KvN_NumCuad.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Bad key text.latex.unicode in file /home/arurz/.local/lib/python3.6/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle, line 112 ('text.latex.unicode : False # use \"ucs\" and \"inputenc\" LaTeX packages for handling')\n",
      "You probably need to get an updated matplotlibrc file from\n",
      "https://github.com/matplotlib/matplotlib/blob/v3.3.0/matplotlibrc.template\n",
      "or from the matplotlib source distribution\n",
      "\n",
      "Bad key savefig.frameon in file /home/arurz/.local/lib/python3.6/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle, line 423 ('savefig.frameon : True')\n",
      "You probably need to get an updated matplotlibrc file from\n",
      "https://github.com/matplotlib/matplotlib/blob/v3.3.0/matplotlibrc.template\n",
      "or from the matplotlib source distribution\n",
      "\n",
      "Bad key pgf.debug in file /home/arurz/.local/lib/python3.6/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle, line 444 ('pgf.debug           : False')\n",
      "You probably need to get an updated matplotlibrc file from\n",
      "https://github.com/matplotlib/matplotlib/blob/v3.3.0/matplotlibrc.template\n",
      "or from the matplotlib source distribution\n",
      "\n",
      "Bad key verbose.level in file /home/arurz/.local/lib/python3.6/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle, line 475 ('verbose.level  : silent      # one of silent, helpful, debug, debug-annoying')\n",
      "You probably need to get an updated matplotlibrc file from\n",
      "https://github.com/matplotlib/matplotlib/blob/v3.3.0/matplotlibrc.template\n",
      "or from the matplotlib source distribution\n",
      "\n",
      "Bad key verbose.fileo in file /home/arurz/.local/lib/python3.6/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle, line 476 ('verbose.fileo  : sys.stdout  # a log filename, sys.stdout or sys.stderr')\n",
      "You probably need to get an updated matplotlibrc file from\n",
      "https://github.com/matplotlib/matplotlib/blob/v3.3.0/matplotlibrc.template\n",
      "or from the matplotlib source distribution\n",
      "In /home/arurz/.local/lib/python3.6/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
      "The text.latex.preview rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "In /home/arurz/.local/lib/python3.6/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
      "The mathtext.fallback_to_cm rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "In /home/arurz/.local/lib/python3.6/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: Support for setting the 'mathtext.fallback_to_cm' rcParam is deprecated since 3.3 and will be removed two minor releases later; use 'mathtext.fallback : 'cm' instead.\n",
      "In /home/arurz/.local/lib/python3.6/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
      "The validate_bool_maybe_none function was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "In /home/arurz/.local/lib/python3.6/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
      "The savefig.jpeg_quality rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "In /home/arurz/.local/lib/python3.6/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
      "The keymap.all_axes rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "In /home/arurz/.local/lib/python3.6/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
      "The animation.avconv_path rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "In /home/arurz/.local/lib/python3.6/site-packages/matplotlib/mpl-data/stylelib/_classic_test.mplstyle: \n",
      "The animation.avconv_args rcparam was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
      "┌ Info: Precompiling DifferentialEquations [0c46a032-eb83-5123-abaf-570d42b7fbaa]\n",
      "└ @ Base loading.jl:1260\n"
     ]
    }
   ],
   "source": [
    "using PyCall\n",
    "using PyPlot\n",
    "using DifferentialEquations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "rc(\"text\", usetex=true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PyObject <module 'mpmath' from '/home/arurz/.local/lib/python3.6/site-packages/mpmath/__init__.py'>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spy = pyimport(\"scipy.interpolate\")\n",
    "np = pyimport(\"numpy\")\n",
    "mp = pyimport(\"mpmath\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "γ = 1;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "k (generic function with 1 method)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function k(t)\n",
    "    return 1/(γ+2*t)^2\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "cuad! (generic function with 1 method)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function cuad!(du,u,p,t)\n",
    " du[1] = u[2]\n",
    " du[2] = (1/u[1]^3)-k(t)*u[1]\n",
    " du[3] = (1/u[1]^2)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "u0 = [1.0;0.0;0.0]\n",
    "tspan = (0.0,20)\n",
    "prob = ODEProblem(cuad!,u0,tspan)\n",
    "sol = solve(prob,Vern7(),dt=0.00000000001)\n",
    ";"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = np.linspace(np.min(sol.t), np.max(sol.t), 200)  \n",
    "\n",
    "spl1 = spy.make_interp_spline(sol.t, sol'[:,1], k=3)\n",
    "spl2 = spy.make_interp_spline(sol.t, sol'[:,2], k=3)\n",
    "spl3 = spy.make_interp_spline(sol.t, sol'[:,3], k=3)\n",
    "\n",
    "ps1 = spl1(t)\n",
    "ps2 = spl2(t)\n",
    "ps3 = spl3(t)\n",
    "\n",
    ";"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AA2oUhYhyzLlzInB/+UsRuomm9Z4zR3SeCtVyP/tZdp4ifUs5gPft24eOjg44HA60tbVNum9JSQlKSkpQWVmJqqoqAEBPTw9aWlpQU1ODjo4ODjJOlOeCQVHL/eUvgV/8QtwiNO5CWpRbbokE7u//PjB/fmbLSpSKlAJ4165dWLlyJV588cUZH6OyshJ79uyBLMvYtm0b3G43L0sT5Zn+fjGhQaiWe/Zs/P2KikTnqdAtQjfemNlyEqlpxgHc09ODHTt2YP369aoUxGQyYf/+/Xj66acZwEQ5LhgEDh0SNdxf/lK05SYaCGPNGuCee4Avfxn44hfFrEJEuWDGATy+bVdN27ZtS8txiUhbg4ORWu4vfylmFYpn4UIxkcE994iaLm8RolzFjvhElBaKImYOCtVy33wzcS33s5+N1HLvuIO1XMoPaQngHTt2oLW1NWZ7Z2cnysvLsW7dunS8LRFpTJbFMI+hWm5fX/z9FiwQtwaFarkrVmS0mES6kHIA9/T0oLOzExs2bAgHq5Kgy2JVVRU6OzvR1NSE3bt3p/rWRKQxRQF+9zvghRdE4L7xRuL7cm+5RdRw77lH1HLnzMlsWYn0JuUAliQJDocjPMiG3W7HwMAAjhw5grVr18bsX1VVhQ0bNuDRRx/F9773vVTfnogybHgY+PWvgeefF8snn8Tfb/58Ucv98pfFwr6VRNFSDuCqqioEg0H4fD54vV50dXXB4/Fg/fr1MBgMsNvtsFqt2Lp1K+666y4A4n7g/kR30xOR7nzyiQG/+tVN+NGPFuCVVxKPsXzzzZFa7p13cq5cosmo1gZstVphtVoBANu3b4fL5YLH44HX60VLSwtcLhcMBgOsVivMZjPkRHOBEZHmxsbErUHPPy8uL//2tyUAYq9ozZkD3HUXcO+9InTN5syXlShbpa0XdGVlJRwOBxwOBwDRVuzxeODz+QAAbrc7XW9NRDMgy2LIx+efF+25iS5SVVSIwL3vPnGJecGCjBaTKGekJYDr6+tjtoUCmYj0QVGADz+MtOW+9lr8DlQGA2CzjWLVqqP47ndvwJ13FnGMZSIVpCWAQ+M8E5G+XLkCvPJKJHQlKf5+RUViqMd77xVtunPmXMCBAx/httuWMnyJVJLSUJRut1vV24kOHz4Mr9fL3tFEKurrE4NhPP+8uEf3woX4+61cCXzlKyJ077wzejAMdtkgUl9KQ1Fu374dNTU1cLvdWJHinfSPPPIIJEnC448/ntJxiPKdogC//S3w3HNi6eqKv9+sWWIGofvuE6H7mc9ktpxE+S6lS9Dr169Ha2srtm/fDoPBAKfTiS1btkz79cePH8cTTzyBp59+Gk6nk+FLNENXrwIHDkRC98SJ+PstWiR6K997L7B1K1BSktlyElFEym3AoVmMOjs70dbWhtraWlgsFmzYsAEWiwUmkym8ryzL6O/vh8/nQ9e1P8sdDge6urpQwm8CoqQMDIjeys89J6bwCwTi77d2beTS8saNgNGY2XISUXyqdcKqqqpCVVVVuEZ78OBBHDt2DJIkYWBgAABQVlYGs9kMu92OPXv2qDaVIVG+8PsjtdxXX43fa7mwUNyb+9WvisvLnDOXSJ/S0gt627ZtnFaQSAVjY8Dbb0dC97334u9XWipquPffL3ovFxdntpxElDxOR0ikMxcvAl6vCNznn088b67FImq5998PbNokOlURUfZI23/Zl156CS0tLZAkCWazGbfffjsefPBBFPNPc6IYvb0ibJ97ToRvvLGWDQbgC18QgXv//cDq1eA9uURZrCAdB923bx9qa2uhKApKS0vh8Xiwc+dOlJaW4qmnnkrHWxJlldA0fv/wD8DnPieGd3Q4RAiPD9/584GvfQ34l38R9/O+/jrgdIqp/Ri+RNktLTXg7u7ucMerkPPnz6O1tRU7d+6E3+/Hww8/nI63JtKtsTHgzTeBZ58FfvrTxKNQLV0qei3ffz+wZQswb15Gi0lEGZKWAF65cmXMtpKSEjgcDmzfvh0OhwPPPPMMvvGNb6Tj7Yl04/JloLNTBO5zzyVuz73ttsilZZsNKEjLtSki0pO0BPC5c+cQCATitveaTCa0tbXhkUceScdbh9lsNrhcLmzYsAEA0NbWBlmW0djYmNb3JTp/Xgz9+Oyz4j7deEM/Go3A5s2RTlScrJ4o/6QlgJuamrBlyxY89dRTWLs2dg5RACgtLU3HW4f5fD5UV1eHH9vtdng8nrS+J+Wv3l5Rw332WeCll4CRkdh95s0D7r5btOnedx9QVpbxYhKRjqQlgEtKStDW1oatW7eitLQU3/3ud1FXVxdVIx4cHEzHW4c5HA7YbDbIsgy73Q6r1ZrW96P8c/SouLT87LPAW2+JjlUTlZWJ9tyvfx2orhadqoiIgDTehmQ2m3Hs2DE4nU7s3LkTDocDZrMZZrMZg4ODaGtrS9dbAwAsFgvnHyZVKQrg80U6Ub37bvz9li8Xtdyvf13MKsT7c4konrR/NbhcLrhcLvh8PnR2dsLj8aCrqys8TrTdbsfGjRtht9uxbt26dBeHKCmjo2LIx1DonjwZf79bbxWB+7WvAVYrbxEioqll7G9zq9UKq9WKnTt3AhBttF6vF16vFw8//DAaGxthsVhw9OhRVd6vv78fzc3NMJlMkK9NZsoOWDQdV66IeXOfflq06064ow5AZFCMr31NLKtWZbqURJTtNLs4FgrkUCj29PRASnRj5AxIkgSXyxV+XF9fD6fTGbWNKGR4WPRYfvppMRjG0FDsPoWFQFWVqOnefz+wZEnmy0lEuUM3rVOVlZWorKxU7Xjt7e1Rj+vq6lBdXY2mpqaoKRLH27t3L/bu3RuzPRgMAgAuXLgQrk1TZg1dS8SheMk4Q4EAsH9/IX7+80J4PIW4dCn2uvHChQqqq0dw770jsNtHoubPzadfhXR8/pQcngPtXYh3T2EKdBPA6Ra6H9jr9aK2tjbuPoFAAKdOnUp4jCNHjqh2iZxmxufzpfT6oaFCvP32Erz5ZgUOH16E0dHYyXEXLLiK22/vwxe+cBrr1p3F7NniD7DDh1N665yQ6udPqeM50M7w8LCqx8vJAK6vr0ddXR3sdnvMc5Nd5i4uLsayZctitgeDQfT29mLt2rWoqKhQtaw0PUNDQ/D5fLBarSgqKkrqtWfPGvDCC6Km+8orszA6GlvTve66IO69dwRf+coI7rxzFLNnFwMoBrBanX9Alkvl8yd18Bxo7/Tp06oeLycD2O12w2azRW0LjU092f3ADQ0NaGhoiNkeCARQUlKChQsXJrx8TZlRVFQ0rXNw6hTwzDOiTffVV4FrrQhRKiqAb3wD2LYNuPPOAhiNcwDMUb3MuWS6nz+lD8+BdgKBgKrHy8kAbmxsjLkH2Ov1wmQyhS9FU+45flwE7tNPi0kP4lmxQgRuba2YhYhjLhORVnIygKurq9HR0RFu65VlGS6XC/v27eNfjjnmo4+Ajg4Ruomaxj7zGRG627bxHl0i0o+cDGC73Q6v1wun0wlAtPu2tLTEbROm7CNJQGurWI4cib/PmjWRmu6ttzJ0iUh/cjKAARHCDNzcceKEAc8+uxLf//5CHDoUfx+bLVLT/cxnMls+IqJk5WwAU/Y7dQpobxc13bfeKgFQErPP7bcD27eLzlQq3kZORJR2DGDSlb4+0abb2gq89lr8faxWEbrbtzN0iSh7MYBJc2fPiluGWluBAwfi3zL02c+OYf36j/DXf70MNltx7A5ERFmGAUyaGBgQMwy1tooJ7MfGYvdZvRrYsUMsS5cO4cCBj2CxLM18YYmI0oABTBlz/jzws5+J0N2/X0z1N9HKlZHQXbMm0ns5n8ZdJqL8wACmtBoaAn7+cxG6v/oVcPVq7D433STac3fsANav5y1DRJQfGMCkuuFh4IUXROi+8AJw+XLsPjfcEAndjRsZukSUfxjApIrLl8V8uq2tosYbb9KQpUuBujoRvF/4AoeBJKL8xgCmGbtyRbTltrWJtt1405QuWiRGo9qxA7jjDsAYO/sfEVFeYgBTUkZGgM5OUdN99lnRsWqisjIxGtWOHcDmzcAs/pYREcXgVyNNaXQUePllEbrPPCNuIZqopAT4+tdF6FZVAYWFGS8mEVFWYQBTXGNjYiSq1lYx09CZM7H7FBUBX/2qCN3qamAOp9IlIpo2BjCFBYNiHt3WVjEcZG9v7D7z5wNf+YoI3bvvBubNy3w5iYhyAQM4zykKcPCgCN22NuCTT2L3mTsXuPdeEbr33AMsWJD5chIR5RoGcB5SFODQoUjoHj8eu8/s2aKGu2OHqPEWFWW8mEREOY0BnCcUBfjd70TgtrYCx47F7jNrFrB1qwjdr35VdKwiIqL0YADnsFDotreL5cMPY/cxGkWv5e3bRS/msrLMl5OIKB8xgHOMogDvvCNquolCt6BA3J+7Y4eYyH7RosyXk4go3zGAc0AodNvbRfDGC12DAbjzTjEUZG0tsGRJ5stJREQRDOAslUzobt8uarpLOZUuEZFuMICzSDAobhn66U/F8sEHsfuMr+lu28bQJSLSKwawzl25Avz61yJwn3su/uAYDF0iouzDANahs2fFLEPPPSem+Is3y5DBIGYXCl1erqjIfDmJiGjmGMA6MDoKvP028KtfiaWrS7TxTjR3rhhz+atfFYNjLF6c+bISEZE6GMAaGB0FDh8GXn1VLL/+NSDL8fctKwPuuw/42tfEIBkcBpKIKDcwgDPgzBkRuL/5jQjcN98ELlxIvP9tt4lhIL/8ZXGZmfPpEhHlHn61q0BRxMT0fX2AJAF+v/j5wQfAkSPxO06NV1oqard33y1+sj2XiCj3MYCTsGPHAhiNwMiIWK5eBfr7gXPnxGXl6aqoEL2WQ8uaNWJ0KiIiyh8M4CS89VZh0q8pLQXWrRPL+vXApk1AZaXoxUxERPmLATxDhYViyr6yMuC66yJLZSVgNgMWC7ByJbBsGcOWiIhiMYCT8OGHMszmYhiNDFUiIkoNAzgJc+eyRzIREamDXX+IiIg0wPrcNCjXhqUaGhpCIBDQuDT5KRAIYHh4GIFAAAXsMp5x/Py1x3OgvaFr4wIr8YYqnAEG8DQ89thjAIA1a9ZoXBIiItLaY489hh/84AcpH8egqBXlOayiogK9vb1YsmQJPow38S6l3erVq9Hb24ulS5fig3jzMFJa8fPXHs+B9m6++Wb09fVh6dKlOH36dMrHYw14GkKXe4xGI4qLizUuTX4KnYOCggKeAw3w89cez4H2jEYjAKjWBMCGBCIiIg0wgImIiDTAACYiItIAA5iIiEgD7IQ1DQ0NDQgEAuz4oCGeA23x89cez4H21D4HvA2JiIhIA7wETUREpAEGMBERkQbYBjwNwWAQp0+fRlFREQych5CIKC8pioKhoSFUVFSoMhgHA3gaTp8+jeXLl2tdDCIi0oGTJ0/ihhtuSPk4DOBpKCoqAgC88847DGKNyLKM119/HZs2bYLJZNK6OHmHn7/2eA60d/LkSaxZsyacCaliAE9D6LJzUVERbwHQSDAYxPz581FcXMxzoAF+/trjOdBeKHjVaopkJywiIiINsAach65eBY4fB44dA06cAPr7I8vQEDAyAoyOip8GAzB3LjBvXvTP4mKgvFwsZWWR9euvB4qKxOuIiCgxBnCOGxkBjhwBXnsNeP11oLsb+PhjIBhM33suWABUVMRfVqwAbrpJBLVKM3oREWUlBnAOunAB+OlPgaefBjwe4OLFzL7/xYvA0aNiSWTOHBHGlZUikMcvlZXA4sWsRRNRbmMA55D33wf+8R+B//t/RQjHs2ABcPPNwMqVwKpVIvAWLYpcSi4pAQoLI0swCFy+DFy6FPl56RIQCIhL1gMDkZ/nzgF9fUBvL3D6NHD+fOKyXrkCfPSRWBKVc+XKyFJRMRuBQDlWrjSguJi1ZyLKfgzgHPD++8D/+B+ixjtxZO/Fi4EtW4A77hDLmjWA0Zjc8Wfa4fLixUgYnz4NfPKJuPzd0yPaoI8fT1w7v3hRXDo/ciS0ZT6AO/DQQ6IN2mIRy/iQXrkSWL4cmMXfaiLKAvyqymLnz4vg/eEPgbGxyPYFC4BvfQv4wz8ENm1KPnDVMr4WG4+iiNrz8ePRoez3i+X4cdEZbKLLl4F33xXLRIWF4hJ26H3Hh/RNNwGzZ6v2zyMiSgkDOEt5vcB3viNqlSFLlgDf+x7gcIieyHpnMADXXSeWDRtinx8dFb20jx0DfvvbYbz66mlcvboCH39cCL9f9OaeaGQk8aXtggLR7jyx5myxAGYzMH+++v9GIqJEGMBZZmwM+O//HdizJ7Jt3jygqQn4m7/JrRCZNUsEo9kM3H77Vaxa9S42b74OJpMJY2PAqVOipnzsWOwyPBx7vGBQ1LR7esQfMBMtWxY/nFeunPlleCKiRBjAWSQQAL79beCFFyLbtmwB/uVfRM0unxiNwI03iuWuu6KfUxTRGezYsUhAHz0aWU/UOezUKbG88krsc4sWJQ7n8nL22Cai5DGAs8TAAHD33cDBg+Kx0Qg0NwN/9VfsETyRwQAsXSqWO++Mfk5RxGcZqilPrEGfPRv/mGfPiuWtt2KfKylJHM5LlzKciSg+BnAWOHcOsNsjPYLLyoD2dlH7peQYDJFRuz73udjnA4FIKI8PZ78/ur19vPPnAZ9PLBPNnRu5t3nictNNQGkpA5ooXzGAde7SJeArX4mE7/XXA52dwK23aluuXFVcDKxfL5aJLl0CJCl+OB8/Hn90scuXgQ8+EEui94sXzqGAXrBAzX8dEekJA1jHgkFxK1HosufSpcDLLwOf+Yymxcpb8+aJP3zi/fFz9aq4x3niJe1Qp69Ll+IfMxCYeL9ztEWL4odzqP173jz1/n1ElFkMYB37u78Tg2sAwMKFwC9+wfDVq9mzxchiq1bFPqcowJkzkTCeuJw4Ef9+ZyDS9vz22/GfX7RIBPGKFZFQHr++aBEvcRPpFQNYp15+GfjBD8R6QQHQ1gasW6dliWimDAbRdHD99cDnPx/7/Oio6H09PpRDg5P09IhRxCaOcBYSCuju7vjPz50bP5hD6zfcIMblJqLMYwDr0Nmz4najUJviD34AfPnL2paJ0mfWLBGIK1YAX/pS7PNXrkSG8AyF84kTYvn4YxHQiWa3unx58jG3ATGAy4oVYhjPZctEKI9fKirU+FcS0UQMYB36678WYygDQFUVsGuXtuUhbc2ZI5oeEjU/jIyIEP744+hgHr8+2YxYfX1i+c1vEu+zaFExioo24+abF6CyMjaoly1jhzGiZDGAdebFF8VsRoC4ReUnP9FuLGfKDoWFkRp0PIoCDA7GD+bQeugPvkTOni3A2bMmSFLifUym2FC+4YbIPdkVFaJNmr/PRAIDWEeGh4E//dPI40ceEV9cRKkwGMS942VlifsRXLkiatGnTon7nccvp04BJ04E0ddnQDCYuEeXLIvlnXcSl8VoFG3h40N5/M/Q+uLFnNWKch9/xXXkscdEGx8AbN4M/PEfa1seyh9z5kRucYpHlgN46aVXsHr1ZgwNlSQM6k8+iT9JRsjYWGR6yskYDCKEEwV0aP366znDFWUvBrBOnDkjhpYERC3h8cd5+wjpi9GooKJCgcmUeB9FESO3jQ/l3t7IvNCh9U8/TdxxLHScTz8Vy6FDk5ertDTSy3yqZe7cGf3TidKCAawTf//3wIULYv2BB4BbbtG2PEQzYTCIdt5Fi+KPJhYyNib+6BwfzOMDOrTe1xc913U8g4NiSTTa2HjFxdMPa3Yqo3RjAOuAJAFPPCHW588H/vZvtS0PUboZjZHLyFZr4v3GxkSNemIwh36Gasmffjp5T++QQEAsR49Ove+CBSKIFy8Wc1aH/rAYv4zfvmABr1pRchjAOvDII+JWEgBoaGDHK6KQUKet66+feiCaixejA3myJRCY+r0vXhR/HE/W83u8uXNjQzleUIcWk4kzmeU7BrDG+vqAH/9YrC9cKAKYiJK3YAFgNotlKpcvi0vg0wnrgYHpvf/ly8DJk2KZDqNRzMo1MajLy0WP9dCsXaHFaDRM2m5O2YcBrLF/+idxCwgA1NeLDiVElF7jh+icyugo0N8fGfYztJw7F7sttH2qdmsg0g5+5sx0S10Cg+F+mEzKpEEdb/v8+bw8rkcMYA0FAsCPfiTWCwvFCFhEpC+zZkUug0+Hooj7oacT2KFtiWbLij22AYODBgwOTq8dO2TOnPhhHdpWWhq7lJUBRUUM7nRiAGvoJz8Rk7kDYtrBZcu0LQ8Rpc5giITYdGcvu3gxEsj9/eKyd39/9PLppyM4ceICRkaKMThoDH93TMeVK5GObMkwGkVbdbyAHh/U8bYzvKfGANaIogAtLZHHf/mX2pWFiLS1YIFYbrop8T6yfBEHDryCzZs3w2QyYXRUBHW8sE4U4v39kSav6Rgbi7wuWRPDO1FQhxaTSSwlJWLJhyFLGcAaefNN4He/E+uf/zxw223aloeIssusWeIWqcWLk3vd8HBsUIfupQ4t8badP594Wsx4UglvQNSgS0qig3n8z6m2ZcOgK7oPYEmS4HK5YLFYYLo2BI/D4ZjydTabDS6XCxs2bAAAtLW1QZZlNDY2prO40za+9vvd72pXDiLKL/Pni2X58uReNzYm+q1MFdTxlmTDGwCGhsTyySfJvS5kzpzkQ3v8+sKF6b9NTNcBLMsyqqur0d3dHQ7f+vp6uN3uKUPY5/Ohuro6/Nhut8Pj8aSzuNM2OAi0tYl1kwnYvl3T4hARTclojFwuTtbYmAjhqUI6NKFHaD30c7qd1Ma7ciXZXubRDIbYsJ49W93h0XQdwLt374bdbg+HLwA4nU7YbLYpA9jhcMBms0GWZdjtdlgnG24nwzo6xD2DgOh8NW+etuUhIkonozEyI9dMXL06eUAnWg/9DASSr4GHerPL8vithTP7BySg6wDu6OiA0+mM2mY2myHLMnw+36SharFYpnWpWgv//u+R9T/6I+3KQUSUDWbPjgxWMhPBoLicPdMAl+XIaIVq0nUAS5IEc5xhbUwmE7xer65qtdN16hRw4IBYX7Vq8nFwiYgodQUFkd7VK1Yk/3pFEVct3333PDZuVK9cug1gObreH6WsrAz9U3St6+/vR3NzM0wmU/hYeuiA1dYWuRTy7W/zPjkiIr0zGERT4eLFSV7HnoJuA3hgigFYJwtoINJ7OqS+vh5OpzNq20R79+7F3r17Y7YHrw3AeuHChSnfdyo/+clChD72e+8NQJY5uOt0DA0NRf2kzOLnrz2eA+1dCM0ZqxLdBnCq2tvbox7X1dWhuroaTU1NUZ26xgsEAjh16lTCYx45cgRHkxn/bYLe3vk4dEj0zDabZZw+fQCnT8/4cHnJ5/NpXYS8xs9fezwH2hkeHlb1eLoN4LJr3eXi1TgHBgYShmgiofuBvV4vamtr4+5TXFyMZXHGgwwGg+jt7cXatWtRUVGR1PuO98Mfzgmv/+EfzsHmzZtnfKx8MzQ0FO54V1RUpHVx8g4/f+3xHGjvtMo1Jt0GcChg412KlmUZ5eXlCV9bX1+Puro62O32mOekSSb3bGhoQEOc+QADgQBKSkqwcOHCpIN/vP37I+vf+tY8mEy8/yhZRUVFKZ0DSg0/f+3xHGgnMJ2JpJOg6+mgQ7ccxRMvXEPcbndM0IaCXKue0+fOAa+9JtZvvlksRESUv1QN4EAggMOHD+P48eOqHK+2thZ+vz9qm8/ng8lkmjRIGxsbY+4B9nq9MJlM4UvRmfbCCwhPpn3//ZoUgYiIdGTGARwIBPDoo4+ipqYG5eXlMBqN4WA0m80wGo0wGo1YtWoVmpqaZhTKTU1N8Hq9UbXglpYW7Nu3L/xYkiRYLBZ4vd7wturqanR0dIQfy7IMl8uFffv2aXbp5rnnIutf/aomRSAiIh1Jug04EAjggQceQGdnJ6qqqlBbW4s9e/bAZDKhsrIyvN/58+cxMDAASZLg8XhQW1uL8+fPw+l04oEHHpjWe5lMJng8HuzevRsWiwV+vx82my2mE9XEdmK73Q6v1xseRUuSJLS0tEx62TqdLl8GXnxRrC9aJGY/IiKi/JZUAO/btw8dHR1wOBxoC80mkEBJSQlKSkpQWVmJqqoqAEBPTw9aWlpQU1ODjo6OafXkM5vNk967azabMTg4GLPdbrdrFrgTvfqqmHAbAO69Nz/muSQioslNO4B37dqFlStX4sVQVW4GKisrsWfPHsiyjG3btsHtduOmyWagzhHjez/ffbd25SAiIv2YVhtwT08PduzYMe1Lx1MxmUzYv38/uru7VTme3oUC2GAArl0MICKiPDetGvD4tl01bdu2LS3H1ZPeXuC3vxXrNhtw3XXaloeIiPRB1/cB54JxnbNRU6NdOYiISF9SDuAdO3bE3d7Z2YnDhw+nevisN77JfOtW7cpBRET6klQA9/T04Mknn4wKVkWJPz1TVVUV+vv70dTUlFIBs1kwCHg8Yn3hQt5+REREEUkFsCRJcDgcsNlsMBqNqKmpQU9PD44cORJ3/6qqKuzatQuPPvqoKoXNNu+9B5w5I9a/9CVg9mxNi0NERDqS1H3AVVVVCAaD8Pl88Hq96Orqgsfjwfr162EwGGC322G1WrF161bcddddAMT9wP39/WkpvN69/HJkfcsWzYpBREQ6NKPZkKxWa3gs5u3bt8PlcsHj8cDr9aKlpQUulwsGgyE8LGWqk9hnqwMHIuuceZCIiMZTZTrCyspKOByO8AQIPT098Hg84Ymj3W63Gm+TVRQlEsAlJcDatdqWh4iI9CXlAK6vr4/ZFgrkfPb++8DZs2L9zjs5/CQREUVL+TakKg7tFNf4y89f+pJmxSAiIp2a9lCUat9OdPjw4ZzuHT2+Axbbf4mIaKJpBXBlZSW2b9+OmpoafPzxxym/6SOPPIKWlhZ873vfS/lYejS+/beoCFi3TtPiEBGRDk37EvT69evR2tqKBx98EDU1NXjppZeSeqPjx49j165dWLVqFUpLS/H4448nXdhs0dMDfPqpWN+0CZilSlc3IiLKJUlFQ2gWo87OTrS1taG2thYWiwUbNmyAxWKByWQK7yvLMvr7++Hz+dDV1QUAcDgc6OrqQklJiar/CL15883I+he/qF05iIhIv2ZUN6uqqkJVVRWeeOIJPP300zh48CCOHTsGSZIwMDAAACgrK4PZbIbdbseePXuwfv16VQuuZ2+9FVnn8JNERBRPyhdHt23blhfTCiYjFMAGA3D77dqWhYiI9InTEars0iUgNFfFLbeIQTiIiIgmUqV70EsvvYSWlhZIkgSz2Yzbb78dDz74IIqLi9U4fFbx+YDRUbHOy89ERJRIyjXgffv2oba2FoqioLS0FB6PBzt37kRpaSmeeuopNcqYVdj+S0RE05FyDbi7uzvc8Srk/PnzaG1txc6dO+H3+/Hwww+n+jZZgwFMRETTkVQNeNWqVbj77rujtq1cuTJmv5KSEjgcDkiShGPHjuGZZ55JrZRZJBTARUXAZz+rbVmIiEi/kgrgc+fOQVGUmG2BQCDu/iaTCW1tbfD7/TMvYRb55BOxAKL3MydgICKiRJIK4MHBQbz44otR25qamrBlyxYcOXIk4etKS0tnVrosw8vPREQ0XSl3wiopKUFbWxu2bduGjRs34qmnnoqpEQ8ODqb6NlmBAUxERNOlyn3AZrMZx44dw5YtW8I9oFetWoWamhrcfvvtqKurU+NtdG98AH/uc9qVg4iI9E/VgThcLhcGBgZw8OBBOBwOKIqCrq4uWCwWlJeXY8eOHXj00UdxODRSRQ65ehXo7hbrFguwaJG25SEiIn1Ly0hYVqsVO3fuxP79+xEMBnHw4EE4nU4MDg7i4YcfhtVqxapVq9Lx1pr57W+By5fFOi8/ExHRVDIyUZ7VaoXVakVjYyMAoKenB5IkZeKtM4btv0RElAxNZqqtrKxEZWWlFm+dNgxgIiJKBidjUEkogOfOBW67TduyEBGR/jGAVXD2LBAaa8RmA2bP1rY8RESkfwxgFfDyMxERJYsBrILxAfyFL2hXDiIiyh4MYBWwBkxERMliAKdobAx4+22xfsMNwLJl2paHiIiyAwM4Re+9B1y4INZZ+yUiouliAKeIl5+JiGgmGMApYgATEdFMMIBTFArgWbMAq1XbshARUfZgAKdAlkUbMACsWwfMm6dlaYiIKJswgFNw8GBknZefiYgoGQzgFLz5ZmSdAUxERMlgAKeAHbCIiGimGMAzpCiRAF60CDCbtS0PERFlFwbwDB09CgwOivXPfx4wGLQtDxERZRcG8Azx8jMREaWCATxDDGAiIkoFA3iG3nhD/DQYgI0btS0LERFlHwbwDAwOAr/9rVhfuxYoKtK2PERElH0YwDPw6quiFzQAbN6sbVmIiCg7MYBn4MCByDoDmIiIZoIBPAPjA/jOO7UrBxERZS8GcJLOnwcOHRLrv/d7wHXXaVseIiLKTgzgJL3+OhAMinVefiYiopliACeJ7b9ERKQGBnCS9u+PrP/+72tXDiIiym4M4CR8/HEBDh8W6xs3AosXa1ocIiLKYrO0LsBUJEmCy+WCxWKByWQCADgcjrS9bjK/+EVheH3btpQORUREeU7XASzLMqqrq9Hd3R0O0fr6erjd7knDdKavm8qvfsUAJiIidej6EvTu3btht9vDIQoATqcTTqczLa+byuHD4u+VdeuAlStTOhQREeU5XQdwR0cHbDZb1Daz2QxZluHz+VR/3XTV1qZ8CCIiynO6DmBJkmA2m2O2m0wmeL1e1V83Xbz8TEREqdJtAMuynPC5srIy9Pf3q/q66dq2DVi9OqVDEBER6bcT1sDAwKTPJwramb4OAPbu3Yu9e/fGbA9eG/pqxYoRPPaYjEkOQWkyNDQU9ZMyi5+/9ngOtHfhwgVVj6fbANZCIBDAqVOnEj7/X/7LGzh8OJjBEtFEarTh08zx89cez4F2hoeHVT2ebgO4rKwMQPwa68DAQFQPZzVeBwDFxcVYtmxZzPZgMIje3l7cd58FFRUVU5ad1Dc0NASfzwer1YqioiKti5N3+Plrj+dAe6dPn1b1eLoN4FBQxrukLMsyysvLVX0dADQ0NKChoSFmeyAQQElJCRYuXDhpgFP6FRUV8RxoiJ+/9ngOtBMIBFQ9nm47YQGRW4fisdvtqr+OiIgoU3RbAwaA2tpa+P3+qG0+nw8mkwlWq1X11yWiKAoAcQlI7b+AaHoCgQCGh4cRCARQUKDrvxtzEj9/7fEcaC/UAS6UCSlTdGxwcFAxm83K4OBgeJvD4VDa29vDj/1+v2I2mxWPx5PU65Lx0EMPKQC4cOHChQsX5aGHHppRlkxkUBS1ojw9JElCS0sLLBYL/H4/LBZL1HjOkiTBZrOhvb096vLyVK9LRkVFBXp7e7FkyRJ8+OGHKf+bKHmrV69Gb28vli5dig8++EDr4uQdfv7a4znQ3s0334y+vj4sXbpUlQ5Zur4EDYj2XJfLNenzg4ODSb8uGaHLPUajEcXFxaock5ITOgcFBQU8Bxrg5689ngPtGY1GAFCtCYANCURERBpgABMREWmAAUxERKQBBjAREZEGdN8JSw8aGhoQCATY8UFDPAfa4uevPZ4D7al9DnR/GxIREVEu4iVoIiIiDTCAiYiINJCzbcBerxcejweyLEOSJNTV1c14JCwiIiK15WQA+3w+SJIUHglLlmVUVlbC7/fPaHSsYDCI06dPo6ioCAaDQe3iEhFRFlAUBUNDQ6ioqFBnNCxVRpTWGYfDEbOtpaVFAaD4/f6kj3fy5EnNB//mwoULFy76WE6ePKlGVCk5WQNua2uDxWJBY2NjeNuGDRsAiNqx2WxO6nhFRUUAgHfeeQfLly9Xr6A0bbIs4/XXX8emTZs4GbkG+Plrj+dAeydPnsSaNWvCmZCqnAzgsrIy9Pf3R20L/cIODAwkfbzQZeeioiLeg6eRYDCI+fPno7i4mOdAA/z8tcdzoL1Q8KrVFJmTAez3+2O2+Xw+AJGaMBER5QdFAUZGxHL1avyf09nW1zdb1XLlZADH09LSArvdDqvVmnCfvXv3Yu/evTHbg8EgAODChQuQZTldRaRJDA0NRf2kzOLnrz2tz0EwGAmj0VHDuJAyhANqdDR6feL+o6PA1auGa9si66HjhPYJHVMcy3BtW2R94uvEtujXjV8fHVWr8+x8lY4j5EUAd3R0QJIkdHd3T7pfIBDAqVOnEj5/5MgRHD16VO3iURJCVzJIG/z81aMoQDBowOhowbUQKQgvIyMFUY/FYsDIyPV4441ejI5+GvNcotdFthkSHn9szBC1z9hY5DWh9WCQd4CoLecDWJZlOJ1OeDyeKTsuFBcXY9myZTHbg8Egent7sXbtWlRUVKSppDSZoaEh+Hw+WK1W1TpA0PTl2uc/MgJcugRcuWLA5cuiRnX5snh85Urs9qmej2wHLl8WNbnLl8W2ifuEanpXrwKKwlBLhcGgYPZsYPZsYNYsBYWFuLYo17YBs2eL7aF18VPsM359/GsnroeOf/HiAL7/ffXKn/MBXFdXB4/HM62ezw0NDWhoaIjZHggEUFJSgoULF7L3ocaKiop4DjSUzs9fUUSAXbgADA9HlkuXon8mWp/q+fHrY2Np+SdkJaMxFEIIh028n9Pdlsn9jcbxf8Ck/4+ZEycKGMDTVV9fD5fLFRW+ob/iiWjmxsaAixdFWE62JLtPrgVjYSEwdy4wZ07k55w5CNfaklmCwcs4daoHn/nMTSgpmTfj44xfRIhp/Snlr5wNYLfbjbq6uqiwlSQJkiQxgClvBYMi8M6fBwKB2J/xtp0/DwwOLkRf3xaMjS1AICBqkdnAaATmzxfLvHnR63Pnip+hcBwflBNDc7LnJ9tXjcGSQmT5Mg4c+AibNy+FyTRPvQOTZnIygL1eL9rb21FXVwe32w1AtAV7PB60tLRoXDqi1Fy5AgwOAgMD4ufEZeL28+ejA3ZmE5DOAqBu26/RCBQVAQsXRi8LFohlYmBOtp7o+cJCVYtMpKqcDOC6ujrIsgyv1xvzXLKjYBGli6KIYDx7Fjh3Tvwcv37uXPxAvXRJm/LOmzeC0lIjTKYCFBfHhueCBbFhOtkyezbAodUpn+VkAA8ODmpdBMpTw8NAb69Y+vqAM2digzW0fu6c6I2bbvPmASUlQHFx7M942+LtMzYm49VXD2Dz5s3sBEekkpwMYCI1KYqohfb1RcI1FLATHwcC6SnDvHlAWRlQWpp4SfT8bBUG7+H4M0TqYwBT3gsEgJMno5cTJ6IfX76s3vvNmQMsWgRcd534mWj9uusioTpnjnrvT0T6wACmnHfxIiBJkcXvB3p6IiF7/nzq71FUBCxdCixZIn6GlsWLY4N14UK2fRIRA5hyxNAQ8MEHYjl2LDpsP/105sctKgKWLwduuCE6WCeG7YIF6v1biCg/MIApaygK0NdngM8ngvb99yM/JxnCO6E5c0Sw3nijCNmJy403io5IRETpwAAmXbp4EXjnHeDwYeDIEaCrayHeffceDA8nd2Pn0qWA2QxYLNE/zWbg+ut5KZiItMMAJs3JMvD220BXlwjbw4eBo0cnDhiR+Fe1rAy45RZg9Wrxc9UqEbSVlWIwBiIiPWIAU0aNjAC/+x3w1lvAb34jlg8/nN5rFy0axm23FeL3fq8wHLa33CI6N7EmS0TZhgFMaXXhAvDGG8DLLwOvvAJ0d099S8+cOcCaNcC6dcDatWJZseI8Dh9+mQNBEFHOYACTqi5dAl59VQTuyy8DBw8Co6OJ9589WwTt5z4H3H47YLUCn/mMmLtzPFme0QDGRES6xQCmlPn9wC9/CfziFyJ0Jxur2GIRYRta1q3jIBNElJ8YwJS0YFBcVn76aRG6H32UeN9bbgG+9CWxbN4seh4TEREDmKZpbAx47TWgo0MEb29v/P0qKoAvfxmw20XoLlmS0WISEWUNBjAlpCii09T/+T8iePv6YvcxGoEvfhG45x4RvLfdxh7JRETTwQCmGJ9+CvzbvwE//jHw7ruxz8+eDdx9N1BbC3zlKwA7JRMRJY8BTABEbfett4B//megvT12nto5c0QNt64OuO8+MUcsERHNHAM4z42MAP/v/wH/+I+Azxf7/KZNwHe+I4KXoUtEpB4GcJ66dAl46ingkUfEtHzjXXcd8Cd/IpZVq7QpHxFRrmMA55lLl8Rl5kcfBc6ciX7OZgP+4i+AHTuAuXO1KR8RUb5gAOeJ0VHRm/lv/zZ26r577gGamsTlZvZgJiLKDAZwHnj+eWDnTjF3bojBIGq6u3aJsZaJiCizGMA57MQJ4L/+V+BnP4vefv/9wMMPA7feqk25iIgIKNC6AKS+kRGguVkMAzk+fDdtEqNZ/exnDF8iIq2xBpxj3n8f+E//CTh0KLJtyRJg717gm99kGy8RkV6wBpwjFAX40Y9ET+ZQ+BoMwJ//uWj7/da3GL5ERHqimxpwIBCAJEkwmUy46aabtC5OVjlzBvjjPwZeeCGybfVq4F//Fdi4UbtyERFRYpoEcCAQgNvthsfjQVdXF2RZhqJEJlw3XKuqmc1m1NbWor6+nqGcwKFDwFe/Cpw8Gdn2Z38m2oDnz9euXERENLmMXoIOBALYvn07Kisr8fbbb6O2thZerxfHjh1DMBgMLwMDAzh27BieeOIJKIqC2tparFq1Ck8++WQmi6t7ra2iY1UofK+/XtSC//mfGb5ERHqXsRrwvn370NHRAYfDgba2tkn3LSkpQUlJCSorK1FVVQUA6OnpQUtLC2pqatDR0YGioqJMFFuXgkHgoYfErUQhn/888MwzwNKl2pWLiIimLyMBvGvXLqxcuRIvvvjijI9RWVmJPXv2QJZlbNu2DW63Oy8vS4+MAH/0R2IChZD//J+BJ54QMxYREVF2SPsl6J6eHuzYsQMPPPCAKsczmUzYv38/uru7VTleNrl8WczBGwrfggLgf/5P4F/+heFLRJRt0l4DrqysTMtxt23blpbj6tXFi8DXvw54POLxnDli3t6vfEXbchER0czo5jYkSiwQAO69V4xiBQALFojRrK41jxMRURbSdCCOHTt2xN3e2dmJw4cPZ7YwOnXpkhi7ORS+JSXA/v0MXyKibJexAO7p6cGTTz4ZFazj7/0dr6qqCv39/WhqaspQ6fRpZETMWHTggHhcVga89BLwxS9qWy4iIkpdxgJYkiQ4HA7YbDYYjUbU1NSgp6cHR44cibt/VVUVdu3ahUcffTRTRdQVRRHDSP785+LxwoXAr34FWK3alouIiNSRsTbgqqoqBINB+Hw+eL1edHV1wePxYP369TAYDLDb7bBardi6dSvuuusuAOJ+4P7+/kwVUVceewxwu8X67NmizZfDShIR5Y6Md8KyWq2wXqvGbd++HS6XCx6PB16vFy0tLXC5XDAYDLBarTCbzZBlOdNF1NzPfw40NkYe//jHwJYt2pWHiIjUp3kv6MrKSjgcDjgcDgCirdjj8cDn8wEA3KFqYJ44ehT4gz8Ql6AB4PvfB779bW3LRERE6tM0gOvr62O2hQJZDT6fD62trXC5XKocL90uXgS+8Q1x2xEgBt146CFty0REROmh6W1IVWm8l8bn86X1+OnwV38FvPOOWL/lFjHCFefwJSLKTRkZilLt24kOHz6csHe0JEmoq6uD1+tFWVmZqu+bTu3tQGiypwULxMQKeTzfBBFRzsvIUJTbt29HTU0N3G43VqxYkdLxHnnkEUiShMcffzzu82azGe3t7QCA1tbWlN4rU06eBB58MPL4n/8ZWL1au/IQEVH6ZeQS9Pr169Ha2ooHH3wQNTU1eOmll5J6/fHjx7Fr1y6sWrUKpaWlCcM3GymKCN/z58Xjb35TzHZERES5LWOdsEKzGHV2dqKtrQ21tbWwWCzYsGEDLBYLTCZTeF9ZltHf3w+fz4euri4AgMPhQFdXF0pKSjJV5Iz48Y+B0CyNy5YBjz/Odl8ionyQ8V7QVVVVqKqqwhNPPIGnn34aBw8exLFjxyBJEgYGBgAAZWVlMJvNsNvt2LNnD9avX5/pYmbEqVPAX/915LHbDYz7O4SIiHKYprchbdu2TVfTCu7duxd79+6N2R4MBgEAFy5cUHVgkL/4i/kIBGYDAL797Sv44hcvIQ/HHZmWoaGhqJ+UWfz8tcdzoL0LFy6oejzNB+LQk0AggFOnTiV8/siRIzh69Kgq73Xo0CI8+6yYVaG4+Aq+/OVOHDgwosqxc1logBbSBj9/7fEcaGd4eFjV4zGAxykuLsayZctitgeDQfT29mLt2rWoqKhI+X2uXAEaGiL3GO3ePYb77uMUR5MZGhqCz+eD1WpFEe/Pyjh+/trjOdDe6dOnVT2eLgM4EAjg4YcfxqFDh2C1WrFjxw6sW7cu7e/b0NCAhoaGuOUpKSnBwoULozqLzdQjjwCSJNbvuAP47nfno6BgfsrHzQdFRUWqnAOaGX7+2uM50E4gNEyhSjQdCSuRxsZGlJeXw263w+/3Y8uWLfjTP/1TrYulirNngb//e7FuMIh7fgt0eRaIiCiddFkDttlseHD8yBQQA3A8+uij+N73vjft48iyrLvZlL7//chYz3/8x8DatdqWh4iItKHLupff74/p6bdz585p3QMsyzKcTifq6uogSRLa2tpQV1eH5ubmdBV32j76CHjiCbG+YAHwd3+nbXmIiEg7uqwBNzU14a677sI3v/lN1NbW4qabbgIAlJeXT/lak8mk29mP/r//DxgbE+uNjcDSpZoWh4iINKTLGnBJSQk6Oztx7NgxmM1mbNy4ETU1NZBCPZey0O9+B/zHf4j1666LHoCDiIjyjy4DGBAh/MQTTyAYDIZHw/qP//gPGI1GbNy4EU+Gpg7KEg89JMZ9BoCmJs50RESU7zS/BB0IBFBcXDzpPqHhK0O8Xi8OHTqU7qKp5tAh4Gc/E+sVFUCOdOgmIqIUaBrAK1euRE9PD0wmE7Zv3w6TyTSte37tdjvsdntmCqmCf/iHyPp/+2/AvHnalYWIiPRB0wB2OBwYGBjAnj17wts6OzuxdetWbN26NalbjvTq/feBZ54R60uWAH/yJ9qWh4iI9EHTNuDGxsao8AXE5eb9+/fj3Llz2Lhxo+ojj2Ta7t2Rtt+/+Rtg7lxty0NERPqg205Ye/bsQWlpKRwOh9ZFmbGTJ4F//3exXlYGfPe72paHiIj0Q7cBDABWqxXt7e1aF2PGfvjDyH2/f/7nwMKF2paHiIj0QzcBHO9Ss9frhdls1qA0qRseBtxusV5YyJ7PREQUTTcB3NraipUrV6KmpgZNTU0oLy+HLMtoa2vTumgz8m//BgwOivVvflN0wCIiIgrRTQA/+OCDOHbsGNra2lBZWYnS0lJ4vV6sX79e66IlTVGAf/qnyOO//EvtykJERPqkmwAOKSkpgcPhQFtbGywWC44cOaJ1kZLW2Qm8+65Y37QJsNm0LQ8REemP7gI4xGq14hvf+EbMtITZ4B//MbLO2i8REcWjaQBv37590jGdy8vL0d3dncESpe7YMeCFF8T6DTcAX/+6tuUhIiJ90jSA29raYLPZsGvXLjz55JNRPaEPHTqEtra2rBpyEgD+1/+KDLzxZ38GzNJ8tG0iItIjzeNh/fr1WL9+PXp6euDxeCBJEvx+PwYGBtDU1ISdO3dqXcRpu3gR+PGPxfq8eUAWXj0nIqIM0TyAQyorK1FZWal1MVLS3g4MDYn1b30LKC/XtjxERKRfuu2ElY2eeiqyztovERFNhgGskg8+AF57Tax/9rPA5z6nbXmIiEjfGMAqGV/7feABwGDQrixERKR/DGAVXL0K/Ou/ivXCQuAP/1Db8hARkf4xgFXw/PPAmTNi/WtfA667TtPiEBFRFmAAq2D8WCIPPKBdOYiIKHswgFN08iTw4otifcUKIMvGDSEiIo0wgFP0v/83EAyK9e98ByjgJ0pERNPAuEiBokRGvjIYRAATERFNBwM4BW+8AfT0iHW7HbjxRm3LQ0RE2YMBnIJ/+7fIOm89IiKiZDCAZ+jqVaC1VazPn89pB4mIKDkM4Bn65S+BwUGx/rWvAQsXalocIiLKMgzgGRp/+fkP/kC7chARUXZiAM+ALAM//7lYX7wYqK7WtDhERJSFGMAz0NEBXLki1r/1LWCWbmZVJiKibMEAngFefiYiolQxgJN04gRw4IBYv/lmwGbTtjxERJSdGMBJ+vd/j6z/wR9w3l8iIpoZBnASFAX4yU8ij7/9be3KQkRE2Y0BnIT33jPivffE+qZNgNmsbXmIiCh7MYCT8OyzheF1Dj1JRESpYAAn4ac/nQ0AKCwE6uo0LgwREWW1nL2DVZIkuFwuWCwWmEwmAIDD4UjpmGfPir9X7r0XKCtLtYRERJTPcjKAZVlGdXU1uru7w+FbX18Pt9udcggDvPeXiIhSl5OXoHfv3g273R4OXwBwOp1wOp0pH7ukRNSAiYiIUpGTAdzR0QHbhBEyzGYzZFmGz+dL6dh1dcDcuSkdgoiIKDcDWJIkmOPcI2QymeD1elM6Ni8/ExGRGnIugGVZTvhcWVkZ+vv7Z3zsioog7rxzxi8nIiIKy7lOWAMDA5M+P1lA7927F3v37o3ZHgwGAQD33nsBgUBKxaMZGhoaivpJmcXPX3s8B9q7cOGCqsfLuQBORSAQwKlTpxI+v2rVIRw4EMxgiWiiVNvwKTX8/LXHc6Cd4eFhVY+XcwFcdu0G3Xg13YGBgaie0RMVFxdj2bJlMduDwSB6e3tx770WVFRUqFVUSsLQ0BB8Ph+sViuKioq0Lk7e4eevPZ4D7Z0+fVrV4+VcAIcCNt6laFmWUV5envC1DQ0NaGhoiNkeCARQUlKChQsXThrglH5FRUU8Bxri5689ngPtBFRug8y5TlhA5JajeOx2e2YLQ0REFEdOBnBtbS38fn/UNp/PB5PJBKvVqlGpiIiIInLuEjQANDU1wWazQZbl8KWalpYW7Nu3b0bHUxQFgGiDUfsSBE1PIBDA8PAwAoEACgpy8u9GXePnrz2eA+2FeqCHMiFVORnAJpMJHo8Hu3fvhsVigd/vh81mQ21t7YyO99hjjwEA1qxZo2YxiYgoCz322GP4wQ9+kPJxDIpaUZ7DKioq0NvbiyVLluDDDz/Uujh5afXq1ejt7cXSpUvxwQcfaF2cvMPPX3s8B9q7+eab0dfXh6VLl6rSIzona8BqC13uMRqNKC4u1rg0+Sl0DgoKCngONMDPX3s8B9ozGo0AoFoTABsSiIiINMAAJiIi0gADmIiISAMMYCIiIg2wE9Y0NDQ0IBAIsOODhngOtMXPX3s8B9pT+xzwNiQiIiIN8BI0ERGRBhjARBTF5/PB6XTGfU6SJNTX16O5uRlutxtutzvDpcsPk50Dm80Gr9cLWZYhyzLcbjeam5szXEJSA9uAJyFJElwuFywWS3hMaYfDoW2h8ozNZoPL5cKGDRsAAG1tbZBlGY2NjRqXLDf5fD5UVVXF/T2XZRnV1dXo7u4O/3+or6+H2+3m/wsVTXYOQs9XV1eHH9vtdng8nkwVLy94vV54PB7IsgxJklBXVxdzPtTIBwZwAvyy0Qd+2WSGJElwOp3YuHEjysrK4u6ze/du2O32qLlonU4nbDYb/0+oYDrnABBf8qHJZux2O2d4U5nP5wuHKyCyoLKyEn6/P2qbKvmgUFyNjY2Kw+GI2ub3+xWTyaRRifKTw+FQWlpaFJfLpXR3d2tdnLxgtVqVxsbGmO1ms1lpaWmJ2Q6A50Zlic6BoiiKy+XKcGnyy8TvfUVRlJaWFgWA4vf7FUVRLx/YBpxAR0cHbDZb1Daz2QxZluHz+TQqVf6xWCxwOBxobGzkX/oakyQJZrM5ZrvJZILX69WgRETqa2tri2lTDzWBhb771coHXoJOYKovG4YB5RNZlhM+V1ZWhv7+/swVJs/19/ejubkZJpMpfF7YJ0I98X6fQ5eZBwYGAKiXDwzgOPhlox/8stGH0BdPIpP9nyF1jW+fBETbo9PpjNpGM+f3+2O2hWq1GzZsUDUfeAk6Dn7Z6IckSWhsbAxfhvb7/QlvzyDKB+3t7VGP6+rq0NzczO+lNGppaQl3eFMzHxjApGv8stGHUK/ceJ/7wMBAVM9oyqxQ+yTb4dOjo6MDkiTFfBepgQEcB79s9ItfNtqY2AY2nizLKC8vz3CJ8lN9fX3C331JkjJcmtwnyzKcTic8Hk/4/4Ca+cAAjoNfNvrALxt9CfXyjMdut2e2MHnK7XbH/O6HvqfYMVR9dXV18Hg8UR2u1MwHBnAC/LLRHr9s9KW2tjamg4rP54PJZOL5yJBQf4jxvF4vTCZT+OoQqaO+vh4ulysqfEOdsdTKBwZwAvyy0R6/bLQRGmN4oqampvAYxCEtLS3Yt29f5gqXJxKdg+rqanR0dETt53K5sG/fPjaNqcjtdqOuri7qu16SpHCFQK184HSECciyDJvNFjPUWHV1NWpra7UtXJ4IfdmHPu/QOXG5XDwHKpNlGbt374YkSejo6IDJZILdbsfGjRujbvuSJAktLS2wWCzw+/3hgVIoddM9B6FxioHI5Bi8Kqcer9cLl8uFurq68DZZluHxeNDS0hKu/aqRDwzgSfDLRnv8siGiTCotLU14eXl8XKqRDwxgIiIiDbANmIiISAMMYCIiIg0wgIloSm63GxaLBRaLBW63e9qva25untHriPIB24CJaEputxtlZWUz7n0eCl92YiSKYA2YKM94vV6OJEakAwxgojxTXV3NsbSJdIABTJRHxs9rSkTaYgAT5ZFQzZfDqRJpjwFMlEcOHjzIkcSIdGKW1gUgovTyer1oaWkBICYXt1qt4XFu1Zpk3O12Rw3fZzabOV430RQYwEQ5zm63w263hwf537dvn6qXoJubmwEgasIATlpCNDUGMFGeSFf7r9PpxODgYNT7xJusnIiisQ2YKE94PJ60tf8++OCD4R7Wdrsd3d3daXkfolzCACbKE16vNy29nxsbG9HR0QGbzQaDwQCn06n6exDlIgYwUR6QJAmyLKO6ulr1Y7tcLvj9frS0tMBut6O5uRkdHR2qvw9RrmEAE+WBUPvv+EvQqY6GJUlSeIxns9kMh8MBj8cDq9WKgwcPpnRsonzAACbKA93d3VGXn71eL8rKylI6Zn19PVwuV8z2srKytNS0iXINA5goT5jNZgCALMvhmmqqx5vY2crr9cJkMnGwD6Jp4G1IRHnA5XKhrq4OTqcT5eXlcWuuMznmxDl+TSaTaoN7EOU6BjBRHjCZTPB4PKofc/zgG0SUHF6CJiIi0gADmIiISAMMYCIiIg0wgImIiDTAACaiaXE6nbBYLDE9nyfT3NwMi8WiSq9rolxjUBRF0boQRERE+YY1YCIiIg0wgImIiDTAACYiItIAA5iIiEgDDGAiIiINMICJiIg0wAAmIiLSAAOYiIhIAwxgIiIiDfz/fHEDkMc3cdoAAAAASUVORK5CYII=",
      "text/plain": [
       "Figure(PyObject <Figure size 500x500 with 3 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,(ax1,ax2,ax3)=plt.subplots(3,1,figsize=(5,5),sharex=true)\n",
    "plt.subplots_adjust(hspace = 0.1)\n",
    "\n",
    "ax1.plot(t,ps1,\"b-\", linewidth=2,label=L\"\\omega = 2.5\\qquad \\Delta=1/2\")\n",
    "ax2.plot(t,ps2,\"b-\", linewidth=2)\n",
    "ax3.plot(t,ps3,\"b-\", linewidth=2)\n",
    "\n",
    "ax1.set_aspect(\"auto\")\n",
    "ax2.set_aspect(\"auto\")\n",
    "ax3.set_aspect(\"auto\")\n",
    "\n",
    "ax1.tick_params(direction=\"out\",length=5,width=2,labelsize=14)\n",
    "ax2.tick_params(direction=\"out\",length=5,width=2,labelsize=14)\n",
    "ax3.tick_params(direction=\"out\",length=5,width=2,labelsize=14)\n",
    "\n",
    "ax1.grid(linewidth=1)\n",
    "ax2.grid(linewidth=1)\n",
    "ax3.grid(linewidth=1)\n",
    "\n",
    "ax1.set_ylabel(L\"\\rho(t)\",fontsize=16)\n",
    "ax2.set_ylabel(L\"\\dot{\\rho}(t)\",fontsize=16)\n",
    "ax3.set_ylabel(L\"\\omega_{\\rho}(t)\",fontsize=16)\n",
    "\n",
    "ax3.set_xlabel(L\"t\\ [s]\",fontsize=16,labelpad=0)\n",
    "xlim(0,20)\n",
    "\n",
    "ax1.legend(bbox_to_anchor=(0.3,0.3,0.5,1),loc=9,ncol=1, mode=\"expand\", borderaxespad=0,fontsize=11)\n",
    "\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "function β1(t,ρ0)\n",
    "    return convert(Float64,(ρ0/sol'[t,1])*mp.cos(sol'[t,3])+ρ0*sol'[t,2]*mp.sin(sol'[t,3]))\n",
    "end\n",
    "\n",
    "function β2(t,ρ0)\n",
    "    return convert(Float64,ρ0*sol'[t,1]*mp.sin(sol'[t,3]))\n",
    "end\n",
    "\n",
    "function β3(t,ρ0,dρ0)\n",
    "    return convert(Float64,(1/(ρ0*sol'[t,1])+dρ0*sol'[t,2])*mp.sin(sol'[t,3])+((dρ0/sol'[t,1])-(sol'[t,2]/ρ0))*mp.cos(sol'[t,3]))\n",
    "end\n",
    "\n",
    "function β4(t,ρ0,dρ0)\n",
    "    return convert(Float64,(sol'[t,1]/ρ0)mp.cos(sol'[t,3])-dρ0*sol'[t,1]*mp.cos(sol'[t,3]))\n",
    "end\n",
    "\n",
    ";"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "function qc(q,p,t)\n",
    "    return q*β1(t,1)-p*β2(t,1)\n",
    "end\n",
    "    \n",
    "function pc(q,p,t)\n",
    "    return q*β3(t,1,0)+p*β4(t,1,0)\n",
    "end\n",
    "\n",
    ";"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "qv = zeros(Float64,length(sol.t))\n",
    "for i in 1:length(sol.t)\n",
    "    qv[i] = qc(-3,-3,i)\n",
    "end\n",
    "pv = zeros(Float64,length(sol.t))\n",
    "for i in 1:length(sol.t)\n",
    "    pv[i] = pc(-3,-3,i)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "t1 = np.linspace(np.min(sol.t), np.max(sol.t), 200)  \n",
    "\n",
    "sp1 = spy.make_interp_spline(sol.t, qv, k=3)\n",
    "sp2 = spy.make_interp_spline(sol.t, pv, k=3)\n",
    "\n",
    "ps1 = sp1(t)\n",
    "ps2 = sp2(t)\n",
    "\n",
    ";"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 500x500 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figps = figure(figsize=(5,5))\n",
    "axps = gca(projection=\"3d\")\n",
    "plot3D(ps1,ps2,t1,\"b-\", linewidth=2)\n",
    "axps.view_init(30,-30)\n",
    "xlabel(L\"q\",fontsize=16)\n",
    "ylabel(L\"p\",fontsize=16)\n",
    "zlabel(L\"t\\ [s]\",fontsize=16)\n",
    "axps.tick_params(axis=\"both\",direction=\"out\",length=10,width=3,grid_linewidth=3,labelsize=14)\n",
    "axps.set_zticks(range(0,stop=20,step=5))\n",
    "axps.set_zticklabels([L\"0\",L\"5\",L\"10\",L\"15\",L\"20\"])\n",
    "show()\n",
    "tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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