKd0PWN7ULQK1uErSeviB2n1TX1sx4zZozw2muvCW+++aYQGRnZgglvjiN2IklMTIRKpUJ0dHTttn79+kGlUuHgwYM3fZ7RaMTEiRPxr3/9C127dr2rDBKJBLPiOwMAvj6YhXxt/XnH6O419bP+K41GA4lEAjc3txZISU1RVVWFpKQkxMfH19keHx9/0882MTGx3v6DBw/GsWPHoNfzeldz1ZTP+q+MRiNKSkrg4eHREhGb1ed7L6JUV40ufq4Y0tVX7Ditqqmf9VdffYWLFy/izTffbOmIt8RiJxK1Wo02bdrU296mTRuo1eqbPu+9996DXC7HSy+91Cw57uvsjaggd+iqjfh014VmeU2qq6mf9Z9VVlZi9uzZGD9+POdCMyOFhYUwGAz1pm/x8fG56WerVqsb3L+6uhqFhYUtlpXuTlM+67/68MMPUVZWhtGjR7dExGaTX1KJrw9mAQBmDe4EqVQibqBW1pTPOj09HbNnz8Z3330HuVzcCUdY7JrZvHnzIJFIbvk4duwYANOI2V8JgtDgdgBISkrCxx9/jJUrV950nzv151G7NUeykXOtvFle1xa05Gf9Z3q9HmPHjoXRaMTixYub/X3Q3fvr53i7z7ah/RvaTubnTj/rG9asWYN58+Zh3bp1Df6gZ04W77qISr0RPdu54f7O5p21JTX2szYYDBg/fjzeeustdOrUqbXi3RTnsWtmL774IsaOHXvLfYKDg3Hy5ElcvXq13tcKCgpuOnnrvn37kJ+fj3bt/ljj1WAw4J///CcWLVqErKysJmWOCfVE/w6eOHChCP/7PR3vj4xs0uvYmpb8rG/Q6/UYPXo0MjMz8fvvv3O0zsx4eXlBJpPV+yk+Pz//pp+tr69vg/vL5XJ4enq2WFa6O035rG9Yt24dpkyZgu+//x4DBw5syZh37UpxBVYfNt0gMCu+s03+sHGnn3VJSQmOHTuG5ORkvPjiiwBMp90FQYBcLsfOnTvxwAMPtEp2gMWu2Xl5ecHLy+u2+8XExECj0eDIkSPo27cvAODw4cPQaDSIjY1t8DkTJ06s901h8ODBmDhxIp5++um7yj0rvjMOXDiIDcdzMW1AKNp7O9/V69mClvysgT9KXXp6Onbt2sV/9M2Qvb09oqKikJCQgMcff7x2e0JCAh577LEGnxMTE4Off/65zradO3eid+/esLOza9G81HRN+awB00jdM888gzVr1uDhhx9ujah35X+/X0CVwYh+7T0QG2qb33Pu9LN2dXXFqVOn6mxbvHgxfv/9d/zwww8ICWnlpTtFuWWDBEEQhCFDhgjdu3cXEhMThcTERCEiIkJ45JFH6uzTuXNnYePGjTd9jbu5K/avpqw8IgS9skV4cfXxZnk9+sOdftZ6vV549NFHhbZt2wopKSlCXl5e7UOn04nxFugm1q5dK9jZ2QnLly8XUlNThenTpwtOTk5CVlaWIAiCMGPGjDp3xWZkZAiOjo7CjBkzhNTUVGH58uWCnZ2d8MMPP4j5NqgRbvdZz549W5g4cWLt/qtXrxbkcrnw2Wef1fk7XFxcLNZbuKWswlIhdM5WIeiVLcKRzCKx44jqTj/rvxLzrlgWOxEVFRUJTz75pODi4iK4uLgITz75pHD9+vU6+wAQvvrqq5u+RnMWu9O5xULQK1uEoFe2CKdzzfMbj6W60886MzNTANDgY9euXa2en27ts88+E4KCggR7e3uhV69ewp49e2q/Nm7cuDrFThAEYffu3ULPnj0Fe3t7ITg4WFiyZIkYsakJbvVZT548WRgwYEDt7wcMGNDg3+HJkye3fvBG+Mfq40LQK1uEicsPix3FLNzJZ/1XYhY7iSDUXLVLBOAfa5Lx84kriOvohW+mRN/+CUR0S1qtFiqVChqNhtdIktk6dVmDYZ/uBwBs+cc96BagEjkRNRXviqU6/hXfGXYyCfalF2J/OqdeICKydoIg4N3taQCA4T38WeosHIsd1dHO0xFPRgcBABb8kgajkQO6RETWbG96IQ5cKIK9TIp/1kx/RZaLxY7q+ccDHeCskOPMFS1+PslF54mIrJXRKODdX84CACb0C0Kgh6PIiehusdhRPZ7OCkwb0B4A8MGOc9BVG0RORERELeHHE7lIy9PCRSHHiw90EDsONQMWO2rQM/eEoI2LApevV+DbQ9lixyEiomZWqTdg4Y7zAIBp94XCw8le5ETUHFjsqEGO9nLMGGRaGuXT39OhreTi5ERE1uTbQ5eQW1wBX1clnunfypPoUothsaObGhXVFqHeTrhersfS3RfFjkNERM1EU6HHp7suAABmDOoIB3uZyImoubDY0U3JZVK8MiQMALDiQCbUmkqRExHVlZWVBYlEgpSUlEY/Z+XKlXBzc2uxTESWYMnuiygu16NjG2eM6NVW7DjUjFjs6JYGdfFB7yB3VOqN+G/CebHjEBHRXbpSXIGvDmQCAF4ZEga5jFXAmvDTpFuSSCSY85Bp1O77pBykXy0ROREREd2N/yach67aiD7B7ngwvI3YcaiZsdjRbUUFeWBwVx8YBeC97WfFjkM2Zvv27bjnnnvg5uYGT09PPPLII7h4seFrPnfv3g2JRIKtW7ciMjISSqUS0dHROHXqVL19d+zYgfDwcDg7O2PIkCHIy8ur/drRo0cxaNAgeHl5QaVSYcCAATh+/HiLvUei1nJOXYINxy8DAGYPDYdEIhE5ETU3FjtqlH8PCYNMKsGvafk4knlN7DhkQ8rKyjBz5kxMnz4dSqUSv/zyC7p164Y9e/bc9DnTp0+Hp6cnfH19ceTIEfTv3x96/R93dpeXl2PhwoV4+umn0aZNG+zcuRNhYWHYtGkTAKCkpASTJ0/Gvn378PLLL+P48eOIiopCz549sW/fvhZ/z0Qt5f3tZ2EUgCFdfREV5C52HGoBLHbUKKHezhjTJxCAaakxQeBSY9Q6RowYAb1ej3feeQdvvfUW9u7di8rKSgwdOhS5ubkNPuell15CREQE5s+fj4iICJSXl9eWNgDQ6/V47rnn8Oqrr+LZZ5/Fa6+9BqPRiNGjR+Pw4cN44IEHMGHCBJw8eRLvvvsuPvzwQzg6OqJdu3YYOnQosrM5tyNZnsMZRfjtbD5kUgn+NYRLh1krFjtqtOkPdoSDnQzJ2cXYflotdhyyERcvXsTf//53KJVKzJw5E4MHDwYAeHp64rvvvmvwOY899hg+/vhjTJo0CR4eHnB3d0daWlrt1x0dHfHDDz9g0KBBmDNnDnr27ImysjI8+OCDWLRoEfLz8zFt2jRMnjwZADBz5kxUVFRg8ODBCAwMxJIlS26aV6fTQavV1nkQiU0QBCyoWTpsbJ9AhHo7i5yIWgqLHTVaG1clno0zTWL53vazqKo2ipyIbMEjjzyCa9eu4Z///CcOHz6Mw4cPAwAiIyORlJTU6Nf587VEdnZ2SExMRHx8fO3XBEHA4MGDcfDgQTz11FM4evQo9Ho9PvjgA6SkpMDT0xNVVVWIj4/HwYMHb3qcBQsWQKVS1T4CAwOb+M6Jms9PJ64gJacYjvYyvDywo9hxqAWx2NEdeW5AKLycFcgqKseqxCyx45CVKyoqwtmzZyEIAgYNGoTw8HBcv34dAODm5oaCgoIGn3fo0KHaX1dXV6O4uBhhYWF19lGr1fDx8amzzcfHB2q1Gvv27cPkyZNhNBrRp08fKBQKFBYW1tnnZubMmQONRlP7yMnJadJ7J2oulXoD3qsZrZs2IBRtXJQiJ6KWxGJHd8RZIce/B5uuzfj4t3QUlepETkTWzN3dHe7upgu8c3Nz8fvvv2PmzJkATKeWbnZH3/z58/Hbb7/h9OnTOHv2LBwcHDB8+PB6+/31+Tdes0OHDvjhhx8AAKmpqXjyySfh4OBw2+MCgEKhgKura50HkZi+3JeBK5pK+KmUeDauvdhxqIWx2NEdGxHVFl39XVFSWY3//spJi6nlSKXS2uvoxo8fjxkzZuCDDz4AAGg0Gnh5eTX4vHfffRcvv/wyoqKiUFVVhWHDhsHevu4C576+vvVG3vLz8+Hj44MVK1agrKwMAPDGG2/gpZdeQps2bersQ2QJ8rWVWFyzJOQrQ8K4dJgNYLGjOyaTSvD6I10AAKsPZ+OsmheHU8sZOnQo+vbti2effRYnTpzAgAEDIAgCMjIy8MADD0AQBPTo0aPOc+655x6cPn0aOp0OvXr1gre3d+3XnnrqKRQXFyMmJgYJCQkAgOHDh0MQBOzcuROxsbHo2bMnkpKS0LdvXwwfPhwjR45EVlYWpk+fjoSEBMTGxrbm/wKiJlu48xzKqwyIDHTDo5H+YsehViAXOwBZpn7tPTG0my9+Oa3Gf7ak4tsp0ZzoklrMzJkzMXHiRPTu3RsxMTH44osvkJ2djWnTpgEwXdeWm5uLZ555pvY5N9aPLS0tRUFBAVJSUmBvb48uXUw/lLz88su499578d577+Gxxx7Djz/+iF9//RX79+9v9HGJzNmZKxp8n2SajPiNR8IhlfJ7tC1gsaMmmzM0HL+l5ePAhSL8lpaPgV14eopaxpgxY1BUVIT58+cjLy8P3bp1w7Zt2xAUFAQAyMvLqze3XM+ePWt/nZSUhNWrVyMoKAhZWVkAgNjYWKxduxavvfYaXn/9dYSGhmLdunWIjo5u9HGJzJUgCHh7SxoEAXikux+igjzEjkStRCJwplm6C+/+chZL91xEiJcTdky/F/Zynt0n+jOtVguVSgWNRsMbKajV7DyjxnPfJMFeLsXv/xyAtu6OYkeiVsJ/hemu/P3+UHg52yOzsIzTnxARmYGqaiPe2WaakHvqPSEsdTaGxY7uiovSDrPi/5j+5FpZlciJiIhs26rELGQVlcPLWYG/3d9B7DjUyljs6K6N6h2IcL+a6U8SOP0JEZFYrpdV4ZPf0gEAs+I7wVnBS+ltDYsd3TXT9CfhAIDvDl/COXWJyImIiGzTol/PQ1tZjXA/V4zqzeXsbBGLHTWL2FAvDO7qA6MAvL01Fbwnh4iodV3IL8G3h013h7/+cDhknN7EJrHYUbN59aFw2Mkk2JdeiF3n8sWOQ0RkMwRBwLyfUmEwChgY7oPYDg2vykLWj8WOmk2QpxOe6R8CAHh7Sxr0BqPIiYiIbMP202rsv1AIe7kUb9SsDES2icWOmtXfH+gATyd7ZBSW4ZvES2LHISKyehVVBry91TS9ybR726OdJ6c3sWUsdtSsXJV2+GfN9CeLfj3P6U+IiFrYkt0XkFtcgQA3B7xwH6c3sXUsdtTsxvQJRJivC7SV1fhgx1mx4xARWa3sonIs3ZsBAHjt4XA42MtETkRiY7GjZieTSjD/sW4AgLVHc5CcfV3kRERE1mn+llRUVRvRv4MnhnTzFTsOmQEWO2oRfUM88ESvAAgC8MaPZ2AwcvoTIqLmtOtcPn5Nuwq5VIJ5w7pCIuH0JsRiRy1oztBwuCjkOJWrwZoj2WLHISKyGrpqA+b/nAoAeCo2GB19XEROROaCxY5ajLeLAv+M7wQA+GDHORSV6kRORERkHVbsz0JmYRm8nBV4eWBHseOQGWGxoxY1oV8Qwv1coanQ4/3t58SOQ0Rk8dSaSvzvd9N6sHOGhsFFaSdyIjInLHbUouQyKf7zWFcAwLpjOTjOGymIiO7KO9vSUF5lQK92bni8Z4DYccjMsNhRi+sd7IGRUW0BAK9vPs0bKYiImuhwRhF+OnEFEgkw/7FukHI9WPoLFjtqFbOHhsFFKceZK1qsPswVKYiI7lS1wYg3fzoDABjXtx26BahETkTmiMWOWoWXswL/GmxakeKDHedQyBspiIjuyLeHLuGsugRujnb4V80KP0R/xWJHrebJ6CB09XeFtrIa7/3CFSmIiBpLranEwp3nAQCz4jvD3cle5ERkrljsqNX8eUWK75MuI+nSNZETERFZhrd+PoNSXTV6BLphfN92YschM8ZiR60qKsgdo3vfuJHiDKoNRpETERGZt9/SruKX02rIpBIseCKCN0zQLbHYUat7ZUgYXJVypOZp8d1hrkhBRHQz5VXVeONH0w0TU+8JQbifq8iJyNyx2FGr83RW4F9DwgAAC3eeQ0EJb6QgImrIol/TkVtcgQA3B64wQY3CYkeiGN+3HSICVCiprMZ/tqSKHYeIyOykXtFi+f5MAMB/hneFo71c5ERkCVjsSBQyqQT/93g3SCXATyeuYNe5fLEjERGZDYNRwKubTsFgFPBQhC8eCPMROxJZCBY7Ek33tm54un8IAOC1TadRpqsWORERkXlYfSQbKTnFcFbI8eawrmLHIQvCYkeimjmoEwLcHJBbXIGPEs6LHYeISHT52kq8XzPX578Gd4aPq1LkRGRJWOxIVE4KOd5+3DS33VcHMnHycrG4gYiIRPbWllSU6KoR2VaFCf2CxI5DFobFjkR3f+c2eDTSH0YBmL3hFPSc246IbNSuc/nYejIPMqkE7zwRARnnrKM7xGJHZuGNYV3g5miH1Lw/7gIjIrIlFVUGvL75NADg6dhgdPVXiZyILBGLHZkFL2cF5j4UDgBY9Ot5XCoqEzkREVHr+uT3dFy+XgF/lRIzBnUSOw5ZKBY7Mhsjo9oiNtQTlXoj5m46DUEQxI5ERNQqzqq1WLY3AwAw/7FucFJwzjpqGhY7MhsSiQTvPB4BhVyK/RcKsfF4rtiRiIhanMEo4NWNp1BtFDC4qw8GduGcddR0LHZkVoK9nGqXzXl7ayqKSrncGBFZt5UHs3A82zRn3bxHOWcd3R0WOzI7z8a1R5ivC66X6/H21jSx4xARtZiswjJ8sMM0Z92rD4XDT+UgciKydCx2ZHbsZFK8O6I7JBJgU3Iu9pwvEDsSEVGzMxoF/HvDSVTqjYgN9cS4voFiRyIrwGJHZqlHoBueig0GAMzddArlVVxujIisy3eHL+FI5jU42svw3ojukEg4Zx3dPRY7Mlv/jO+MADcHXL5egfdqltchIrIGOdfKsaDm+9orQ8IQ6OEociKyFix2ZLacFXIseCICAPB14iUcvFAociIiorsnCALmbDyF8ioD+gZ7YCKXDaNmxGJHZu3eTt4YH90OAPCvH06ipFIvciISy+LFixESEgKlUomoqCjs27fvlvvv2bMHUVFRUCqVaN++PZYuXVrn6/fddx8kEkm9x8MPP1y7z7x58+p93dfXt0XeH9mOtUdzsP9CIRRyKd4b2R1SLhtGzYjFjszeqw+Fo627A3KLK/DONt4la4vWrVuH6dOnY+7cuUhOTkZcXByGDh2K7OzsBvfPzMzEQw89hLi4OCQnJ+PVV1/FSy+9hA0bNtTus3HjRuTl5dU+Tp8+DZlMhlGjRtV5ra5du9bZ79SpUy36Xsm6XSmuwP/V3O3/r8GdEeLlJHIisjYsdmT2nBVyfDAyEgCw5kgOdp/LFzkRtbaPPvoIU6ZMwdSpUxEeHo5FixYhMDAQS5YsaXD/pUuXol27dli0aBHCw8MxdepUPPPMM1i4cGHtPh4eHvD19a19JCQkwNHRsV6xk8vldfbz9vZu0fdK1ksQBLy66RRKddXo2c4NT/cPETsSWSEWO7IIMaGetXfJzt5wCpoKnpK1FVVVVUhKSkJ8fHyd7fHx8Th48GCDz0lMTKy3/+DBg3Hs2DHo9Q3/2Vm+fDnGjh0LJ6e6Iyjp6enw9/dHSEgIxo4di4yMjFvm1el00Gq1dR5EALDheC52nyuAvVyKD0Z2h4ynYKkFsNiRxXhlSBhCvJyg1lbirZ/PiB2HWklhYSEMBgN8fOous+Tj4wO1Wt3gc9RqdYP7V1dXo7Cw/k04R44cwenTpzF16tQ626Ojo7Fq1Srs2LEDy5Ytg1qtRmxsLIqKim6ad8GCBVCpVLWPwEDOTUbAVW0l5td835o+sCM6tHERORFZKxY7shgO9jIsHNUdUgmw8XguElKvih2JWtFf5/gSBOGW8341tH9D2wHTaF23bt3Qt2/fOtuHDh2KESNGICIiAgMHDsTWrVsBAF9//fVNjztnzhxoNJraR05Ozq3fGFk9QRAwd9NpaCur0b2tCs/FtRc7ElkxFjuyKFFBHni25pvinI2ncL2sSuRE1NK8vLwgk8nqjc7l5+fXG5W7wdfXt8H95XI5PD0962wvLy/H2rVr643WNcTJyQkRERFIT0+/6T4KhQKurq51HmTbNhzPxa9pV2Enk+D9kd0hl/GfXmo5/NNFFmfGoE7o2MYZhaU6vP7jabHjUAuzt7dHVFQUEhIS6mxPSEhAbGxsg8+JiYmpt//OnTvRu3dv2NnZ1dm+fv166HQ6TJgw4bZZdDod0tLS4Ofnd4fvgmxVzrVyzPvpxinYTgjzZdGnlsViRxZHaSfDh6MjIZNKsOVkHraezBM7ErWwmTNn4ssvv8SKFSuQlpaGGTNmIDs7G9OmTQNgOv05adKk2v2nTZuGS5cuYebMmUhLS8OKFSuwfPlyzJo1q95rL1++HMOHD683kgcAs2bNwp49e5CZmYnDhw9j5MiR0Gq1mDx5csu9WbIaBqOAf64/gVJdNaKC3DFtQKjYkcgGyMUOQNQU3du64W/3heJ/v1/Aa5tPoW+IB7xdFGLHohYyZswYFBUVYf78+cjLy0O3bt2wbds2BAWZZuzPy8urM6ddSEgItm3bhhkzZuCzzz6Dv78/PvnkE4wYMaLO654/fx779+/Hzp07Gzzu5cuXMW7cOBQWFsLb2xv9+vXDoUOHao9LdCvL9mXgSNY1ONnL8N/RPXgXLLUKiXDjimIiC1NVbcRjnx1AWp4W8V188PnEKC6iTWZHq9VCpVJBo9HwejsbknpFi8c+2w+9QcD7I7pjdB/eHU2tg6diyWLZy6X4cFQk7GQS7Ey9is0puWJHIiJCpd6AGetSoDcIGNTFB6N6txU7EtkQFjuyaF38XfHSAx0BAG/+eAZqTaXIiYjI1i3ccQ7nrpbAy9keC56I4JkEalUsdmTxXrgvFN3bqqCtrMas70/AaOTVBUQkjoMXCvHl/kwAwHsjusPLmdf+UutisSOLJ5dJ8dHoHnCwk2H/hUJ8se/WSz4REbUETYUes74/AQAY17cdHgxveJ5FopbEYkdWoUMbZ7w5rAsA02mQlJxicQMRkc2Z99MZXNFUItjTEa89HC52HLJRLHZkNcb0CcTDEX6oNgp4eW0ySiobXuydiKi5bTl5BZuScyGVAB+N6QEnBWcTI3Gw2JHVkEgkeOeJCAS4OeBSUTne+PGM2JGIyAaoNZWYu8m0Cs6L93dAr3buIiciW8ZiR1ZF5WCHj8f2gFQCbErOxcbjl8WORERWzGAUMHN9CjQVenRvq8I/HuwodiSycSx2ZHV6B3vg5Qc7AQBe33waWYVlIiciImv12a4LOHixCI72Mvx3TA/YyfjPKomLfwLJKr34QAf0DfFAWZUBL69NRlW1UexIRGRlDmcUYdGv5wEAbw/vhlBvZ5ETEbHYkZWSSSVYNKYHVA52OHFZg48SzosdiYisyLWyKry0NhlGARjRqy2e6MXVJcg8sNiR1fJ3c8B7IyIAAEv3XMT+9EKRExGRNTAaBcz6/gSuanUI9XbC/Me6ih2JqBaLHVm1Id38MD66HQBgxvoUFJXqRE5ERJZu+f5M/H42H/ZyKT4d34tTm5BZYbEjq/f6w13QsY0zCkp0+NcPJyEIXHKMiJomJacY720/CwB445EuCPdzFTkRUV0sdmT1HOxl+N/4nrCXS/H72XysPJgldiQiskCaCj1eXH0c1UYBD0f44cmaswFE5oTFjmxCmK9r7RI/C7adxZkrGpETEZElEQQBczaexOXrFQj0cMCCERGQSCRixyKqh8WObMbEfkEYGO6DKoMRL3x7HJpyLjlGRI3z7eFsbDulhp1Mgk/H9YKr0k7sSEQNYrEjmyGRSLBwVHe0dXdA9rVyzFyfAqOR19sR0a2lXtHiP1tSAQCvDAlDZKCbuIGIboHFjmyKm6M9lk6Igr1cit/O5uOzXRfEjkREZqxMV40XVx9HVbURD4a1wZR7QsSORHRLLHZkc7oFqPD28G4AgI9+PY895wtETkRE5kgQBPz7h5PIKCyDr6sSH4yK5HV1ZPZY7Mgmje4diPHR7SAIwMtrk5FzrVzsSERkZpbty8DWU3mwk0nw2ZM94eFkL3YkottisSOb9eawLohsq0JxuR4vfJeESr1B7EhEZCYOXijEu7/8MV9dVJCHyImIGofFjmyWQi7D4glR8HCyx+lcLV7ffJqTFxMRrhRX4MU1f6wDO6FfkNiRiBqNxY5sWoCbA/43riekEuD7pMtYezRH7EhEJKJKvQEvfJuEa2VV6Orviv97vBuvqyOLwmJHNq9/By/MGtwZAPDmj2dwIqdY3EBEJJp5P53BicsauDnaYemEKCjtZGJHIrojLHZEAF4YEIr4LjcmLzb9tE5EtmXNkWysPZoDiQT4ZGxPBHo4ih2J6I6x2BGhZvLi0ZEI8XLCFU0lXlqTDAMnLyayGSk5xXjzxzMAgFnxnXFvJ2+RExE1DYsdUQ1XpenUi4OdDPsvFOKjhHNiRyKiVlBYqsML3yahymDE4K4++Nt9oWJHImoyFjuiP+ns64J3R0QAAD7bdRE7z6hFTkRELanaYMSLq48jT1OJ9t5OWMhJiMnCsdgR/cVjPQLwdP9gAMA/15/A+asl4gYiohbz9tY0HMq4Bid7Gb6YGAUXpZ3YkYjuCosdUQNefSgcfYM9UKKrxtNfHUVBiU7sSETUzFYlZmHlwSwAwIejI9GhjYu4gYiaAYsdUQPsZFIsnRiFYE9H5BZX4NlVx7gyBZEV2X0uH/N+Mt0s8e8hnTGkm5/IiYiaB4sd0U14ONljxVN94OZoh5ScYsxcnwIj75Qlsnjn1CV4cfUfK0u8MIA3S5D1YLEjuoX23s74fEIU7GQSbDulxvs7eKcskSUrLNVhytdHUaqrRt8QDyx4IoI3S5BVYbEjuo3o9p54b0R3AMDSPRex9ki2yImIqCkq9QY8t+oYLl+vQLCnIz6fEAV7Of8ZJOvCP9FEjfBEr7Z46cGOAIC5m09jf3qhyImI6E4IgoB//3ASx7OL4aqUY/lTfeDuZC92LKJmx2JH1EgzBnbEYz38YTAKeOG7JKRzGhQii7Ho13T8dOIK5FIJlk6MQqi3s9iRiFoEix1RI0kkErw3ojv6BLujpLIaT6/kNChEluDHlFx8/Fs6AODt4d0QG+olciKilsNiR3QHlHYyfD6xN4I8HXH5OqdBITJ3SZeu4V8/nAQAPHdve4zt207kREQti8WO6A55ONnjq6f6QOXAaVCIzFnOtXI8tyoJVdVGDOrig1eGhIkdiajFsdgRNUF7b2d8MfGPaVA+2MlpUIjMiaZcj2dWHkVRWRW6+rvi47E9IJNyWhOyfix2RE0U3d4T7z5hmgZlyW5Og9LSFi9ejJCQECiVSkRFRWHfvn233H/Pnj2IioqCUqlE+/btsXTp0jpfX7lyJSQSSb1HZWXlXR2XxFdRZcCUr48iPb8UPq4KLJ/cB472crFjEbUKFjuiuzAi6o9pUF7bfBoHLnAalJawbt06TJ8+HXPnzkVycjLi4uIwdOhQZGc3XKYzMzPx0EMPIS4uDsnJyXj11Vfx0ksvYcOGDXX2c3V1RV5eXp2HUqls8nFJfHqDES+uPo5jl67DRSnHyqf7wlelvP0TiayERBAEXhxEdBcEQcD0dSn4MeUKXJRy/DAtFp19uZh4c4qOjkavXr2wZMmS2m3h4eEYPnw4FixYUG//V155BT/99BPS0tJqt02bNg0nTpxAYmIiANOI3fTp01FcXNxsx22IVquFSqWCRqOBq6tro55DTWM0Cpj1wwlsPJ4LhVyKb6dGo0+wh9ixiFoVR+yI7tJfp0GZsPwwsgrLxI5lNaqqqpCUlIT4+Pg62+Pj43Hw4MEGn5OYmFhv/8GDB+PYsWPQ6/W120pLSxEUFIS2bdvikUceQXJy8l0dFwB0Oh20Wm2dB7U8QRDwzrY0bDyeC5lUgsVP9mKpI5vEYkfUDJR2Miyb1Bthvi4oKNHhyS8P40pxhdixrEJhYSEMBgN8fHzqbPfx8YFarW7wOWq1usH9q6urUVhoOl0eFhaGlStX4qeffsKaNWugVCrRv39/pKenN/m4ALBgwQKoVKraR2Bg4B2/Z7pzS/dk4Mv9mQCA90d0x4PhPrd5BpF1YrEjaiZujvb4Zko0QryckFtcgQlfHkZhKScwbi5/XahdEIRbLt7e0P5/3t6vXz9MmDABkZGRiIuLw/r169GpUyf873//u6vjzpkzBxqNpvaRk5Nz+zdHd2Xd0Wy8t/0sAOC1h8MxIqqtyImIxMNiR9SMvF0U+HZqNPxVSmQUlmHi8iPQlOtv/0S6KS8vL8hksnqjZPn5+fVG027w9fVtcH+5XA5PT88GnyOVStGnT5/aEbumHBcAFAoFXF1d6zyo5ew4o8acjacAANMGhGJqXHuRExGJi8WOqJkFuDngu2f7wctZgbQ8LZ5eeQRlumqxY1kse3t7REVFISEhoc72hIQExMbGNvicmJiYevvv3LkTvXv3hp2dXYPPEQQBKSkp8PPza/JxqXUlXizCP9YkwygAo3u3xStDOosdiUh0LHZELSDEywnfTOkLlYMdjmcX47lvuPTY3Zg5cya+/PJLrFixAmlpaZgxYways7Mxbdo0AKbTn5MmTardf9q0abh06RJmzpyJtLQ0rFixAsuXL8esWbNq93nrrbewY8cOZGRkICUlBVOmTEFKSkrtazbmuCSe07kaPLvqGKqqjYjv4oN3Ho+45SlyIlvBGRuJWki4nytWPt0HE748jAMXivDi6mQsmdALdjL+PHWnxowZg6KiIsyfPx95eXno1q0btm3bhqCgIABAXl5enbnlQkJCsG3bNsyYMQOfffYZ/P398cknn2DEiBG1+xQXF+O5556DWq2GSqVCz549sXfvXvTt27fRxyVxnFOXYNKKIyjVVSM6xAOfjOsJOf9eEQHgPHZELS7xYhGe+uoIdNVGPNbDHx+N5tJGtoTz2DWv81dLMO6LQygqq0JEgArfPRsNV2XDp9eJbBF/xCFqYTGhnlgyoRfkUgl+TLmC1zafBn+eIrpz6VdLMH6ZqdR1C3DFt1NY6oj+isWOqBU8EOaDRWN7QCoB1hzJxjvb0ljuiO7AhfxSjFt2GIWlVejiZyp1KkeWOqK/YrEjaiWPdPfHu090BwAs25eJd7efZbkjaoSLBaUYt+wQCkt1CPdzxXdTo+HmaC92LCKzxGJH1IpG9wnEvGFdAACf78nAWz+nwmhkuSO6mYyCUoz74hAKSnQI83XBd1Oj4e7EUkd0Myx2RK3sqf4hNVMzACsPZuHVTadgYLkjqiezsAzjlh1CfokOnX1Mpc6DpY7olljsiEQwProdFo6MhFQCrD2ag1nfn0C1wSh2LCKzkVVYhnFfHMJVrQ6dfJzx3bPR8HRWiB2LyOyx2BGJZERUW/xvnOlu2U3JufjHmmRUVbPcEaVfLcGYLxKh1laiYxtnrK5ZyYWIbo/FjkhED3f3w5IJUbCXSfHLaTVe+DaJK1SQTTuRU4xRnyfiqlbHUkfUBCx2RCIb1MUHX07uDaWdFL+dzcfUr4+hvIpry5LtOXixEOOXHUJxuR6RgW5Y/3wMvF1Y6ojuBIsdkRm4t5M3Vj7dF472Muy/UIinVhxFqY7ljmzHzjNqPPXVUZRVGRAb6sm7X4maiMWOyEz0a++Jb6ZEw0Uhx5Gsa5jw5WFoyvVixyJqcRuPX8YL3x1HVbUR8V18sOKpPnBWcClzoqZgsSMyI1FB7lj9bD+4OdohJacYY5cdglpTKXYsohaz8kAmZq4/AYNRwBO9ArD4yV5Q2snEjkVksVjsiMxMRFsV1j5numA8LU+LxxcfQFqeVuxYRM1KEAR8/Gs65v2cCgB4KjYYC0dGQi7jP0tEd4N/g4jMUJivKzb9LRYd2jgjT1OJUUsTsfd8gdixiJpFtcGIN348g//+eh4AMGNgJ7w5rAukUonIyYgsH4sdkZkK9HDEhmmx6NfeA6W6ajy98ijWHskWOxbRXSmp1GPqqmP45tAlSCTAm8O64OWBHSGRsNQRNQcWOyIzpnK0w6pnovFEzwAYjAJmbzyFD3ac5fqyZJGuFFdg1NJE7D5XAKWdFEuejMLT/UPEjkVkVVjsiMycvVyKD0dH4uUHOwIAPtt1EdPXpUBXzYmMyXKcuqzB8M8O4Ky6BF7OCqx7LgZDuvmKHYvI6rDYEVkAiUSCGYM6YeGoSMilEvx04gomfnkE18uqxI5GdFsJqVcx+vNE5Jfo0NnHBZv/HovIQDexYxFZJRY7IgsyMqotvn6mL1yUprnunlhyEJeKysSORdQgQRCwYn8mnvvmGCr0BsR19ML3L8Sgrbuj2NGIrBaLHZGF6d/BCxteiEWAmwMyC8vw+OKDSLp0TexYRHVUVZvufJ2/JRWCAIyPbocVT/WBq9JO7GhEVk0iCAKvwiayQPkllZiy8hhO5WpgJ5PgtYe7YFJMEO8uNDNarRYqlQoajQaurq5ix2kV+dpK/O274zh26TokEmDO0DA8G9eefzaJWgGLHZEFK6+qxr++P4mtp/IAAI/18MeCJyLgaM/lmMyFrRW7o1nX8LfvjqOgRAcXhRwfjemBQV18xI5FZDNY7IgsnCAIWHEgCwu2paHaKKCTjzOWTohCe29nsaMRbKfYCYKAlQez8H9bTX8OO/u4YOnEKIR4OYkdjcimsNgRWYmjWdfw9++OI79EB2eFHB+M7I6hEX5ix7J5tlDsyquqMWfjKfyYcgUAMCzSH++N4MgxkRhY7IisSH5JJf6xOhmHM003UzwbF4JXhoRx/U0RWXuxyyosw7Rvk3BWXQKZVIK5D4Xj6f7BvJ6OSCQsdkRWptpgxPs7zuGLvRkAgL4hHvh0fE+0cVGKnMw2WXOx235ajX/9cAIlldXwclZg8ZO90DfEQ+xYRDaNxY7ISm0/nYdZ359Eqa4a3i4KfDK2J2JCPcWOZXOssdiVV1XjP1tSseZIDgAgKsgdi5/sBR9X/vBAJDYWOyIrllFQihe+PY5zV0sAAE/3D8a/B4fBwV4mcjLbYW3F7nSuBi+tTUZGQRkkEuC5e9vjn4M6w17O0/1E5oDFjsjKlVdVY/7PqVh71DS6EuLlhIWjIhEV5C5yMttgLcXOaBSwbF8GFu48B71BgI+rAv8d3QOxHbzEjkZEf8JiR2Qjdp3Lx+wNJ3FVq4NUAjx7b3vMGNgJSjuO3rUkayh2ak0l/vl9Cg5cKAIADO7qg3ef6A53J3uRkxHRX7HYEdkQTbkeb205g43HcwEAHds448PRkeje1k3cYFbMkoudIAjYeDwX87ekQlOhh4OdDG8O64IxfQJ51yuRmWKxI7JBO8+o8eqm0ygs1UEmleBv94XiHw905HVSLcBSi11ucQVe3XgKe84XAAAiAlRYNLYHQjnxNZFZY7EjslHXyqrwxo+nseWkaTmycD9XfDgqEl38Lad8WAJLK3ZGo4BvD1/Ce7+cRVmVAfZyKaYP7Ihn49rDjvMhEpk9FjsiG7f1ZB5e23wK18v1sJNJ8NIDHfHCfaGc1LiZWFKxu1hQitkbTuJo1nUAQJ9gd7w7ojtH6YgsCIsdEaGgRIe5m05hZ+pVAEC3AFfMG9YVvYM52ezdsoRiV6k34Mt9Gfjk9wuoqjbC0V6G2UPDMCE6CFIpr6UjsiQsdkQEwHSh/OaUXLz54xloK6sBAI9098PsoWFo6+4ocjrLZc7FThAE/HJajXe2peHy9QoAwL2dvPHO4934mRNZKBY7IqqjoESHjxLOYe3RHAgCoJBL8dy97TFtQCicFFzU/U6Za7E7c0WDt35OxZGadYV9XZWY81AYHo305x2vRBaMxY6IGnTmigb/2ZKKQxmmf/jbuCjw7yFheKJnAE/P3QFzK3YFJTp8uPMc1h37o7g/PyAU0wa0h6M9izuRpWOxI6KbEgQBO1Ov4p1tabhUVA7ANO3FG8O6oA+vv2sUcyl2VdVGrDyYiU9+u4BSnelU+7BIf8weGoYANwfRchFR82KxI6Lb0lUbsPJAFv73+x+l4OHufpg9JAyBHrwW61bELnYGo4AtJ6/gvwnnkfWncv7msC68OYbICrHYEVGjma6/O491R7NhFAA7mQQjerXFtAGhCPZyEjueWRKr2FUbjPgx5Qo+23UBGYVlAABvFwX+PbgzRvRqy9PpRFaKE1URUaN5uyiw4IkIbPlHHO7p4AW9QcDaozl44MPdeHltMs5fLWmxYy9evBghISFQKpWIiorCvn37brn/nj17EBUVBaVSifbt22Pp0qV1vr5s2TLExcXB3d0d7u7uGDhwII4cOVJnn3nz5kEikdR5+Pr6Nvt7a056gxHrj+XgwY/24J/fn0BGYRncHO0wK74Tds26D6N6B7LUEVkxXilLRHesi78rvp0ajaRL1/Dp7xew61wBfky5gh9TrmBwVx+8eH9HRLRVNdvx1q1bh+nTp2Px4sXo378/Pv/8cwwdOhSpqalo165dvf0zMzPx0EMP4dlnn8W3336LAwcO4G9/+xu8vb0xYsQIAMDu3bsxbtw4xMbGQqlU4v3330d8fDzOnDmDgICA2tfq2rUrfv3119rfy2SyZntfzamq2ogNxy/js10Xaqcu8XCyx7Nx7TExJgjOvKOZyCbwVCwR3bXTuRp8tusCtp9R48Z3lHs7eePF+zugT7D7XU+fER0djV69emHJkiW128LDwzF8+HAsWLCg3v6vvPIKfvrpJ6SlpdVumzZtGk6cOIHExMQGj2EwGODu7o5PP/0UkyZNAmAasdu8eTNSUlIanVWn00Gn09X+XqvVIjAwsMVOxV4rq8L3x3Lw9cEsXNFUAgC8nO3x/L2heLJfO97pSmRj+DeeiO5atwAVlkyIQvrVEizefRE/nbiCvecLsPd8AcJ8XTCmTyAe7xkAN0f7O37tqqoqJCUlYfbs2XW2x8fH4+DBgw0+JzExEfHx8XW2DR48GMuXL4der4ednV2955SXl0Ov18PDo+4NBenp6fD394dCoUB0dDTeeecdtG/f/qZ5FyxYgLfeequxb69JBEHA8ezr+PZQNraeykNVtRGAaUqaaQNCMa5vOzjYm+fIIhG1LBY7Imo2HX1c8N8xPTBjYCcs2XMRG49fxll1Cd76ORULfjmLh7r5YkyfdujX3qPRo3iFhYUwGAzw8fGps93HxwdqtbrB56jV6gb3r66uRmFhIfz8/Oo9Z/bs2QgICMDAgQNrt0VHR2PVqlXo1KkTrl69irfffhuxsbE4c+YMPD09Gzz2nDlzMHPmzNrf3xixaw6lumpsTs7Ft4cu4az6j+sZIwJUmNCvHR7rEQClHQsdkS1jsSOiZtfO0xELnojA7CFh+PFELtYcyUFanhabU65gc8oVhHg5YUyfQIzo1RbeLopGveZfi6AgCLcshw3t39B2AHj//fexZs0a7N69G0qlsnb70KFDa38dERGBmJgYhIaG4uuvv65T3v5MoVBAoWjce2qstDwtvjt8CZuO56KsymA6jlyKRyP9MaFfECID3Zr1eERkuVjsiKjFqBztMCkmGBP7BeHkZQ3WHs3GTylXkFlYhnd/OYuFO85hYLgPRkS1RVxHrwZHm7y8vCCTyeqNzuXn59cblbvB19e3wf3lcnm9kbaFCxfinXfewa+//oru3bvf8v04OTkhIiIC6enpjXn7TSYIAs6qS/DLqTxsO63GhfzS2q+193bCk9FBGNmrLVSO9U8pE5FtY7EjohYnkUgQGeiGyEA3vPZwF2w5eQVrjuQgJacY28+osf2MGg52MsR19MKgLj54MNwHHk6m6/Hs7e0RFRWFhIQEPP7447WvmZCQgMcee6zB48XExODnn3+us23nzp3o3bt3nevrPvjgA7z99tvYsWMHevfufdv3odPpkJaWhri4uKb8b7glQRBw5ooW207l4ZfTamTWzD0HAPYyKQZ2aYMJ0UGICfXkWq5EdFO8K5aIRHNWrcX6o5ex/XRe7R2dACCVAL2DPDCoiw8GdfHB4d+2YOLEiVi6dCliYmLwxRdfYNmyZThz5gyCgoIwZ84c5ObmYtWqVQBM051069YNzz//PJ599lkkJiZi2rRpWLNmTe10J++//z5ef/11rF69Gv379689trOzM5ydnQEAs2bNwrBhw9CuXTvk5+fj7bffxp49e3Dq1CkEBQU16j3eaoLiMl01jl26jv3pBdh+Ro2caxW1X7OXS3FfJ288FOGHB8LbwFXJ0Tkiuj0WOyIS3Y3RqoTUq0hIvYrUPG2drwe4OcC1qhBpe39GQdphdPZ1xaL/foR7770XAPDUU08hKysLu3fvrn3Onj17MGPGDJw5cwb+/v545ZVXMG3atNqvBwcH49KlS/WyvPnmm5g3bx4AYOzYsdi7dy8KCwvh7e2Nfv364T//+Q+6dOnS6Pf252Jn7+CEpEvXkXixCIkZRTiRU4xq4x/fgh3sZLg/zBtDu/nh/rA2nHuOiO4Yix0RmZ3L18vxa+pVJKRdxeGMa3XKDwC4KOToFeSO3kHuiAp2R2cfF3g42ZvVKcryqmqcU5fg+IUrmPpgNzz20U6kFlajymCss1+AmwNiQj3xYFgbDOjszXnniOiusNgRkVkr1VUjJbsYxy5dw7Gs60jOvl57Z+ifuSrlCPFyqnk4I8TbCe29nBDs5dRiI18Go4CiMh3ytTrkXCvHWXUJzqq1OKcuwaVr5RAEwKgrR86i0Qicvh5ShSP8VErEtPdEv1BPxLT3RKCHY4tkIyLbxGJHRBal2mDEWXUJjmVdw9FL15GSXYzc4opbPsfbRYE2Lgq4KOVwVtjBVSk3/Voph4vSDs4K0+8Vcil01UboDQL0BiOqqo3QG4zQVRuh0xtQUGoqcfklOlzVVqKorAoG482/hXq7KNBeJcX6fzyIVbtTEde1HYI8Hc1qZJGIrAuLHRFZvEq9AZeKypFZWIqMwjJkFpQhs9D0KCqratFjSyWAp7MC/iolOvu6oLOvK8J9XdDZ1wWezopb3jxBRNTceDEHEVk8pZ2splS51PuaplyPrKIyXCuvQkllNUoq9SitrEZJZTVKddXQVupNv640Xf9mL5PCXi6FnUwKhVwKO5nE9Gs7KbycFWjjooSP6x//9XCyh1wmFeFdExHVx2JHRFZN5WiHSEc3sWMQEbUK/phJREREZCVY7IiIiIisBIsdERERkZVgsSMiIiKyEix2RERERFaCxY6IiIjISrDYEREREVkJFjsiIiIiK8FiR0RERGQlWOyIiIiIrASLHREREZGVYLEjIiIishIsdkRERERWgsWOiIiIyEqw2BERERFZCRY7IiIiIivBYkdERERkJVjsiIiIiKwEix0RERGRlZAIgiCIHYKIyFoJgoCSkhK4uLhAIpGIHYeIrByLHREREZGV4KlYIiIiIivBYkdERERkJVjsiIiIiKwEix0RERGRlWCxIyIiIrISLHZEREREVoLFjoiIiMhK/D+0vckMToeLmAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7fa1fd505b20>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha_var = sympy.symbols('alpha')\n",
    "sympy.plot(C_L.subs({C_L0: 0.1, C_La: 3, alpha: alpha_var}),\n",
    "           (alpha_var, -0.5, 0.4),\n",
    "           xlabel='alpha',\n",
    "           ylabel='CL')\n",
    "sympy.plot(C_D.subs({C_D0: 0.02, k_CLCD: 0.1, C_L0: 0.1, C_La: 3, alpha: alpha_var}),\n",
    "           (alpha_var, -0.5, 0.4),\n",
    "           xlabel='alpha',\n",
    "           ylabel='CL')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "888a4b63-b45f-4781-9973-7c7116c62838",
   "metadata": {},
   "source": [
    "# Dynamics"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33e1bc90-00e1-4670-8f18-7ddab2834873",
   "metadata": {},
   "source": [
    "Sum of forces."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "25d871a2-38c1-4aa5-995a-c5207e716c0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle (- \\frac{S \\rho \\left(C_{D0} + k_{CLCD} \\left(C_{L0} + C_{La} \\alpha{\\left(t \\right)}\\right)^{2}\\right) V^{2}{\\left(t \\right)} \\cos{\\left(\\alpha{\\left(t \\right)} \\right)}}{2} - \\frac{S \\rho \\left(C_{L0} + C_{La} \\alpha{\\left(t \\right)}\\right) V^{2}{\\left(t \\right)} \\sin{\\left(\\alpha{\\left(t \\right)} \\right)}}{2} + g m \\sin{\\left(\\alpha{\\left(t \\right)} - \\gamma{\\left(t \\right)} \\right)} + th)\\mathbf{\\hat{b}_x} + (\\frac{S \\rho \\left(C_{D0} + k_{CLCD} \\left(C_{L0} + C_{La} \\alpha{\\left(t \\right)}\\right)^{2}\\right) V^{2}{\\left(t \\right)} \\sin{\\left(\\alpha{\\left(t \\right)} \\right)}}{2} - \\frac{S \\rho \\left(C_{L0} + C_{La} \\alpha{\\left(t \\right)}\\right) V^{2}{\\left(t \\right)} \\cos{\\left(\\alpha{\\left(t \\right)} \\right)}}{2} + g m \\cos{\\left(\\alpha{\\left(t \\right)} - \\gamma{\\left(t \\right)} \\right)})\\mathbf{\\hat{b}_z}$"
      ],
      "text/plain": [
       "(-S*rho*(C_D0 + k_CLCD*(C_L0 + C_La*alpha(t))**2)*V(t)**2*cos(alpha(t))/2 - S*rho*(C_L0 + C_La*alpha(t))*V(t)**2*sin(alpha(t))/2 + g*m*sin(alpha(t) - gamma(t)) + th)*b.x + (S*rho*(C_D0 + k_CLCD*(C_L0 + C_La*alpha(t))**2)*V(t)**2*sin(alpha(t))/2 - S*rho*(C_L0 + C_La*alpha(t))*V(t)**2*cos(alpha(t))/2 + g*m*cos(alpha(t) - gamma(t)))*b.z"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F_b = (-L*frame_w.z - D*frame_w.x + W*frame_e.z + T*frame_b.x).express(frame_b).simplify()\n",
    "F_b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b2625e0d-cb29-43e2-8a59-7728c550f6e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle (- \\frac{S \\rho \\left(C_{D0} + k_{CLCD} \\left(C_{L0} + C_{La} \\alpha{\\left(t \\right)}\\right)^{2}\\right) V^{2}{\\left(t \\right)}}{2} - g m \\sin{\\left(\\gamma{\\left(t \\right)} \\right)} + th \\cos{\\left(\\alpha{\\left(t \\right)} \\right)})\\mathbf{\\hat{w}_x} + (- \\frac{S \\rho \\left(C_{L0} + C_{La} \\alpha{\\left(t \\right)}\\right) V^{2}{\\left(t \\right)}}{2} + g m \\cos{\\left(\\gamma{\\left(t \\right)} \\right)} + th \\sin{\\left(\\alpha{\\left(t \\right)} \\right)})\\mathbf{\\hat{w}_z}$"
      ],
      "text/plain": [
       "(-S*rho*(C_D0 + k_CLCD*(C_L0 + C_La*alpha(t))**2)*V(t)**2/2 - g*m*sin(gamma(t)) + th*cos(alpha(t)))*w.x + (-S*rho*(C_L0 + C_La*alpha(t))*V(t)**2/2 + g*m*cos(gamma(t)) + th*sin(alpha(t)))*w.z"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F_w = (-L*frame_w.z - D*frame_w.x + W*frame_e.z + T*frame_b.x).express(frame_w).simplify()\n",
    "F_w"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "725cbd0e-e3ec-46c7-9094-aa6962236073",
   "metadata": {},
   "source": [
    "Find linear momentum take derivative in earth frame (Newton-Euler EOMs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e70db739-f6ae-42b9-985f-23bbc1afc2f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{S \\rho \\left(C_{D0} + k_{CLCD} \\left(C_{L0} + C_{La} \\alpha{\\left(t \\right)}\\right)^{2}\\right) V^{2}{\\left(t \\right)}}{2} + g m \\sin{\\left(\\gamma{\\left(t \\right)} \\right)} + m \\frac{d}{d t} V{\\left(t \\right)} - th \\cos{\\left(\\alpha{\\left(t \\right)} \\right)}\\\\0\\\\\\frac{S \\rho \\left(C_{L0} + C_{La} \\alpha{\\left(t \\right)}\\right) V^{2}{\\left(t \\right)}}{2} - g m \\cos{\\left(\\gamma{\\left(t \\right)} \\right)} - m V{\\left(t \\right)} \\frac{d}{d t} \\gamma{\\left(t \\right)} - th \\sin{\\left(\\alpha{\\left(t \\right)} \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[S*rho*(C_D0 + k_CLCD*(C_L0 + C_La*alpha(t))**2)*V(t)**2/2 + g*m*sin(gamma(t)) + m*Derivative(V(t), t) - th*cos(alpha(t))],\n",
       "[                                                                                                                       0],\n",
       "[          S*rho*(C_L0 + C_La*alpha(t))*V(t)**2/2 - g*m*cos(gamma(t)) - m*V(t)*Derivative(gamma(t), t) - th*sin(alpha(t))]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LM = m*V*frame_w.x\n",
    "eom_trans = LM.diff(t, frame_e).simplify() - F_w\n",
    "eom_trans = eom_trans.to_matrix(frame_w)\n",
    "eom_trans"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb081483-cfff-41bc-8349-02a9851fec23",
   "metadata": {},
   "source": [
    "Sum of moments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c3907c6e-6021-4057-9cc2-2503aaab009b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{S \\rho \\left(C_{M0} + C_{MQ} Q{\\left(t \\right)} + C_{Ma} \\alpha{\\left(t \\right)} + C_{Me} elv\\right) V^{2}{\\left(t \\right)}}{2}\\mathbf{\\hat{w}_y}$"
      ],
      "text/plain": [
       "S*rho*(C_M0 + C_MQ*Q(t) + C_Ma*alpha(t) + C_Me*elv)*V(t)**2/2*w.y"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M_b = (M*frame_b.y).express(frame_w).simplify()\n",
    "M_b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "544e4c5d-1df4-42b2-ae06-dadbf3c8fb5d",
   "metadata": {},
   "source": [
    "Finding angular momentum, take derivative in earth frame (Newton-Euler EOms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "088609bd-d673-431c-82d2-f7154fa8e074",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle J_{y} Q{\\left(t \\right)}\\mathbf{\\hat{w}_y}$"
      ],
      "text/plain": [
       "J_y*Q(t)*w.y"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AM = J_y*frame_b.ang_vel_in(frame_e).express(frame_w).subs(gamma.diff(t) - alpha.diff(t), Q)\n",
    "AM"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "263f69f0-b885-45eb-a395-223152131198",
   "metadata": {},
   "source": [
    "# Equations of Motion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "aa8f5ecd-c61f-4d5a-8c61-03d81f644187",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\J_{y} \\frac{d}{d t} Q{\\left(t \\right)} - \\frac{S \\rho \\left(C_{M0} + C_{MQ} Q{\\left(t \\right)} + C_{Ma} \\alpha{\\left(t \\right)} + C_{Me} elv\\right) V^{2}{\\left(t \\right)}}{2}\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[                                                                                      0],\n",
       "[J_y*Derivative(Q(t), t) - S*rho*(C_M0 + C_MQ*Q(t) + C_Ma*alpha(t) + C_Me*elv)*V(t)**2/2],\n",
       "[                                                                                      0]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eom_rot = (AM.diff(t, frame_e) - M_b).to_matrix(frame_b)\n",
    "eom_rot"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a95c9ab2-6506-4c93-8a75-ea54073c2ffa",
   "metadata": {},
   "source": [
    "Create first order ODE model.\n",
    "\n",
    "$\\dot{x} = f(x, u, p)$\n",
    "\n",
    "x: states\n",
    "u: inputs\n",
    "p: parameters\n",
    "\n",
    "$\\gamma = \\theta - \\alpha$\n",
    "\n",
    "$\\dot{\\gamma} = \\dot{\\theta} - \\dot{\\alpha}$\n",
    "\n",
    "$\\dot{\\theta} \\equiv Q$\n",
    "\n",
    "$Q = \\dot{\\gamma} + \\dot{\\alpha}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "82def154-8d12-4bb1-8a22-087f9144373a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}J_{y} \\frac{d}{d t} Q{\\left(t \\right)} - \\frac{S \\rho \\left(C_{M0} + C_{MQ} Q{\\left(t \\right)} + C_{Ma} \\alpha{\\left(t \\right)} + C_{Me} elv\\right) V^{2}{\\left(t \\right)}}{2}\\\\\\frac{S \\rho \\left(C_{D0} + k_{CLCD} \\left(C_{L0} + C_{La} \\alpha{\\left(t \\right)}\\right)^{2}\\right) V^{2}{\\left(t \\right)}}{2} + g m \\sin{\\left(\\gamma{\\left(t \\right)} \\right)} + m \\frac{d}{d t} V{\\left(t \\right)} - th \\cos{\\left(\\alpha{\\left(t \\right)} \\right)}\\\\\\frac{S \\rho \\left(C_{L0} + C_{La} \\alpha{\\left(t \\right)}\\right) V^{2}{\\left(t \\right)}}{2} - g m \\cos{\\left(\\gamma{\\left(t \\right)} \\right)} - m V{\\left(t \\right)} \\frac{d}{d t} \\gamma{\\left(t \\right)} - th \\sin{\\left(\\alpha{\\left(t \\right)} \\right)}\\\\- Q{\\left(t \\right)} + \\frac{d}{d t} \\alpha{\\left(t \\right)} + \\frac{d}{d t} \\gamma{\\left(t \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[                                 J_y*Derivative(Q(t), t) - S*rho*(C_M0 + C_MQ*Q(t) + C_Ma*alpha(t) + C_Me*elv)*V(t)**2/2],\n",
       "[S*rho*(C_D0 + k_CLCD*(C_L0 + C_La*alpha(t))**2)*V(t)**2/2 + g*m*sin(gamma(t)) + m*Derivative(V(t), t) - th*cos(alpha(t))],\n",
       "[          S*rho*(C_L0 + C_La*alpha(t))*V(t)**2/2 - g*m*cos(gamma(t)) - m*V(t)*Derivative(gamma(t), t) - th*sin(alpha(t))],\n",
       "[                                                               -Q(t) + Derivative(alpha(t), t) + Derivative(gamma(t), t)]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eoms = sympy.Matrix.vstack(eom_trans, eom_rot)\n",
    "eoms = sympy.Matrix([\n",
    "    eom_rot[1],\n",
    "    eom_trans[0],\n",
    "    eom_trans[2],\n",
    "    gamma.diff(t) + alpha.diff(t) - Q\n",
    "])\n",
    "eoms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "0f436326-a2d7-4624-b27a-f82a30d24e1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}V{\\left(t \\right)} & \\alpha{\\left(t \\right)} & \\gamma{\\left(t \\right)} & Q{\\left(t \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([[V(t), alpha(t), gamma(t), Q(t)]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sympy.Matrix([V, alpha, gamma, Q])\n",
    "x.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "5d85713c-70a0-47d6-bfed-1235f05deda6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}th & elv\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([[th, elv]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = sympy.Matrix([th, elv])\n",
    "u.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4ee9bad1-7123-497b-a08c-2d6047a83271",
   "metadata": {},
   "outputs": [],
   "source": [
    "h_dot = V*sympy.sin(gamma)\n",
    "y = sympy.Matrix([V, alpha, gamma, Q, h_dot])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "365ee7d4-aa4c-4ca2-be3f-4facf5b6c8a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{d}{d t} V{\\left(t \\right)} & \\frac{d}{d t} \\alpha{\\left(t \\right)} & \\frac{d}{d t} \\gamma{\\left(t \\right)} & \\frac{d}{d t} Q{\\left(t \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([[Derivative(V(t), t), Derivative(alpha(t), t), Derivative(gamma(t), t), Derivative(Q(t), t)]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dx = x.diff(t)\n",
    "dx.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "868d5b45-b45f-4dfd-9708-c299aa6a795c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{- \\frac{C_{D0} S \\rho V^{2}{\\left(t \\right)}}{2} - \\frac{C_{L0}^{2} S k_{CLCD} \\rho V^{2}{\\left(t \\right)}}{2} - C_{L0} C_{La} S k_{CLCD} \\rho V^{2}{\\left(t \\right)} \\alpha{\\left(t \\right)} - \\frac{C_{La}^{2} S k_{CLCD} \\rho V^{2}{\\left(t \\right)} \\alpha^{2}{\\left(t \\right)}}{2} - g m \\sin{\\left(\\gamma{\\left(t \\right)} \\right)} + th \\cos{\\left(\\alpha{\\left(t \\right)} \\right)}}{m}\\\\\\frac{- \\frac{S \\rho \\left(C_{L0} + C_{La} \\alpha{\\left(t \\right)}\\right) V^{2}{\\left(t \\right)}}{2} + g m \\cos{\\left(\\gamma{\\left(t \\right)} \\right)} + m Q{\\left(t \\right)} V{\\left(t \\right)} + th \\sin{\\left(\\alpha{\\left(t \\right)} \\right)}}{m V{\\left(t \\right)}}\\\\\\frac{\\frac{S \\rho \\left(C_{L0} + C_{La} \\alpha{\\left(t \\right)}\\right) V^{2}{\\left(t \\right)}}{2} - g m \\cos{\\left(\\gamma{\\left(t \\right)} \\right)} - th \\sin{\\left(\\alpha{\\left(t \\right)} \\right)}}{m V{\\left(t \\right)}}\\\\\\frac{S \\rho \\left(C_{M0} + C_{MQ} Q{\\left(t \\right)} + C_{Ma} \\alpha{\\left(t \\right)} + C_{Me} elv\\right) V^{2}{\\left(t \\right)}}{2 J_{y}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[(-C_D0*S*rho*V(t)**2/2 - C_L0**2*S*k_CLCD*rho*V(t)**2/2 - C_L0*C_La*S*k_CLCD*rho*V(t)**2*alpha(t) - C_La**2*S*k_CLCD*rho*V(t)**2*alpha(t)**2/2 - g*m*sin(gamma(t)) + th*cos(alpha(t)))/m],\n",
       "[                                                                                 (-S*rho*(C_L0 + C_La*alpha(t))*V(t)**2/2 + g*m*cos(gamma(t)) + m*Q(t)*V(t) + th*sin(alpha(t)))/(m*V(t))],\n",
       "[                                                                                                (S*rho*(C_L0 + C_La*alpha(t))*V(t)**2/2 - g*m*cos(gamma(t)) - th*sin(alpha(t)))/(m*V(t))],\n",
       "[                                                                                                                     S*rho*(C_M0 + C_MQ*Q(t) + C_Ma*alpha(t) + C_Me*elv)*V(t)**2/(2*J_y)]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol = sympy.solve(eoms, dx)\n",
    "f = sympy.Matrix([sol[dxi] for dxi in dx])\n",
    "f.simplify()\n",
    "f"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4993029b-027f-4628-959e-cd42c8dc9d66",
   "metadata": {},
   "source": [
    "### Solve Initial Value Problem to Simulate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "51bb8440-2e71-43a7-8276-b0801962b535",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{array}{ccccccccccccc}m & J_{y} & g & C_{La} & C_{L0} & k_{CLCD} & C_{D0} & C_{M0} & C_{Me} & C_{MQ} & C_{Ma} & \\rho & S\\end{array}\\right]$"
      ],
      "text/plain": [
       "Matrix([[m, J_y, g, C_La, C_L0, k_CLCD, C_D0, C_M0, C_Me, C_MQ, C_Ma, rho, S]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params = {\n",
    "    m: 1,\n",
    "    J_y: 1,\n",
    "    g: 9.8,\n",
    "    C_La: 3,\n",
    "    C_L0: 0.1,\n",
    "    k_CLCD: 0.1,\n",
    "    C_D0: 0.03,\n",
    "    C_M0: 0.01,\n",
    "    C_Me: 0.1,\n",
    "    C_MQ: -0.1,\n",
    "    C_Ma: -0.1, # negative to be stable\n",
    "    rho: 1.225,\n",
    "    S: 1,\n",
    "}\n",
    "p = sympy.Matrix(list(params.keys()))\n",
    "p.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "7224795e-3255-4280-a80e-76660b49468c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 1, 9.8, 3, 0.1, 0.1, 0.03, 0.01, 0.1, -0.1, -0.1, 1.225, 1]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p0 = [params[k] for k in params.keys()]\n",
    "p0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "5631f4e6-2c80-4b1c-b623-4a2c9411e934",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.9810125, 10.738750000000001, -9.738750000000001, -0.05512500000000001]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_eval = sympy.lambdify([[V, alpha, gamma, Q], [th, elv], p], f[:])\n",
    "f_eval([1, 0, 0, 1], [1, 0], p0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3318457d-a46f-4230-8a95-47315aa92fbb",
   "metadata": {},
   "source": [
    "Make sure your numerical evaluation function is fast."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96cabde4-1520-4349-8d27-c42d3faafa91",
   "metadata": {},
   "source": [
    "This function takes 3 arguments, x (states), u (input), p (parameters)\n",
    "\n",
    "$\\dot{x} = f(x, u, p)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "a5dc5eb6-79d6-4e79-89f4-090ba22f351e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.4 µs ± 679 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit -n 10000\n",
    "f_eval([10, 0, 0, 0], [1, 0], p0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "0c9ab1cf-5b4c-43cd-8a84-56a655339dfe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YWOGVu3uIXc5N3d/XH4/GBQMAFn53BGeLKsUtiIjIjDDckOQVVdbgve1ZAIAXxkfAy9FG5Ira5vnxEejf2RVVtVo8uS4dNRqt2CUREZkFhhuSvLd+zURVrRa9A5wxKSZA7HLaTKmQ44OHo+HeyRqnCyvx6s8nxS6JiMgsMNyQpB3NK8MPhy4CABLvjIRcbphVvjuKp4MN/j0pCgDwzYFc/HKsQNyCiIjMAMMNSZYgCFiy5QQA4L4+fma7btOQbh74+7BQAMCiDceQd7Va5IqIiEwbww1J1vaTl3E4twy2SgX+MTZc7HJuy8L4bugT6IxKdR0WfHcEWs5/Q0R0Qww3JEk6nYB/NwwifjQu2GwGEd+IUiHH+w9Fo5PKCgcvlOLzvdlil0REZLIYbkiSthy7hNOFlXCwscLsIaFil2MQAa52eCkhAgDwzm9ZyLrMx8OJiFrCcEOSU6fVYdkf9TP7/m1wZzjZKUWuyHAmxQRgRLgnarU6LPzPEWi0OrFLIiIyOQw3JDkbD+cjp7gKrvbWeHRQiNjlGJRMJsMb9/WEs50Sx/Mr8OGOs2KXRERkchhuSFLqtDp8tLP+A3/OsFB0UlmJXJHheTra4NWGWZaX7zyL4/nlIldERGRaGG5IUrYdL0Tu1Wq42Ckx+Y5Ascsxmjt7+2J8T29odQIWb8xAHW9PERHpMdyQZAiCoF/1e/rAYNhZS6/X5q8S7+oORxsrZOSXY23yebHLISIyGQw3JBl7zhTjZEEFbJUKTB8QLHY5RufpYIPnx9c/PfXu71mc3I+IqAHDDUlGY6/NQ/0C4GJvLXI1HePB2AD07+yK6xotnt+UAUHg5H5ERAw3JAlH8sqQkl0CK7kMjw/uLHY5HUYmk+H1+3rB2kqOPWeK8eORfLFLIiISHcMNScLqvTkAgLt6+8LP2VbkajpWiLs9nh7ZFQDwypaTuFpVK3JFRETiYrghs1dUUYOtGfWrZT8aJ615bdrqb0M6I9zbAaXVGrz922mxyyEiEhXDDZm9dam5qNMJ6BPojJ7+TmKXIwqlQo5X76mf++bbtDyk55aKXBERkXgYbsis1dbp8M2BXAD1j39bsthgV9zfxx+CAPzzpxNcOZyILBbDDZm1bccLcKVSDQ8HFcb18BG7HNEtGhcOh4a5b9an5opdDhGRKBhuyKx90TB53ZQ7AmFtxR9nDwcVnh0dBgB4+7dMlFxTi1wREVHH46cBma2TlypwOLcMSoVM0ksttNeUOwIR6eOI8usavPVrptjlEBF1OIYbMlvfpdXfdhkd6Q1PBxuRqzEdVgo5Xr2nOwDgu4N5OMzBxURkYRhuyCzVaLTYlF4/Yd1D/QJErsb09A1yxcS+/gCAf/50HDoOLiYiC8JwQ2bp1+OFqKipg5+zLeJC3cUuxyT9Y1w4HFRWOJ5fgR8OXxS7HCKiDsNwQ2bp24ZbUg/GBkAul4lcjWly76TCvIaZi9/6NROVNRqRKyIi6hgMN2R2coqrsD/7KuQy4IGGWy/UsukDgxHibo/ia2os33lO7HKIiDoEww2Zne/S8gAAQ7t5wNfC1pFqL2srOV4YHwGgfv2tC1erRa6IiMj4GG7IrGh1AjY2jB95MJaPf7fFyAhPDO7qjlqtDm/+miV2OURERsdwQ2Yl+VwxiirVcLZTYkS4p9jlmAWZTIZ/JkRCIZdh+6kiZJVzjBIRSRvDDZmVxse/E3r5cEbidujq5YCpDRMdbjwvR51WJ3JFRETGw08HMhvVtXX47XghAODeaA4kbq8F8d3gbKtEQbUM/zmUL3Y5RERGw3BDZmP7ycuoqtUi0NUOfQKdxS7H7DjbWWPeiFAAwLI/z6L8Oh8NJyJpYrghs9F4S+qeaD/IZBw3cisejvWHt62A0moN3v/jjNjlEBEZBcMNmYUrlWrsOVMMALgnylfkasyXlUKOe4Prx9t8mXIe2VeuiVwREZHhMdyQWfj52CVodQJ6Bzijs0cnscsxa+HOAoZ1c0edTsDSrafFLoeIyOAYbsgsNN6Sui/aT+RKpGHR2DBYyWX449Rl7G3oESMikgqGGzJ5F0qqcOxiORRyGSb08hG7HEkI9bDH1P5BAIDXfjkJLVcNJyIJYbghk/dLRgEAYEBnN7h3UolcjXTMH9UVTrZKnC6s1C9pQUQkBQw3ZPK2NoSb8T3Za2NIznbWWDCqftXwd3/PRAVXDSciiWC4IZN2oaQKx/MroJDLMKa7l9jlSM6U/kEI9bBHSVUtlu84K3Y5REQGwXBDJu2vt6TceEvK4JQKOV6cEAkAWLPvPC6UVIlcERHR7WO4IZPGW1LGNyzMQ79q+Ot8NJyIJIDhhkwWb0l1DJlMhpcSIiGXAb+eKETKuRKxSyIiui0MN2SyeEuq43TzcsCUO/hoOBFJA8MNmSzekupYC+K7wcHGCicuVWDDoYtil0NEdMsYbsgk5V2t5i2pDuZqb42nR9Y/Gv7275m4pq4TuSIiolsjerjJz8/H1KlT4ebmBjs7O0RFReHQoUNtOnbfvn2wsrJCVFSUcYukDvfbiUIAQGywC29JdaBpA4IR7GaHK5VqrEjio+FEZJ5EDTelpaWIi4uDUqnEtm3bcPLkSbz77rtwdna+6bHl5eWYNm0aRo4cafxCqcNtP3kZADA60lvkSiyLtZUcz4+PAAB8uicHeVerRa6IiKj9rMR88zfffBMBAQFYs2aNfltwcHCbjp09ezYmT54MhUKBH3/80TgFkihKq2qRdv4qACA+krekOlp8pBcGhroh+VwJ3vz1ND6a3EfskoiI2kXUnpvNmzcjJiYGEydOhKenJ6Kjo/Hpp5/e9Lg1a9bg3LlzePnllzugSupoO04XQScA4d4OCHC1E7sciyOTyfDihEjIZMDPxwpwsCFoEhGZC1F7brKzs7FixQosXLgQzz//PFJTUzFv3jyoVCpMmzatxWPOnDmDRYsWYc+ePbCyunn5arUaarVa/3VFRQUAQKPRQKMx7Fo6jecz9HlNRUe179fj9U9JjQr36PDvJa9hva4etpjU1w/fHczHki0n8MPf7oBcLuuIEm+L1K8fIP02sn3mz1htbM/5ZIIgiDahhbW1NWJiYpCcnKzfNm/ePKSlpSElJaXZ/lqtFv3798fMmTPxxBNPAAASExPx448/4siRIy2+R2JiIpYsWdJs+7p162Bnx14BU1OrBV44qECtToZne9YhoJPYFVmuilrgtSMKqLUyTO2iRawH574hIvFUV1dj8uTJKC8vh6OjY6v7ihpugoKCEB8fj88++0y/bcWKFXjttdeQn5/fbP+ysjK4uLhAoVDot+l0OgiCAIVCgd9//x0jRoxockxLPTcBAQEoLi6+6TenvTQaDbZv3474+HgolUqDntsUdET7dmReweyv0+HjZINdzwyGTNaxvQW8hk2t3J2Dd7afgZeDCr/Pj4OdtaidvTcl9esHSL+NbJ/5M1YbKyoq4O7u3qZwI+rfVHFxccjMzGyyLSsrC0FBQS3u7+joiIyMjCbbPv74Y+zYsQM//PADQkJCmh2jUqmgUjV/lFipVBrtB8uY5zYFxmzfjtPFAOoHtVpbWxvlPdqC17De40NC8d2hi8i7eh2fJ+dhYXy3Dqju9kn9+gHSbyPbZ/4M3cb2nEvUAcULFizA/v37sXTpUpw9exbr1q3DqlWrMHfuXP0+ixcv1o+/kcvl6NGjR5M/np6esLGxQY8ePWBvby9WU8gAtDoBf57mI+CmxEapwPPj6h8NX7X7HC6VXRe5IiKimxM13MTGxmLTpk1Yv349evTogVdffRXLli3DlClT9PsUFBQgNzdXxCqpoxzJK0XxtVo42Fjhjs6uYpdDDcb28Ea/EFfUaHR461euGk5Epk/0GYoTEhKQkZGBmpoanDp1CrNmzWry+tq1a5GUlHTD4xMTE284mJjMy+8NE/cND/OEUiH6jyY1kMlkeKnh0fAfj1xCem6p2CUREbWKnyBkMv48VQSAE/eZop7+Tri/jz8A4JWfT0LE5xCIiG6K4YZMQt7VapwtugaFXIYh3TzELoda8H9jwmBnrUB6bhk2H70kdjlERDfEcEMmISmzvtemb5ALnGyl/QSBufJytMGcYaEAgDe3ncb1Wq3IFRERtYzhhkzCzswrAIBhYey1MWWPD+4MP2dbXCqvwWd7ssUuh4ioRQw3JLoajRbJ5+rntxke5ilyNdQaG6UC/xgXDgD4OOkcLlfUiFwREVFzpj3dKFmE/dklqNHo4O1og3BvB7HLoZu4s5cP1u7LweHcMrz1aybendRb7JKIWiUIAkqqanGhpBoXS6txpVKNkqpalFxT42qVBjUaLWo0WqjrdKjRaKEVBCjlclgpZLBSyGFjJYejrRJOf/nj5aiCj5MtfJ1t4ONkC3sVP05NCa8GiS6p4ZbU8HCPDl9ugdpPJpPhn3d2xz3L92HD4YuYMTAYPf2dxC6LCABwTV2Hk5cqcOJSOY7nV+B0YQUulFTjmrrOqO/rbKdEsJs9unh2qv/j0QldvTohwMXOLBadlRqGGxKVIAjYcbp+MPEw3pIyG1EBzrg32g+b0vPxys8n8J/ZAxhMSRSlVbU4kHMVB3JKsD/7Kk4XVqClmQpkMsDH0QYBrnbwdLSBm701PBxUcLGzhr1KAZWVHCpl/X8VMhnqdAI0Wh3qtAKua7Qov65B+XUNKmo0KKvSoLCiBgXl13GprAbX1HUoq9bgSHUZjuSVNXlfB5UVuvs5ope/M3r4OSHSy77F+siwGG5IVDnFVci9Wg2lQoa4Lu5il0Pt8NzYMGw7XoC086XYdrwQ43v6iF0SWQBBEJB5uRJ/nLyM7Scv4+jF8mb7+DjZoLuvE3r4OSLSxxGdPezh72IHG6WihTPevooaDfJLryP7ShXOFFXibNE1nC26huziKlSq67A/+yr2Z1/V729npcCWsnTc0dkNscGu6OHnxIlLDYzhhkTV+JRUvxBXdOI9a7Pi42SL2UNC8f6fZ7B06ymMCPc02ocH0amCCmxKz8fWjAJcLG26xllXz064o7Mr+nd2Q78QV3g62HRobY42Sjj6KBHh4wjgvyFfo9XhbNE1ZFwsR0Z+OY7ll+NUQQWq63T48/QV/Hm6/u8/W6UC0YHO6N/ZDYO7uqOXvzMUvJV1W/hpQqJqnN+GT0mZp9lDO+O7tDxcLL2OT3dn46mRXcUuiSTkckUNNqXn48f0fJwurNRvV1nJMbirO0ZFeGFEuCc8HTs2zLSVUiFHhI8jInwcMSk2AABQdV2Nzzb8Cmu/SBzKLcfBC1dRVq1B8rkSJJ8rwb+3Z8HRxgpxXdwxuKsHBnd1R4CrncgtMT8MNySaKnUdDjR01XK8jXmys7bC4vHhePrbI/ho51ncHeWHQDf+RUy3ThAEnC0H5n17FNtPFaFOVz9AxVohx8gIT9wd5Ysh3TxgZ22eH1/WVnIEOwDjBwXj70oldDoBZ69cw4Gcq9h3phjJ54pRUVOHbccLse14IQAg2M0Og7t6YESEJwZ0dmMPaRuY508HSULyuRLUanUIcLVFqIe92OXQLbqrty++S8tD8rkSvLz5OFbPiOXgYmq367VabDh8EV8k5+BMkRWA+oV0+wa54IG+/hjfwwdOdtKbvVwul6GblwO6eTngkf5BqNPqcCy/HHvPFGPPmStIzy3D+ZJqnC+5gK/2X4CtUoFBXd0xMtzTpHutxMZwQ6LZc6b+fvPQbnwE3JzJZDK8cncPjHt/N3ZmXsFvJwoxtgcHF1PbVNRo8FXKBazem4OSqloAgLVcwL19AjAjLqRhHIvlsFLI0SfQBX0CXTBvZFdU1miwP/sqdmYWYcepIhRW1GB7w2BqAOjl74QR4Z4YFeGF7r6O/Lu0AcMNiWbvmfpZiQd35ZIL5q6LZyc8MTQUH+44iyVbTmJwVw9OakatKrmmxup9Ofgy+QIqG+ag8XexxfQBgeh05QQeuCsSSqX0emray8FGifhIL8RHekG4R8CJSxXYcboIf54uwtG8Mhy7WI5jF8ux7I8z8HJUYUS4J0aGeyGuiztsrS339hX/9iFR5F2tRnZxFRRyGQaEuoldDhnA3OFd8NORS8i9Wo1lf2ThhQmRYpdEJqiyRoPP9uTgsz3ZqGpYfLWrZyfMGR6KhF6+gE6LrVtPiFylaZLJZOjh54Qefk6YN7IriiprkHT6Cv48fRl7zhTjcoUa61PzsD41DyorOQZ1ccfICC+MjPCEl4XdvmK4IVHsPVvfaxMV4AxHG/7rTApslAosubs7Hl2ThtX7zuO+Pv4Wd0uBbkxdp8XX+3OxfOdZXG24/dTDzxFPDu+K0ZFe+ll8NTquNt9Wng42mBQbgEmxAVDXabE/+yr+PHUZf54qQn7ZdfzZ0MODTUBPPyeMjLCc21cMNySK/96S4sR9UjI8zBPjenhj2/FCvLApAz88MZBTz1s4QRDw87ECvLHtNPLL6uen6exuj2fHhGFcD2/Jf8h2FJWVAkO7eWBoNw8suUvA6cJK/HnqMv44VYSjF8uQkV8/186yP87A29EGIyI8ER/hhQGh0nz6iuGGOpxWJ+h7bhhupOefd0Zid9YVHM4tw7dpeZh8R6DYJZFITl6qQOKWE0jNqZ/ywctRhfmjumFiX39YcUZeo5HJZPr5dZ4c0RVXKtXYeboIf5yqv31VWFGDdQdyse5Arv7pq1ERnhge7tnhEyAaC8MNdbjj+eUov66Bg8oKvf2dxS6HDMzHyRYLR4fh1Z9P4vWtpzA83AM+TrZil0UdqLSqFv/enoVvDlyATgBslHL8fWgX/G1IZ4se5CoWDweV/vZVjUaLlOwS/HHyMnacLkJBedOnr3oHOGNUuCdGRnghwsfBbHvWGG6owzU+Aj6wixv/9SZRMwYGY8vRSziSV4YXNx3HZ9NjzPYvSWo7QRDw/cGLWLrtFMqqNQCACb188Pz4CPg5M+CaAhulAsPDPDE8zBOCUP/01Z+nivDn6cs4drEcR/PKcDSvDO9uz4Kfsy1GhHtieLgH7ghxM6snIM2nUpKM3Q3jbQbxEXDJUshleOuBXpjwwR78eboIm49ewt1RfmKXRUaUU1yF5zdmICW7BAAQ7u2Al+/szqchTdhfn756elRXXK6oqX/M/NRl7D1bjPyy6/hqf/3kgVZyGfoEumBQV3cM6uqOXn5OJv2PU4Yb6lDX1HVIzy0FAAzheBtJ6+blgKdGdMW/t2dhyZaTGNTFHW6dVGKXRQam0eqwanc2PvjzDNR1Otgo5VgY3w2PxYWY9IcfNeflaIOH+wXi4X6BuF6rRfK5Yvx5ugh7zlxB3tXrSD1/Fannr+Lf27PgYGOFAZ3dMKirO/p3dkMXj04m9fAAww11qAPZJdBoBQS42iLIjUsuSN0TQ0OxNaMApwsrkbjlJD58OFrsksiAjl0sw3M/HNMvajm4qzv+dU9Pri8mAbbWioY5crwAALkl1dhz9gr2nilG8rkSlF/X4PeTl/F7w1gdFzslYoNd0S/EFX0DnKAVxKye4YY62B7OSmxRrK3keOuBXrhn+T5sOXoJd/X2RXykl9hl0W3SaHX4cMdZLN95FlqdABc7Jf55ZyTuifLj2CqJCnSzwxS3IEy5IwhanYDj+eXYe7YY+84W43BuKUqrm4YdW4UCo0drRZtlmuGGOlTjYGLekrIcvfydMWtwZ6zcnY0XNmUgJsgFLvbWYpdFt+jM5Uos+M8RHM+vAADc2dsXS+7qDldeU4uhkMvQO8AZvQOcMXd4F9TW6XD8UjlSc64iLaf+1pWzQgOViPPnMNxQh7lUdh3nrlRBLgMGhDLcWJIF8d2w/dRlZF+pwos/HsdHk6P5L3wzo9MJWL0vB2/9lonaOh2c7ZR47Z4e9UsmkEWztvrvYp9PDA1FjboW32/eJmpNHO1FHaZxVuLeAc5wsuWSC5bERqnAsgejYCWX4ZeMAvx05JLYJVE75F2txsOf7sdrv5xCbZ0Ow8I88Nv8IQw21CKFXAZHkTvyGG6owySfqw83cey1sUi9/J0xb2RXAMBLPx3XT8VPpksQBGw4dBFjl+3GgZyrsLNW4PX7emLNjFiLW4iRzAvDDXUIQRCQfK5+/ouBXTjvhaWaMywUUQHOqKypwzP/OQKdTuRHKuiGKms0WPDdETzz/VFU1WoRG+yCX58egof7BfKWIpk8hhvqEOeuVKGoUq2/N0uWyUohx3sPRsFWqcD+7KtYvS9H7JKoBUfzypDw4V78eOQSFHIZnh3dDd/+bQAf8SazwXBDHaJx1tKYIBdJrkBLbRfibo8XEyIAAG/9momMi+UiV0SNdDoBq3afw/0rknGhpBp+zrb4z+z+eHJEVyhMaII2opthuKEOkdIw3mZAZ96SImByv0DER3qhVqvDk+sPo6JGI3ZJFu9KpRoz1qZh6dbTqNMJGNfDG1vnDUbfIFexSyNqN4YbMjqdTkAKx9vQX8hkMrz9QC/4OdviQkk1Fm/IgCBw/I1Ydmddwbj392B31hWorORYem9PfDylD5zs+FQjmSeGGzK604WVKK3WwM5agV7+zmKXQybC2c4aH02O1j8e/vWBXLFLsjgarQ6vbzuFaatTUXxNjTAvB2x5ahAm38FBw2TeGG7I6BofAe8X4golF9Kjv4gOdMGiceEAgFe3nMTxfI6/6Si5JdV44JMUrNyVDQCY2j8QPz0Zh25eDiJXRnT7+ElDRre/YTDxwFDekqLmZg4KwaiI+vE3s786hKtVtWKXJHlbjl7ChA/24GheGRxtrPDJ1D547Z6eHOxPksFwQ0ZVp9XhQPZVAMBATt5HLZDJZHh3Ym8Eu9khv+w65nxzCBqtTuyyJOl6rRaLNhzDU+vTUamuQ0yQC7bNH4KxPXzELo3IoBhuyKiOX6pApboOTrZKRPg4il0OmSgnOyU+nRYDe+v6+W/+9cspsUuSnMzCStz10V58m5YHmQx4akQXfPu3/vBzthW7NCKDY7gho2ocb3NHiCvnyaBWdfVywHsPRgEA1iafx38O5olbkEQIgoB1B3Jx10d7caboGjwcVPhm5h14ZnQYrDgGjiSKP9lkVPpHwDnehtpgdHdvLBjVDQDw4qbjONAwXotuTfl1DZ5cl47nN2VAXafD0G4e2Pb0YAzswlvEJG0MN2Q0tXU6pJ1vGG/Dv0ypjZ4a0QXjenijVqvDrC8P4mxRpdglmaX03FJM+GAPfskogJVchufHh2PNjFi4d1KJXRqR0THckNEcyStDjUYH907W6OrZSexyyEzI5TK892AU+gQ6o6KmDtNXp6GookbsssyGTidg5a5zmPhJCi6WXkeAqy1++PtA/G1IKOS8NUwWguGGjKZxvM2AUHdOCEbtYqNU4LPpsejsbo/8sut4dG0aKrlEw01dqVTj0bVpeH1b/RIKE3r64Jd5gxEV4Cx2aUQdiuGGjCaZ423oNrjaW2Pto/3g3skaJy5VYObag6iurRO7LJO1/eRljF22G7v+soTCR5Oj4WjDJRTI8jDckFHUaLQ4klsGAOjPxTLpFgW62WHto/3gYGOF1PNX8bcvD6FGoxW7LJNSpa7D4o3HMOvLgyipqkW4twM2P8klFMiyMdyQURzNK0OtVgcPBxWC3ezELofMWA8/J6x9tB/srBXYe7YYc745jNo6TvIH/HfQ8PrU+rlr/jakM356Mg5h3lxCgSwbww0ZxcELpQCAfsGu/Ncj3ba+QS5YPSMWNko5dpwuwuyvDuJ6reX24Gh1wIc7zuGBT1JwvqQavk42+ObxO/D8+AiorLiEAhHDDRlFak79I+CxwS4iV0JS0b+zGz6dFgMbpRw7M69g+upUVFjgIOOTBRV4N0OBD3aeg1Yn4O4oX2ybP4TLmxD9BcMNGZxWJ+BwQ89NbIiryNWQlAzu6oGvZt4BB1X9GJzJn+5HyTW12GV1CHWdFu/8lon7PzmA/GoZXOyUeP+hKLz/UDScbDlomOivGG7I4E4V1K8n5aCyQrg315Miw4oNdsX6v/WHm701judX4N6Pk3HmsrQn+kvPLUXCB3vx0c6zqNMJiHLTYetTA3F3lJ/YpRGZJIYbMriDDbMS9wly4XpSZBQ9/JzwnycGIMDVFrlXq3Hfx8nYmVkkdlkGV1Zdixc2ZeC+Fck4U3QN7p2s8eFDvfFoNx1nGiZqBcMNGVza+YbBxLwlRUYU6tEJP80dhH7BrqhU12Hm2jR8vu88BEHsym6fTifg29RcDH8nCd8cyIUgAPdF+2H7gqEY291L7PKITJ6V2AWQtAiCgNTzjYOJGW7IuFztrfH143fgxR8z8J+DF/HGr1no7iLHgGG18HI2z3Eo6bmlSNxyEkfzygAAYV4OeOXu7rijYb4ojcbyBlETtRfDDRnUhZJqXKlUw1ohRy9/J7HLIQtgbSXHm/f3Qk9/Z7z680mcKAXuWp6Cdyb1xuCuHmKX12bnrlzDO79lYtvxQgBAJ5UVFsR3w7QBQVAq2MlO1B4MN2RQjauA9/J3go2S821Qx5DJZHikfxCi/Bzw+OpkXK5U45HPU3F/H3+8lBABZztrsUu8ocLyGnyw4wy+S8uDVidALgPu7+OP/xsTBk9HG7HLIzJLov9zID8/H1OnToWbmxvs7OwQFRWFQ4cO3XD/vXv3Ii4uDm5ubrC1tUV4eDjee++9DqyYWtMYbvgIOIkh3NsBz/TUYlr/QMhkwIbDFzHq37uw7kAu6rSmNavx+eIqLNpwDIPf2oF1B3Kh1QkYFeGFX+cPwdsTezPYEN0GUXtuSktLERcXh+HDh2Pbtm3w9PTEuXPn4OzsfMNj7O3t8eSTT6JXr16wt7fH3r17MXv2bNjb2+Nvf/tbxxVPLdIPJuZ4GxKJSgG8ND4cd0f7Y9GGYzhTdA3Pb8rAF8nn8dzYMIwI9xRt1mxBEHDwQim+SD6PrRkF0DUMfu4X7Ipnx4RxED6RgYgabt58800EBARgzZo1+m3BwcGtHhMdHY3o6Ogm+2/cuBF79uxhuBFZUWUNcoqrIJPVPwZOJKa+QS74Zd5gfL3/At7/8wwyL1di5hcHEe7tgNlDOyOhl2+HjWUpv67Bj+n5+ObABWRdvqbfPiLcE3OGhSKG/xggMihRw83mzZsxZswYTJw4Ebt27YKfnx/mzJmDWbNmtfkc6enpSE5OxmuvvWbESqktDjb02oR5OXDGVDIJ1lZyPDYoBPf38cfHSWfx9f4LOF1YiQXfHcW/fjmFe6L88ECMP8K8HAzem1NRo8Gfpy7j56MF2H3mCjTa+m4aG6Ucd/X2xfSBwejuy0H3RMYgarjJzs7GihUrsHDhQjz//PNITU3FvHnzoFKpMG3atFaP9ff3x5UrV1BXV4fExEQ8/vjjLe6nVquhVv93evaKigoA9Y9TGvqRysbzSfVRzZu170B2MQAgJsjZbL8Hln4Nzd2N2menBJ6N74JZg4LwzYE8fHUgF8XXavHZ3hx8tjcHga62GNbNA4O6uKGXvxPc7Ns/ALm0uhYnCypxIOcq9mdfxbH8Cmh1/510J8yrEx6M8cfdvX3g2BD+b+U6WOo1lAqptw8wXhvbcz6ZIIg35ZW1tTViYmKQnJys3zZv3jykpaUhJSWl1WNzcnJw7do17N+/H4sWLcJHH32Ehx9+uNl+iYmJWLJkSbPt69atg52d3e03gvTePqbAxSoZpnfVoo+7BGZSI8nS6oBTZTIcuCLDiVIZtELTXhtXlQAvWwGuqvr/t1EA1gpAIQPqdIBGB1TVAWW1MpSqgUvVMpTXNu/58bIVEO1Wv1yCD/+6Ibot1dXVmDx5MsrLy+Ho2PrSPqKGm6CgIMTHx+Ozzz7Tb1uxYgVee+015Ofnt/k8r732Gr766itkZmY2e62lnpuAgAAUFxff9JvTXhqNBtu3b0d8fDyUSundlmmtfZU1dYhZugM6Adjzf0PgbaZPeljyNZSCW2lflboOyeeuYmfWFRy6UIrs4upbfv8AF1tEBzhjQKgrBnR2hZ+z7S2f60Z4Dc2b1NsHGK+NFRUVcHd3b1O4EfW2VFxcXLNAkpWVhaCgoHadRxCEJgHmr1QqFVSq5muwKJVKo/1gGfPcpqCl9mXklEEnAAGutghwcxCpMsOxxGsoJe1pn7NSifG9/TC+d/0ilBU1GpzIr8CFkirklVajoKwGVbV1qK7Vok4rQKWUQ2Ulh7OtNbydbODtZIOunp0Q5u0AB5uO+57yGpo3qbcPMHwb23MuUcPNggULMHDgQCxduhSTJk1CamoqVq1ahVWrVun3Wbx4MfLz8/Hll18CAJYvX47AwECEh4cDqJ/35p133sFTTz0lShuo3kEuuUAS4WijxIBQNwwIdRO7FCK6RaKGm9jYWGzatAmLFy/GK6+8gpCQECxbtgxTpkzR71NQUIDc3Fz91zqdDosXL0ZOTg6srKwQGhqKN954A7NnzxajCdQgNac+3HB+GyIiEpvoyy8kJCQgISHhhq+vXbu2yddPPfUUe2lMjLpOiyMNi/xxvg4iIhKb6MsvkPk7nl8OdZ0ObvbWCPWwF7scIiKycAw3dNsal1yICXYRbVp7IiKiRgw3dNvScjiYmIiITAfDDd0Wna5+IUAAXPSPiIhMAsMN3ZasokqUX9fAzlqBSB/DTopIRER0Kxhu6LY0jrfpE+gCqw5aYZmIiKg17f40+vXXX7F3717918uXL0dUVBQmT56M0tJSgxZHpo/jbYiIyNS0O9z83//9n35l7YyMDDzzzDMYP348srOzsXDhQoMXSKZLEASkNc5MHOIicjVERET12j2JX05ODiIjIwEAGzZsQEJCApYuXYrDhw9j/PjxBi+QTNfF0usoKK+BlVyG6ACGGyIiMg3t7rmxtrZGdXX9qrl//PEHRo8eDQBwdXXV9+iQZWjstenh5wRba4XI1RAREdVrd8/NoEGDsHDhQsTFxSE1NRXfffcdgPrVvP39/Q1eIJmuxsHEfASciIhMSbt7bj766CNYWVnhhx9+wIoVK+Dn5wcA2LZtG8aOHWvwAsl0pXElcCIiMkFt7rn5/fffMXz4cAQGBuLnn39u9vp7771n0MLItF2tqsXZomsAgJggjrchIiLT0eaemyeeeAIeHh548MEHsX79epSXlxuzLjJxjb02XT07wcXeWuRqiIiI/qvN4SY7Oxu7d+9Gz5498d5778HLywsjR47EBx98gPPnzxuxRDJFB/WPgPOWFBERmZZ2jbnp1asXXnzxRaSmpiI7OxsTJ07Er7/+ioiICPTu3Rv//Oc/cfDgQWPVSiYktXEwMcfbEBGRibnl+fJ9fX3xxBNPYOvWrSguLsZLL72E8+fPY+zYsVi6dKkhayQTU11bhxP59bclY4I53oaIiExLux8Fb4m9vT0eeOABPPDAA9DpdCgpKTHEaclEHckrR51OgK+TDfxd7MQuh4iIqIlbCjepqalISkpCUVERdDqdfrtMJsO7774LDw8PgxVIpufQhTIAHG9DRESmqd3hZunSpXjxxRcRFhYGLy8vyGQy/Wt//X+SroMX6sfbcH4bIiIyRe0ON++//z5Wr16NGTNmGKEcMnVaHZCeVwaA4YaIiExTuwcUy+VyxMXFGaMWMgMXq4DrGh2cbJXo6tlJ7HKIiIiaaXe4WbBgAZYvX26MWsgMZFfW33qMDXaBXM7bkEREZHrafVvq2WefxYQJExAaGorIyEgolcomr2/cuNFgxZHpOVfRGG54S4qIiExTu8PNU089hZ07d2L48OFwc3PjIGILIgiCvucmhuGGiIhMVLvDzZdffokNGzZgwoQJxqiHTNi5K1WoqpPBRilHTz8nscshIiJqUbvH3Li6uiI0NNQYtZCJO9gwv01vfydYW93y5NZERERG1e5PqMTERLz88suorq42Rj1kwg41zG8TE8QlF4iIyHS1+7bUBx98gHPnzsHLywvBwcHNBhQfPnzYYMWRaWmcvK9vkLO4hRAREbWi3eHmnnvuMUIZZOoKyq/jYlkNZBAQHeAsdjlEREQ31O5w8/LLLxujDjJxqTlXAQD+9kAnlUHWWyUiIjIKjgqlNjl4vv6WVGdHQeRKiIiIWsdwQ22Sdr6+56azA8MNERGZNoYbuqnyag0yL1cCYLghIiLTx3BDN3XwwlUIAhDiZgdHa7GrISIiah3DDd1UWsN4m5hgzm9DRESmz6Dh5pVXXsHu3bsNeUoyAY3jbfoGOotbCBERURsYNNysWbMGY8eOxZ133mnI05KIajRaHLtYBoA9N0REZB4MOmFJTk4OampqsGvXLkOelkR0JK8MGq0ATwcVAl1scULsgoiIiG6izT03R44cadN+NjY2GDNmzK3WQybmYMMtqdgQV8hkMpGrISIiurk2h5s+ffqgb9++WLFiBcrLy41ZE5mQ1IbBxLFcLJOIiMxEm8PNvn370KdPHyxatAg+Pj6YOnUqdu7caczaSGRanYDDDYtlxoa4ilwNERFR27Q53AwYMACffvopCgsLsWLFCly8eBGjRo1CaGgo/vWvf+HixYvGrJNEcKqgAtfUdXBQWSHc21HscoiIiNqk3U9L2draYvr06UhKSkJWVhYefvhhrFy5EiEhIRg/frwxaiSRNC6W2TfYBQo5x9sQEZF5uK1HwUNDQ7Fo0SK88MILcHR0xG+//WaousgEHLzQMJg4mLekiIjIfNzyo+C7du3C6tWrsWHDBigUCkyaNAkzZ840ZG0kIkEQkJrTMN6G4YaIiMxIu8JNXl4e1q5di7Vr1yInJwcDBw7Ehx9+iEmTJsHe3t5YNZIIzpdUo/iaGtYKOXr5O4ldDhERUZu1OdzEx8dj586d8PDwwLRp0/DYY48hLCzMmLWRiNIaxtv0DnCCjVIhcjVERERt1+ZwY2triw0bNiAhIQEKBT/spK5xPakY3pIiIiIz0+Zws3nzZmPWQSamMdz0Y7ghIiIzY9CFM0kaiiprcL6kGjIZ0IczExMRkZlhuKFm0hqekgr3doSTrVLkaoiIiNqH4YaaabwlFRvMXhsiIjI/DDfUzH/DDcfbEBGR+WG4oSYqazQ4VVABAOjHxTKJiMgMMdxQE4culEInAIGudvBytBG7HCIionYTPdzk5+dj6tSpcHNzg52dHaKionDo0KEb7r9x40bEx8fDw8MDjo6OGDBgANe0MqCD5+sHE8dwvA0REZkpUcNNaWkp4uLioFQqsW3bNpw8eRLvvvsunJ2db3jM7t27ER8fj61bt+LQoUMYPnw47rzzTqSnp3dc4RKWyvltiIjIzN3ywpmG8OabbyIgIABr1qzRbwsODm71mGXLljX5eunSpfjpp5+wZcsWREdHG6FKy6Gu0+JIXhkAIJbjbYiIyEyJGm42b96MMWPGYOLEidi1axf8/PwwZ84czJo1q83n0Ol0qKyshKtryx/GarUaarVa/3VFRf1gWY1GA41Gc3sN+B+N5zP0eTtK+oVS1Nbp4GqvRICTdbN2mHv72kLqbWT7zJ/U28j2mT9jtbE955MJgiAY9N3bwcamfsDqwoULMXHiRKSmpmL+/PlYuXIlpk2b1qZzvP3223jjjTdw6tQpeHp6Nns9MTERS5YsabZ93bp1sLOzu70GSMwf+TJsyVWgl6sOM8N0YpdDRESkV11djcmTJ6O8vByOjo6t7itquLG2tkZMTAySk5P12+bNm4e0tDSkpKTc9Pj169fj8ccfx08//YRRo0a1uE9LPTcBAQEoLi6+6TenvTQaDbZv3474+HgoleY3s++srw4jKasYz48Lw6MDg5q9bu7tawupt5HtM39SbyPbZ/6M1caKigq4u7u3KdyIelvKx8cHkZGRTbZFRERgw4YNNz32u+++w8yZM/H999/fMNgAgEqlgkqlarZdqVQa7QfLmOc2Fp1OwOHcMgBA/1D3Vus3x/a1l9TbyPaZP6m3ke0zf4ZuY3vOJerTUnFxccjMzGyyLSsrC0FBzXsN/mr9+vWYMWMG1q1bhwkTJhizRIuRebkSFTV1sLNWINLHsD1aREREHUnUcLNgwQLs378fS5cuxdmzZ7Fu3TqsWrUKc+fO1e+zePHiJuNv1q9fj2nTpuHdd99F//79UVhYiMLCQpSXl4vRBMloXHKhT6ALrBSiT39ERER0y0T9FIuNjcWmTZuwfv169OjRA6+++iqWLVuGKVOm6PcpKChAbm6u/uuVK1eirq4Oc+fOhY+Pj/7P008/LUYTJCM1p2F+Gz4CTkREZk7UMTcAkJCQgISEhBu+vnbt2iZfJyUlGbcgCyQIgj7ccLFMIiIyd7z/QMi9Wo2iSjWUChmiA53FLoeIiOi2MNwQDjT02vTyd4aNUiFyNURERLeH4YaQxvE2REQkIQw3pH9SiotlEhGRFDDcWLiiihqcL6mGTAb0CXIRuxwiIqLbxnBj4VIbem0ivB3hZCvt2TKJiMgyMNxYOI63ISIiqWG4sXAHGG6IiEhiGG4sWHm1BpmXKwFw8j4iIpIOhhsLdvDCVQgCEOJuDw+H5iunExERmSOGGwuWykfAiYhIghhuLFjjYOJYjrchIiIJYbixUNdrtTh2sRwAcAfDDRERSQjDjYVKzytFnU6At6MN/F1sxS6HiIjIYBhuLFTqX25JyWQykashIiIyHIYbC6VfT4q3pIiISGIYbiyQRqvD4QtlAPikFBERSQ/DjQU6nl+O6xotnO2U6OrZSexyiIiIDIrhxgI13pKKCXKFXM7xNkREJC0MNxYoVb+elIvIlRARERkew42F0eoE/WKZ/Tu7iVwNERGR4THcWJhTBRWorKmDg8oKkT6OYpdDRERkcAw3FmZ/dgmA+vltrBS8/EREJD38dLMwKefqw80A3pIiIiKJYrixIFqdoB9MzPE2REQkVQw3FuTkpQpUqhvG2/hyvA0REUkTw40FaRxv0y/EFQrOb0NERBLFcGNBGsPNgFDekiIiIuliuLEQdVodx9sQEZFFYLixECcLGsbb2FghgvPbEBGRhDHcWIjGW1J3cLwNERFJHMONhdifzVtSRERkGRhuLECdVoc0jrchIiILwXBjAU40zG/jyPE2RERkARhuLMB/57dx43gbIiKSPIYbC9AYbvp3dhW5EiIiIuNjuJG4Oq0OaedLAXDyPiIisgwMNxJ3/FIFrjWOt/HmeBsiIpI+hhuJ23e2GAAwMNQdco63ISIiC8BwI3F7z9SHm7guvCVFRESWgeFGwq7XanHoQv14m7gu7iJXQ0RE1DEYbiTs4IWrqNXq4OtkgxB3e7HLISIi6hAMNxK2t3G8TRd3yGQcb0NERJaB4UbCGgcTD+ItKSIisiAMNxJ1taoWJy5VAAAGcjAxERFZEIYbiUo5VwJBALp5dYKng43Y5RAREXUYhhuJ2neu8RFw3pIiIiLLwnAjURxvQ0RElorhRoLyrlbjQkk1FHIZ+oVwsUwiIrIsDDcS1NhrExXgDAcbpcjVEBERdSyGGwnad64EAMfbEBGRZWK4kRitTsDeM1cAcLwNERFZJoYbicnIL0dptQYOKitEBzqLXQ4REVGHY7iRmN1Z9b02cV3coVTw8hIRkeXhp5/E7GoIN0PDPESuhIiISBwMNxJSXq1Bem4pAGBIN4YbIiKyTKKHm/z8fEydOhVubm6ws7NDVFQUDh06dMP9CwoKMHnyZISFhUEul2P+/PkdV6yJ23u2GDoB6OrZCX7OtmKXQ0REJApRw01paSni4uKgVCqxbds2nDx5Eu+++y6cnZ1veIxarYaHhwdeeOEF9O7du+OKNQO7sooAAEPZa0NERBbMSsw3f/PNNxEQEIA1a9botwUHB7d6THBwMN5//30AwOrVq41ZnlkRBIHjbYiIiCByuNm8eTPGjBmDiRMnYteuXfDz88OcOXMwa9Ysg72HWq2GWq3Wf11RUQEA0Gg00Gg0BnufxnP+9b8dKbOwEpcr1LBRyhHt52CUGsRsX0eRehvZPvMn9TayfebPWG1sz/lkgiAIBn33drCxsQEALFy4EBMnTkRqairmz5+PlStXYtq0aTc9ftiwYYiKisKyZctuuE9iYiKWLFnSbPu6detgZ2d3y7Wbmj/zZdicq0Cksw6zI3Ril0NERGRQ1dXVmDx5MsrLy+Ho6NjqvqKGG2tra8TExCA5OVm/bd68eUhLS0NKSspNj29LuGmp5yYgIADFxcU3/ea0l0ajwfbt2xEfHw+lsmPXdJq25iBSsq/ipQnhmNY/0CjvIWb7OorU28j2mT+pt5HtM3/GamNFRQXc3d3bFG5EvS3l4+ODyMjIJtsiIiKwYcMGg72HSqWCSqVqtl2pVBrtB8uY525JZY0GBy/UPwI+PNzL6O/d0e0Tg9TbyPaZP6m3ke0zf4ZuY3vOJerTUnFxccjMzGyyLSsrC0FBQSJVZJ72nCmGRisgxN0enT06iV0OERGRqETtuVmwYAEGDhyIpUuXYtKkSUhNTcWqVauwatUq/T6LFy9Gfn4+vvzyS/22I0eOAACuXbuGK1eu4MiRI7C2tm7WC2Qp/jh1GQAwMtxT5EqIiIjEJ2q4iY2NxaZNm7B48WK88sorCAkJwbJlyzBlyhT9PgUFBcjNzW1yXHR0tP7/Dx06hHXr1iEoKAjnz5/vqNJNhlYnICmz/hHwkRFeIldDREQkPlHDDQAkJCQgISHhhq+vXbu22TYRx0CbnPTcUlytqoWjjRVigl3ELoeIiEh0oi+/QLfnj1P1sxIPC/PkKuBERERguDF7fzaOt4ngeBsiIiKA4cas5ZZU40zRNSjkMgzrxnBDREQEMNyYtcanpGKDXeBkJ+35EoiIiNqK4caM/Xm6PtyM4lNSREREegw3ZqqiRoMD2VcB8BFwIiKiv2K4MVN/nrqMOp2ALp6dEOJuL3Y5REREJoPhxkxtyygEAIzr4S1yJURERKaF4cYMVdfWYVdW/azEYxluiIiImmC4MUNJmVegrtMh0NUOkT6tL/tORERkaRhuzNC24/+9JSWTyUSuhoiIyLQw3JiZGo0WOxrmt+EtKSIiouYYbszM3jPFqKrVwsfJBr39ncUuh4iIyOQw3JiZxltSY7p7Qy7nLSkiIqL/xXBjRmo0Wvx+ko+AExERtYbhxowkZV5BZU0dfJxsEBvsKnY5REREJonhxoxsPpoPALirty9vSREREd0Aw42ZqKzR4I9TRQCAu6J8Ra6GiIjIdDHcmInfTlxGbZ0OXTw7ceI+IiKiVjDcmImfjtTfkrq7ty8n7iMiImoFw40ZuFKpxr6zxQB4S4qIiOhmGG7MwM/HLkEnAFEBzghysxe7HCIiIpPGcGMGvj94EQBwD3ttiIiIborhxsQdzy/HyYIKWCvkuCfaT+xyiIiITB7DjYn7z8E8AMDo7l5wtrMWuRoiIiLTx3Bjwmo0WvyYXv+U1IOxASJXQ0REZB4YbkzYbycKUVFTBz9nW8SFuotdDhERkVlguDFhjbekHujrz+UWiIiI2ojhxkTlXa3GvrMlkMmAiTH+YpdDRERkNhhuTNTX+y8AAAZ1cYe/i53I1RAREZkPhhsTdL1Wi2/T6m9JTR8QLG4xREREZobhxgRtPpqP8usa+LvYYni4p9jlEBERmRWGGxMjCAK+SK6/JTVtQBAUHEhMRETULgw3JubghVKcLKiAykqOSTGc24aIiKi9GG5MzGd7sgEA90T5cUZiIiKiW8BwY0LOXbmG309eBgDMGhIicjVERETmieHGhKzalQ1BAEZFeKGLp4PY5RAREZklhhsTcbmiBpsa1pH6+7DOIldDRERkvhhuTMTqvTmo1eoQG+yCvkGuYpdDRERkthhuTEDxNTW+TKl//PuJoaEiV0NERGTeGG5MwCdJ53Bdo0VvfyeM4KR9REREt4XhRmSXK2rwVcM6Ugviu0Em46R9REREt4PhRmQf7zwLdZ0OMUEuGNrNQ+xyiIiIzB7DjYgulFRhfWr9ApkLR7PXhoiIyBAYbkT0xrbTqNXqMLirOwaGuotdDhERkSQw3IjkQHYJth0vhFwGvDghUuxyiIiIJIPhRgQ6nYDXfjkFAHi4XyDCvDkbMRERkaEw3Ijg27Q8ZOSXw0FlhQXx3cQuh4iISFIYbjpYUWUNXt9W32szP74b3DupRK6IiIhIWhhuOtgrW06isqYOPf2cMGNgsNjlEBERSQ7DTQfaeboIPx8rgFwGvH5fTyjkfPSbiIjI0BhuOkhFjQYv/ngcAPBYXAh6+DmJXBEREZE0Mdx0kMTNJ5Bfdh0BrrYcRExERGREDDcd4JdjBdh4OB9yGfDepCjYq6zELomIiEiyGG6MLL/sOp7flAEAmDOsC2KCXUWuiIiISNpEDzf5+fmYOnUq3NzcYGdnh6ioKBw6dKjVY3bt2oW+ffvCxsYGnTt3xieffNJB1bZPjUaLv399COXXNejl74SnR3UVuyQiIiLJE/X+SGlpKeLi4jB8+HBs27YNnp6eOHfuHJydnW94TE5ODsaPH49Zs2bh66+/xr59+zBnzhx4eHjg/vvv77jib0IQBLz043Ecu1gOFzsllk/uA6VC9CxJREQkeaKGmzfffBMBAQFYs2aNfltwcHCrx3zyyScIDAzEsmXLAAARERE4ePAg3nnnHZMKN2//lonvD12EXAZ88HA0AlztxC6JiIjIIojalbB582bExMRg4sSJ8PT0RHR0ND799NNWj0lJScHo0aObbBszZgwOHjwIjUZjzHJvalP6JeRUAi/+dAIfJ50DALxydw8M7uohal1ERESWRNSem+zsbKxYsQILFy7E888/j9TUVMybNw8qlQrTpk1r8ZjCwkJ4eXk12ebl5YW6ujoUFxfDx8enyWtqtRpqtVr/dUVFBQBAo9EYNAyVXFNj8aYT0ApWAPIhkwGLx4bhwb6+oocuQ2lsh1Ta0xKpt5HtM39SbyPbZ/6M1cb2nE8mCIJg0HdvB2tra8TExCA5OVm/bd68eUhLS0NKSkqLx3Tr1g2PPvooFi9erN+2b98+DBo0CAUFBfD29m6yf2JiIpYsWdLsPOvWrYOdneFuFV2+Dmw6L0d2hQy+9sA4fx3CnEX71hIREUlKdXU1Jk+ejPLycjg6Ora6r6g9Nz4+PoiMjGyyLSIiAhs2bLjhMd7e3igsLGyyraioCFZWVnBzc2u2/+LFi7Fw4UL91xUVFQgICMDo0aNv+s1pr6kaDbZv3474+HgolUqDntsUaCTePkD6bWT7zJ/U28j2mT9jtbHxzktbiBpu4uLikJmZ2WRbVlYWgoKCbnjMgAEDsGXLlibbfv/9d8TExLT4TVSpVFCpmq+8rVQqjfaDZcxzmwKptw+QfhvZPvMn9TayfebP0G1sz7lEHVC8YMEC7N+/H0uXLsXZs2exbt06rFq1CnPnztXvs3jx4ibjb5544glcuHABCxcuxKlTp7B69Wp8/vnnePbZZ8VoAhEREZkYUcNNbGwsNm3ahPXr16NHjx549dVXsWzZMkyZMkW/T0FBAXJzc/Vfh4SEYOvWrUhKSkJUVBReffVVfPDBByb1GDgRERGJR/RFjhISEpCQkHDD19euXdts29ChQ3H48GEjVkVERETmilPmEhERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaQw3BAREZGkMNwQERGRpDDcEBERkaSIvvxCRxMEAUD7lk5vK41Gg+rqalRUVEhytVeptw+QfhvZPvMn9TayfebPWG1s/Nxu/BxvjcWFm8rKSgBAQECAyJUQERFRe1VWVsLJyanVfWRCWyKQhOh0Oly6dAkODg6QyWQGPXdFRQUCAgKQl5cHR0dHg57bFEi9fYD028j2mT+pt5HtM3/GaqMgCKisrISvry/k8tZH1Vhcz41cLoe/v79R38PR0VGyP7SA9NsHSL+NbJ/5k3ob2T7zZ4w23qzHphEHFBMREZGkMNwQERGRpDDcGJBKpcLLL78MlUoldilGIfX2AdJvI9tn/qTeRrbP/JlCGy1uQDERERFJG3tuiIiISFIYboiIiEhSGG6IiIhIUhhuiIiISFIYbtrp448/RkhICGxsbNC3b1/s2bOn1f137dqFvn37wsbGBp07d8Ynn3zSQZW2z+uvv47Y2Fg4ODjA09MT99xzDzIzM1s9JikpCTKZrNmf06dPd1DV7ZOYmNisVm9v71aPMZfrBwDBwcEtXo+5c+e2uL+pX7/du3fjzjvvhK+vL2QyGX788ccmrwuCgMTERPj6+sLW1hbDhg3DiRMnbnreDRs2IDIyEiqVCpGRkdi0aZORWnBzrbVRo9HgH//4B3r27Al7e3v4+vpi2rRpuHTpUqvnXLt2bYvXtaamxsitae5m13DGjBnN6uzfv/9Nz2su1xBAi9dCJpPh7bffvuE5TeUatuVzwVR/Dxlu2uG7777D/Pnz8cILLyA9PR2DBw/GuHHjkJub2+L+OTk5GD9+PAYPHoz09HQ8//zzmDdvHjZs2NDBld/crl27MHfuXOzfvx/bt29HXV0dRo8ejaqqqpsem5mZiYKCAv2frl27dkDFt6Z79+5Nas3IyLjhvuZ0/QAgLS2tSdu2b98OAJg4cWKrx5nq9auqqkLv3r3x0Ucftfj6W2+9hX//+9/46KOPkJaWBm9vb8THx+vXj2tJSkoKHnzwQTzyyCM4evQoHnnkEUyaNAkHDhwwVjNa1Vobq6urcfjwYbz00ks4fPgwNm7ciKysLNx11103Pa+jo2OTa1pQUAAbGxtjNKFVN7uGADB27NgmdW7durXVc5rTNQTQ7DqsXr0aMpkM999/f6vnNYVr2JbPBZP9PRSozfr16yc88cQTTbaFh4cLixYtanH/5557TggPD2+ybfbs2UL//v2NVqOhFBUVCQCEXbt23XCfnTt3CgCE0tLSjivsNrz88stC796927y/OV8/QRCEp59+WggNDRV0Ol2Lr5vT9QMgbNq0Sf+1TqcTvL29hTfeeEO/raamRnBychI++eSTG55n0qRJwtixY5tsGzNmjPDQQw8ZvOb2+t82tiQ1NVUAIFy4cOGG+6xZs0ZwcnIybHEG0FL7pk+fLtx9993tOo+5X8O7775bGDFiRKv7mOo1/N/PBVP+PWTPTRvV1tbi0KFDGD16dJPto0ePRnJycovHpKSkNNt/zJgxOHjwIDQajdFqNYTy8nIAgKur6033jY6Oho+PD0aOHImdO3cau7TbcubMGfj6+iIkJAQPPfQQsrOzb7ivOV+/2tpafP3113jsscduukCsOV2/Rjk5OSgsLGxyfVQqFYYOHXrD30fgxte0tWNMSXl5OWQyGZydnVvd79q1awgKCoK/vz8SEhKQnp7eMQXegqSkJHh6eqJbt26YNWsWioqKWt3fnK/h5cuX8csvv2DmzJk33dcUr+H/fi6Y8u8hw00bFRcXQ6vVwsvLq8l2Ly8vFBYWtnhMYWFhi/vX1dWhuLjYaLXeLkEQsHDhQgwaNAg9evS44X4+Pj5YtWoVNmzYgI0bNyIsLAwjR47E7t27O7Datrvjjjvw5Zdf4rfffsOnn36KwsJCDBw4ECUlJS3ub67XDwB+/PFHlJWVYcaMGTfcx9yu3181/s615/ex8bj2HmMqampqsGjRIkyePLnVxQjDw8Oxdu1abN68GevXr4eNjQ3i4uJw5syZDqy2bcaNG4dvvvkGO3bswLvvvou0tDSMGDECarX6hseY8zX84osv4ODggPvuu6/V/UzxGrb0uWDKv4cWtyr47frffwULgtDqv4xb2r+l7abkySefxLFjx7B3795W9wsLC0NYWJj+6wEDBiAvLw/vvPMOhgwZYuwy223cuHH6/+/ZsycGDBiA0NBQfPHFF1i4cGGLx5jj9QOAzz//HOPGjYOvr+8N9zG369eS9v4+3uoxYtNoNHjooYeg0+nw8ccft7pv//79mwzKjYuLQ58+ffDhhx/igw8+MHap7fLggw/q/79Hjx6IiYlBUFAQfvnll1YDgDleQwBYvXo1pkyZctOxM6Z4DVv7XDDF30P23LSRu7s7FApFs2RZVFTULIE28vb2bnF/KysruLm5Ga3W2/HUU09h8+bN2LlzJ/z9/dt9fP/+/U3yX4gtsbe3R8+ePW9YrzlePwC4cOEC/vjjDzz++OPtPtZcrl/jU27t+X1sPK69x4hNo9Fg0qRJyMnJwfbt21vttWmJXC5HbGysWVxXHx8fBAUFtVqrOV5DANizZw8yMzNv6fdS7Gt4o88FU/49ZLhpI2tra/Tt21f/BEqj7du3Y+DAgS0eM2DAgGb7//7774iJiYFSqTRarbdCEAQ8+eST2LhxI3bs2IGQkJBbOk96ejp8fHwMXJ1xqNVqnDp16ob1mtP1+6s1a9bA09MTEyZMaPex5nL9QkJC4O3t3eT61NbWYteuXTf8fQRufE1bO0ZMjcHmzJkz+OOPP24pVAuCgCNHjpjFdS0pKUFeXl6rtZrbNWz0+eefo2/fvujdu3e7jxXrGt7sc8Gkfw8NNjTZAnz77beCUqkUPv/8c+HkyZPC/PnzBXt7e+H8+fOCIAjCokWLhEceeUS/f3Z2tmBnZycsWLBAOHnypPD5558LSqVS+OGHH8Rqwg39/e9/F5ycnISkpCShoKBA/6e6ulq/z/+277333hM2bdokZGVlCcePHxcWLVokABA2bNggRhNu6plnnhGSkpKE7OxsYf/+/UJCQoLg4OAgievXSKvVCoGBgcI//vGPZq+Z2/WrrKwU0tPThfT0dAGA8O9//1tIT0/XPyn0xhtvCE5OTsLGjRuFjIwM4eGHHxZ8fHyEiooK/TkeeeSRJk8z7tu3T1AoFMIbb7whnDp1SnjjjTcEKysrYf/+/R3ePkFovY0ajUa46667BH9/f+HIkSNNfi/VarX+HP/bxsTEROHXX38Vzp07J6SnpwuPPvqoYGVlJRw4cMCk2ldZWSk888wzQnJyspCTkyPs3LlTGDBggODn5yeZa9iovLxcsLOzE1asWNHiOUz1Grblc8FUfw8Zbtpp+fLlQlBQkGBtbS306dOnyaPS06dPF4YOHdpk/6SkJCE6OlqwtrYWgoODb/jDLTYALf5Zs2aNfp//bd+bb74phIaGCjY2NoKLi4swaNAg4Zdffun44tvowQcfFHx8fASlUin4+voK9913n3DixAn96+Z8/Rr99ttvAgAhMzOz2Wvmdv0aH1X/3z/Tp08XBKH+MdSXX35Z8Pb2FlQqlTBkyBAhIyOjyTmGDh2q37/R999/L4SFhQlKpVIIDw8XNcy11sacnJwb/l7u3LlTf47/beP8+fOFwMBAwdraWvDw8BBGjx4tJCcnd3zjhNbbV11dLYwePVrw8PAQlEqlEBgYKEyfPl3Izc1tcg5zvoaNVq5cKdja2gplZWUtnsNUr2FbPhdM9fdQ1tAAIiIiIkngmBsiIiKSFIYbIiIikhSGGyIiIpIUhhsiIiKSFIYbIiIikhSGGyIiIpIUhhsiIiKSFIYbIiIikhSGGyIyGcOGDcP8+fPFLoOIzBzDDREREUkKww0RmYQZM2Zg165deP/99yGTySCTyXD+/Pk2HXv06FEMHz4cDg4OcHR0RN++fXHw4EH968nJyRgyZAhsbW0REBCAefPmoaqqSv+6Wq3Gc889h4CAAKhUKnTt2hWff/65oZtIRB2E4YaITML777+PAQMGYNasWSgoKEBBQQECAgLadOyUKVPg7++PtLQ0HDp0CIsWLYJSqQQAZGRkYMyYMbjvvvtw7NgxfPfdd9i7dy+efPJJ/fHTpk3Dt99+iw8++ACnTp3CJ598gk6dOhmlnURkfFw4k4hMxrBhwxAVFYVly5a16zhHR0d8+OGHmD59erPXpk2bBltbW6xcuVK/be/evRg6dCiqqqqQm5uLsLAwbN++HaNGjbrdJhCRCbASuwAiotu1cOFCPP744/jqq68watQoTJw4EaGhoQCAQ4cO4ezZs/jmm2/0+wuCAJ1Oh5ycHGRkZEChUGDo0KFilU9EBsbbUkRk9hITE3HixAlMmDABO3bsQGRkJDZt2gQA0Ol0mD17No4cOaL/c/ToUZw5cwahoaGwtbUVuXoiMjT23BCRybC2toZWq72lY7t164Zu3bphwYIFePjhh7FmzRrce++96NOnD06cOIEuXbq0eFzPnj2h0+mwa9cu3pYikgj23BCRyQgODsaBAwdw/vx5FBcXQ6fT3fSY69ev48knn0RSUhIuXLiAffv2IS0tDREREQCAf/zjH0hJScHcuXNx5MgRnDlzBps3b8ZTTz2lf8/p06fjsccew48//oicnBwkJSXhP//5j1HbSkTGw3BDRCbj2WefhUKhQGRkJDw8PJCbmwugPoAkJia2eIxCoUBJSQmmTZuGbt26YdKkSRg3bhyWLFkCAOjVqxd27dqFM2fOYPDgwYiOjsZLL70EHx8f/TlWrFiBBx54AHPmzEF4eDhmzZrV5FFxIjIvfFqKiEza9evX4erqiq1bt2L48OFil0NEZoA9N0Rk0nbt2oURI0Yw2BBRm7HnhoiIiCSFPTdEREQkKQw3REREJCkMN0RERCQpDDdEREQkKQw3REREJCkMN0RERCQpDDdEREQkKQw3REREJCkMN0RERCQpDDdEREQkKf8PPUxdGtaVtKIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def simulate():\n",
    "    t = np.linspace(0, 20, 1000)\n",
    "    res = scipy.integrate.solve_ivp(\n",
    "        fun=lambda t, x: f_eval(x, [1, 0], p0),\n",
    "        t_span=[t[0], t[-1]], t_eval=t, y0=[6, 0.1, 0, 0])\n",
    "    \n",
    "    plt.figure()\n",
    "    plt.plot(res.t, res.y.T[:, 0])\n",
    "    plt.xlabel('t, sec')\n",
    "    plt.ylabel('V, m/s')\n",
    "    plt.grid()\n",
    "    plt.title('Velocity');\n",
    "    \n",
    "    plt.figure()\n",
    "    plt.plot(res.t, np.rad2deg(res.y.T[:, 1]))\n",
    "    plt.xlabel('t, sec')\n",
    "    plt.ylabel('$\\\\alpha$, deg')\n",
    "    plt.grid()\n",
    "    plt.title('Angle of Attack');\n",
    " \n",
    "    plt.figure()\n",
    "    plt.plot(res.t, np.rad2deg(res.y.T[:, 2]))\n",
    "    plt.xlabel('t, sec')\n",
    "    plt.ylabel('$\\\\gamma$, deg')\n",
    "    plt.grid()\n",
    "    plt.title('Flight Path Angle');\n",
    "    \n",
    "    plt.figure()\n",
    "    plt.plot(res.t, np.rad2deg(res.y.T[:, 3]))\n",
    "    plt.xlabel('t, sec')\n",
    "    plt.ylabel('Q, deg/s')\n",
    "    plt.grid()\n",
    "    plt.title('Pitch Rate');\n",
    "simulate()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea5a2d2c-94f3-4500-b2e5-94390e597625",
   "metadata": {},
   "source": [
    "# Aircraft Trim\n",
    "\n",
    "Finding equilibrium $x_0$, $u_0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "d1206357-4355-4461-ac02-3bbec719f7c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# trim cost, penalize state derivatives\n",
    "trim_cost = sympy.Matrix([\n",
    "    f[0]**2 + f[1]**2 + f[2]**2 + f[3]**2])\n",
    "\n",
    "# calculate trim cost\n",
    "trim_steady_level_obj = sympy.lambdify(\n",
    "    [[alpha, th, elv], V, params.keys()],\n",
    "    trim_cost.subs({\n",
    "        gamma:0,\n",
    "        Q: 0\n",
    "    })[0])\n",
    "\n",
    "# calculate trim cost jacobian\n",
    "trim_steady_level_jac = sympy.lambdify(\n",
    "    [[alpha, th, elv], V, params.keys()],\n",
    "    trim_cost.subs({\n",
    "        gamma:0,\n",
    "        Q: 0\n",
    "    }).jacobian([alpha, th, elv])[:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "e443d33f-9d43-41af-bca3-f0ef446da070",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      fun: 7.514775069826027e-25\n",
      " hess_inv: <3x3 LbfgsInvHessProduct with dtype=float64>\n",
      "      jac: array([-7.01237904e-12, -1.04825328e-12, -6.94135125e-12])\n",
      "  message: 'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH'\n",
      "     nfev: 20\n",
      "      nit: 15\n",
      "     njev: 20\n",
      "   status: 0\n",
      "  success: True\n",
      "        x: array([ 0.02021962,  1.99600204, -0.07978038])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{V(t): 10,\n",
       " alpha(t): 0.02021962262929675,\n",
       " gamma(t): 0,\n",
       " Q(t): 0,\n",
       " th: 1.9960020419541868,\n",
       " elv: -0.07978037737079575}"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def do_trim(V_0, p0):\n",
    "    trim_res = scipy.optimize.minimize(\n",
    "        fun=lambda x_d: trim_steady_level_obj(\n",
    "            x_d, V_0, p0),\n",
    "        # increases solver performance if you can\n",
    "        # privde jacobian of the cost function, which\n",
    "        # we can\n",
    "        jac=lambda x_d: trim_steady_level_jac(\n",
    "            x_d, V_0, p0),\n",
    "        x0 = [0, 1, 0],\n",
    "        tol=np.finfo(float).eps, bounds=[\n",
    "            [-1, 1],  # alpha bounds, rad\n",
    "            [0, 5],   # throttle bounds, N\n",
    "            [-1, 1]], # elevator bounds, rad\n",
    "        #method='Nelder-Mead'\n",
    "    )\n",
    "    print(trim_res)\n",
    "    alpha_0, th_0, elv_0 = trim_res.x\n",
    "    trim = {\n",
    "        V: V_0,\n",
    "        alpha: alpha_0,\n",
    "        gamma: 0,\n",
    "        Q: 0,\n",
    "        th: th_0,\n",
    "        elv: elv_0\n",
    "    }\n",
    "    return trim\n",
    "\n",
    "trim = do_trim(V_0=10, p0=p0)\n",
    "trim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "9595b46f-9133-4415-8dff-776674fe5bef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}-0.399118807992998 & -5.94456905301602 & -9.8 & 0\\\\-0.196807113162693 & -18.1754405960036 & 0 & 1\\\\0.196807113162693 & 18.1754405960036 & 0 & 0\\\\-1.13328183642958 \\cdot 10^{-13} & -6.125 & 0 & -6.125\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[   -0.399118807992998, -5.94456905301602, -9.8,      0],\n",
       "[   -0.196807113162693, -18.1754405960036,    0,      1],\n",
       "[    0.196807113162693,  18.1754405960036,    0,      0],\n",
       "[-1.13328183642958e-13,            -6.125,    0, -6.125]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = f.jacobian(x).subs(trim).subs(params)\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "29570604-e896-49ad-964c-cd3b9034efde",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.999795590394625 & 0\\\\0.00202182449154941 & 0\\\\-0.00202182449154941 & 0\\\\0 & 6.125\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[   0.999795590394625,     0],\n",
       "[ 0.00202182449154941,     0],\n",
       "[-0.00202182449154941,     0],\n",
       "[                   0, 6.125]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = f.jacobian(u).subs(trim).subs(params)\n",
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "02d55662-efb8-4944-bc98-c655b40e8bb5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}V{\\left(t \\right)} & \\alpha{\\left(t \\right)} & \\gamma{\\left(t \\right)} & Q{\\left(t \\right)} & V{\\left(t \\right)} \\sin{\\left(\\gamma{\\left(t \\right)} \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([[V(t), alpha(t), gamma(t), Q(t), V(t)*sin(gamma(t))]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "19b7aaa3-4bb4-4e79-a45f-5ed40ecfbab7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0 & 0 & 0\\\\0 & 1 & 0 & 0\\\\0 & 0 & 1 & 0\\\\0 & 0 & 0 & 1\\\\0 & 0 & 10 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1, 0,  0, 0],\n",
       "[0, 1,  0, 0],\n",
       "[0, 0,  1, 0],\n",
       "[0, 0,  0, 1],\n",
       "[0, 0, 10, 0]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = y.jacobian(x).subs(trim).subs(params)\n",
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "bbbf744c-9260-4660-9c3d-7b0f58d96d0d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0\\\\0 & 0\\\\0 & 0\\\\0 & 0\\\\0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0, 0],\n",
       "[0, 0],\n",
       "[0, 0],\n",
       "[0, 0],\n",
       "[0, 0]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D = y.jacobian(u).subs(trim).subs(params)\n",
    "D"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "917747d3-d62f-40c9-85b4-f187b3d670db",
   "metadata": {},
   "source": [
    "Now we can obtain the transfer function matrix relating all inputs to all outputs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "8f0fb1fd-3d40-4a96-a5e3-91829cf3ed96",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\n",
       "\\left(\\begin{array}{rllrllrllrll|rllrll}\n",
       "-0.&\\hspace{-1em}399&\\hspace{-1em}\\phantom{\\cdot}&-5.&\\hspace{-1em}94&\\hspace{-1em}\\phantom{\\cdot}&-9.&\\hspace{-1em}8&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&1\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "-0.&\\hspace{-1em}197&\\hspace{-1em}\\phantom{\\cdot}&-18.&\\hspace{-1em}2&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&1\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0.&\\hspace{-1em}00202&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "0.&\\hspace{-1em}197&\\hspace{-1em}\\phantom{\\cdot}&18.&\\hspace{-1em}2&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&-0.&\\hspace{-1em}00202&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "-1.&\\hspace{-1em}13&\\hspace{-1em}\\cdot10^{-13}&-6.&\\hspace{-1em}12&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&-6.&\\hspace{-1em}12&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&6.&\\hspace{-1em}12&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "\\hline\n",
       "1\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&1\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&1\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&1\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&10\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "\\end{array}\\right)\n",
       "\\]"
      ],
      "text/plain": [
       "<LinearIOSystem:sys[2]:['u[0]', 'u[1]']->['y[0]', 'y[1]', 'y[2]', 'y[3]', 'y[4]']>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys_aircraft = control.ss(A, B, C, D)\n",
    "sys_aircraft"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "9d06cb7c-e33e-47d5-86bd-956e11226734",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}th & elv\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([[th, elv]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "ec2c812a-103c-494c-bdec-44f07506c480",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}V{\\left(t \\right)} & \\alpha{\\left(t \\right)} & \\gamma{\\left(t \\right)} & Q{\\left(t \\right)} & V{\\left(t \\right)} \\sin{\\left(\\gamma{\\left(t \\right)} \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([[V(t), alpha(t), gamma(t), Q(t), V(t)*sin(gamma(t))]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "69476f1c-9c91-4458-98fb-a8aa01e6f68c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\begin{bmatrix}\\frac{0.9998 s^3 + 24.3 s^2 + 117.5 s + 0.1214}{s^4 + 24.7 s^3 + 127.9 s^2 + 51.52 s + 11.81}&\\frac{1.018 \\times 10^{-14} s^2 - 36.41 s - 1091}{s^4 + 24.7 s^3 + 127.9 s^2 + 51.52 s + 11.81}&\\\\\\frac{0.002022 s^3 - 0.1836 s^2 - 1.2 s - 7.105 \\times 10^{-15}}{s^4 + 24.7 s^3 + 127.9 s^2 + 51.52 s + 11.81}&\\frac{6.125 s^2 + 2.445 s + 11.81}{s^4 + 24.7 s^3 + 127.9 s^2 + 51.52 s + 11.81}&\\\\\\frac{-0.002022 s^3 + 0.1836 s^2 + 1.188 s + 1.2}{s^4 + 24.7 s^3 + 127.9 s^2 + 51.52 s + 11.81}&\\frac{-3.153 \\times 10^{-17} s^2 + 111.3 s + 37.27}{s^4 + 24.7 s^3 + 127.9 s^2 + 51.52 s + 11.81}&\\\\\\frac{-2.22 \\times 10^{-16} s^3 - 0.01238 s^2 + 1.2 s + 3.622 \\times 10^{-15}}{s^4 + 24.7 s^3 + 127.9 s^2 + 51.52 s + 11.81}&\\frac{6.125 s^3 + 113.8 s^2 + 49.08 s - 2.611 \\times 10^{-12}}{s^4 + 24.7 s^3 + 127.9 s^2 + 51.52 s + 11.81}&\\\\\\frac{-0.02022 s^3 + 1.836 s^2 + 11.88 s + 12}{s^4 + 24.7 s^3 + 127.9 s^2 + 51.52 s + 11.81}&\\frac{1113 s + 372.7}{s^4 + 24.7 s^3 + 127.9 s^2 + 51.52 s + 11.81}&\\\\ \\end{bmatrix}$$"
      ],
      "text/plain": [
       "TransferFunction([[array([  0.99979559,  24.30326836, 117.47331023,   0.12136002]), array([ 1.01803188e-14, -3.64104854e+01, -1.09098082e+03])], [array([ 2.02182449e-03, -1.83576261e-01, -1.20025461e+00, -7.10542736e-15]), array([ 6.125     ,  2.4446027 , 11.81334697])], [array([-0.00202182,  0.18357626,  1.18787093,  1.20025461]), array([-3.15312118e-17,  1.11324574e+02,  3.72658886e+01])], [array([-2.21999217e-16, -1.23836750e-02,  1.20025461e+00,  3.62210262e-15]), array([ 6.12500000e+00,  1.13769176e+02,  4.90792356e+01, -2.61124455e-12])], [array([-0.02021824,  1.83576261, 11.87870931, 12.00254606]), array([1113.24573651,  372.65888606])]], [[array([  1.        ,  24.6995594 , 127.90711277,  51.52383827,\n",
       "        11.81334697]), array([  1.        ,  24.6995594 , 127.90711277,  51.52383827,\n",
       "        11.81334697])], [array([  1.        ,  24.6995594 , 127.90711277,  51.52383827,\n",
       "        11.81334697]), array([  1.        ,  24.6995594 , 127.90711277,  51.52383827,\n",
       "        11.81334697])], [array([  1.        ,  24.6995594 , 127.90711277,  51.52383827,\n",
       "        11.81334697]), array([  1.        ,  24.6995594 , 127.90711277,  51.52383827,\n",
       "        11.81334697])], [array([  1.        ,  24.6995594 , 127.90711277,  51.52383827,\n",
       "        11.81334697]), array([  1.        ,  24.6995594 , 127.90711277,  51.52383827,\n",
       "        11.81334697])], [array([  1.        ,  24.6995594 , 127.90711277,  51.52383827,\n",
       "        11.81334697]), array([  1.        ,  24.6995594 , 127.90711277,  51.52383827,\n",
       "        11.81334697])]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G_aircraft = control.ss2tf(sys_aircraft)\n",
    "G_aircraft"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3ec379b-92e0-4abe-be5b-e7449fec899c",
   "metadata": {},
   "source": [
    "## Velocity due to Thrust Transfer Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "dfa85f52-82ea-42c3-a395-36fd5fce5533",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}V{\\left(t \\right)} & \\alpha{\\left(t \\right)} & \\gamma{\\left(t \\right)} & Q{\\left(t \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([[V(t), alpha(t), gamma(t), Q(t)]])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "b3f05737-f012-4c3f-ac35-c57fdf67c3d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}th & elv\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([[th, elv]])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "549d9c62-79e8-4054-98c6-2c2670dab974",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}V{\\left(t \\right)} & \\alpha{\\left(t \\right)} & \\gamma{\\left(t \\right)} & Q{\\left(t \\right)} & V{\\left(t \\right)} \\sin{\\left(\\gamma{\\left(t \\right)} \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([[V(t), alpha(t), gamma(t), Q(t), V(t)*sin(gamma(t))]])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "9a14eb14-9870-4ef1-b5ce-38327b594614",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "thrust -> climb rate\n",
      "closed loop poles:  [-32.60327074+0.j         -16.1008773 +0.j\n",
      "  -6.45019155+3.61200721j  -6.45019155-3.61200721j\n",
      "  -1.30902212+1.49448172j  -1.30902212-1.49448172j\n",
      "  -0.47698403+0.j        ]\n",
      "1 states have been removed from the model\n",
      "Kv 15.240235594045403\n",
      "ess 0.06561578355066346\n",
      "G:\n",
      "\n",
      "        -0.2022 s^3 + 18.36 s^2 + 118.8 s + 120\n",
      "-------------------------------------------------------\n",
      "s^5 + 34.7 s^4 + 374.9 s^3 + 1331 s^2 + 527.1 s + 118.1\n",
      "\n",
      "G_c:\n",
      "\n",
      "         -12.13 s^5 + 916.5 s^4 + 2.383e+04 s^3 + 1.242e+05 s^2 + 1.633e+05 s + 5.401e+04\n",
      "---------------------------------------------------------------------------------------------------\n",
      "s^7 + 64.7 s^6 + 1404 s^5 + 1.349e+04 s^4 + 6.428e+04 s^3 + 1.401e+05 s^2 + 1.668e+05 s + 5.401e+04\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def thrust_to_velocity_controller_analysis(G_aircraft):\n",
    "    print('thrust -> climb rate')\n",
    "    t = np.linspace(0, 20, 1000)\n",
    "    tol = 1e-2\n",
    "    s = control.tf([1, 0], [1])\n",
    "    G_a = 1/(s/10 + 1) # actuator, first order plant representing electric motor\n",
    "    G = G_aircraft[4, 0]*G_a  # plant, Q due to d_e * Servo transfer function\n",
    "    lowpass = 1/(s/30 + 1)\n",
    "    H = 30 + 15/s + 1*s*lowpass  # PID controller with low pass filter\n",
    "    G_o = G*H  # open loop\n",
    "    G_c = control.feedback(G_o) # closed loop\n",
    "    print('closed loop poles: ', control.pole(G_c))\n",
    "\n",
    "    r = 0.1*np.ones(len(t))\n",
    "    res = control.forced_response(G_c, T=t, U=r);\n",
    "    y = res.y[0, :]\n",
    "\n",
    "    Kv = np.real(control.minreal(s*G_o)(0))\n",
    "    print('Kv', Kv)\n",
    "\n",
    "    print('ess', 1/Kv)\n",
    "    print('G:')\n",
    "    print(G)\n",
    "\n",
    "    print('G_c:')\n",
    "    print(G_c)\n",
    "    plt.rcParams['figure.figsize'] = (8, 4)\n",
    "\n",
    "    plt.figure()\n",
    "    plt.plot(t, y, label='y') # don't forget these are deviations from trim\n",
    "    plt.plot(t, r, label='r') # don't forget these are deviations from trim\n",
    "    plt.hlines(0, t[0], t[-1], linestyles='--', label='trim')\n",
    "    plt.legend()\n",
    "    plt.grid()\n",
    "    plt.xlabel('t, sec')\n",
    "    plt.ylabel('$\\dot{h}$, m/s')\n",
    "    plt.title('Climb Rate')\n",
    "\n",
    "    plt.figure()\n",
    "    e = r - y\n",
    "    plt.plot(t, e)\n",
    "    plt.grid()\n",
    "    plt.xlabel('t, sec')\n",
    "    plt.ylabel('error, m/s')\n",
    "    plt.title('Climb Rate Error')\n",
    "\n",
    "    plt.figure()\n",
    "    res = control.forced_response(H*G_a, U=e, T=t);\n",
    "    u = res.y[0, :]\n",
    "\n",
    "    plt.plot(t, u + trim[th], label='u')  # don't forget these are deviations from trim\n",
    "    plt.hlines(trim[th], t[0], t[-1], linestyles='--', label='trim')\n",
    "    plt.legend()\n",
    "    plt.grid()\n",
    "    plt.xlabel('t, sec')\n",
    "    plt.ylabel('thrust, N')\n",
    "    plt.title('Thrust Output')\n",
    "\n",
    "    plt.figure()\n",
    "    control.rlocus(G, xlim=[-4, 1], ylim=[-2, 2])\n",
    "    rvect, kvect = control.rlocus(G, kvect=[1], plot=False)\n",
    "    h = plt.plot(np.real(rvect), np.imag(rvect),  marker='s', color='r', alpha=0.5)\n",
    "    plt.legend([h[0]], ['CL poles'])\n",
    "    plt.title('uncompensated root locus')\n",
    "\n",
    "    plt.figure()\n",
    "    control.rlocus(G*H, xlim=[-4, 1], ylim=[-2, 2])\n",
    "    rvect, kvect = control.rlocus(G*H, kvect=[1], plot=False)\n",
    "    h = plt.plot(np.real(rvect), np.imag(rvect),  marker='s', color='r', alpha=0.5)\n",
    "    plt.legend([h[0]], ['CL poles'])\n",
    "    plt.title('compensated root locus')\n",
    "    return locals()\n",
    "    \n",
    "data = thrust_to_velocity_controller_analysis(G_aircraft)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "id": "e6741dfe-878d-483e-98ee-f018cea4bb46",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{-3.153 \\times 10^{-17} s^2 + 111.3 s + 37.27}{s^4 + 24.7 s^3 + 127.9 s^2 + 51.52 s + 11.81}$$"
      ],
      "text/plain": [
       "TransferFunction(array([-3.15312118e-17,  1.11324574e+02,  3.72658886e+01]), array([  1.        ,  24.6995594 , 127.90711277,  51.52383827,\n",
       "        11.81334697]))"
      ]
     },
     "execution_count": 223,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G = G_aircraft[2, 1]\n",
    "G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "95f980ad-cdad-4a0e-92e3-c72976195f06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{- \\frac{C_{D0} S \\rho V^{2}{\\left(t \\right)}}{2} - \\frac{C_{L0}^{2} S k_{CLCD} \\rho V^{2}{\\left(t \\right)}}{2} - C_{L0} C_{La} S k_{CLCD} \\rho V^{2}{\\left(t \\right)} \\alpha{\\left(t \\right)} - \\frac{C_{La}^{2} S k_{CLCD} \\rho V^{2}{\\left(t \\right)} \\alpha^{2}{\\left(t \\right)}}{2} - g m \\sin{\\left(\\gamma{\\left(t \\right)} \\right)} + th \\cos{\\left(\\alpha{\\left(t \\right)} \\right)}}{m}\\\\\\frac{- \\frac{S \\rho \\left(C_{L0} + C_{La} \\alpha{\\left(t \\right)}\\right) V^{2}{\\left(t \\right)}}{2} + g m \\cos{\\left(\\gamma{\\left(t \\right)} \\right)} + m Q{\\left(t \\right)} V{\\left(t \\right)} + th \\sin{\\left(\\alpha{\\left(t \\right)} \\right)}}{m V{\\left(t \\right)}}\\\\\\frac{\\frac{S \\rho \\left(C_{L0} + C_{La} \\alpha{\\left(t \\right)}\\right) V^{2}{\\left(t \\right)}}{2} - g m \\cos{\\left(\\gamma{\\left(t \\right)} \\right)} - th \\sin{\\left(\\alpha{\\left(t \\right)} \\right)}}{m V{\\left(t \\right)}}\\\\\\frac{S \\rho \\left(C_{M0} + C_{MQ} Q{\\left(t \\right)} + C_{Ma} \\alpha{\\left(t \\right)} + C_{Me} elv\\right) V^{2}{\\left(t \\right)}}{2 J_{y}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[(-C_D0*S*rho*V(t)**2/2 - C_L0**2*S*k_CLCD*rho*V(t)**2/2 - C_L0*C_La*S*k_CLCD*rho*V(t)**2*alpha(t) - C_La**2*S*k_CLCD*rho*V(t)**2*alpha(t)**2/2 - g*m*sin(gamma(t)) + th*cos(alpha(t)))/m],\n",
       "[                                                                                 (-S*rho*(C_L0 + C_La*alpha(t))*V(t)**2/2 + g*m*cos(gamma(t)) + m*Q(t)*V(t) + th*sin(alpha(t)))/(m*V(t))],\n",
       "[                                                                                                (S*rho*(C_L0 + C_La*alpha(t))*V(t)**2/2 - g*m*cos(gamma(t)) - th*sin(alpha(t)))/(m*V(t))],\n",
       "[                                                                                                                     S*rho*(C_M0 + C_MQ*Q(t) + C_Ma*alpha(t) + C_Me*elv)*V(t)**2/(2*J_y)]])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f"
   ]
  }
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