AE-245 - Lista 01 - Q4a.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bibliotecas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sym\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## DECLARA SIMBOLOS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x1, L, E, I1, I2, P, C1, C2, C3, C4, C5, C6, C7, C8 = sym.symbols('x1 L E I1 I2 P C1 C2 C3 C4 C5 C6 C7 C8')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## POLINOMIOS DE 3º GRAU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "y1 = C1 + C2*x1 + C3*x1**2 + C4*x1**3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## APLICA CONDIÇÃO DE CONTORNO y(0) = 0 PARA OBTER C1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "C1_ = sym.solve(y1.subs(x1,0), C1)[0]\n",
    "y1 = y1.subs(C1,C1_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## APLICA CONDIÇÃO DE CONTORNO y(L) = 0 PARA OBTER C2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "C2_ = sym.solve(y1.subs(x1,L),C2)[0]\n",
    "y1 = y1.subs(C2,C2_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SEGUNDA DERIVADA DE y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "ddy1 = y1.diff(x1,x1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ENERGIA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "en = sym.integrate((E*I1*ddy1**2)/2, (x1, 0, L/2)) + sym.integrate((E*I2*ddy1**2)/2, (x1, L/2, L)) - P*y1.subs(x1,L/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## RESOLVER SISTEMA PARA ENCONTRAR C3 E C4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "C3_, C4_ = sym.solve((en.diff(C3), en.diff(C4)), C3, C4).values()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EQUAÇÃO DA LINHA ELASTICA FINAL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{P x_{1} \\left(L^{2} \\left(I_{1} + 3 I_{2}\\right) + L x_{1} \\left(I_{1} - 5 I_{2}\\right) - 2 x_{1}^{2} \\left(I_{1} - I_{2}\\right)\\right)}{4 E \\left(I_{1}^{2} + 14 I_{1} I_{2} + I_{2}^{2}\\right)}$"
      ],
      "text/plain": [
       "P*x1*(L**2*(I1 + 3*I2) + L*x1*(I1 - 5*I2) - 2*x1**2*(I1 - I2))/(4*E*(I1**2 + 14*I1*I2 + I2**2))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y1 = y1.subs([(C3,C3_), (C4,C4_)]).simplify()\n",
    "y1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## VALIDA SE TODAS AS CONDIÇÕES DE CONTORNO FORAM SATISFEITAS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y(0) = 0:  True\n",
      "y(L) = 0:  True\n"
     ]
    }
   ],
   "source": [
    "print(\"y(0) = 0: \", y1.subs(x1,0).simplify() == 0)\n",
    "print(\"y(L) = 0: \", y1.subs(x1,L).simplify() == 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PLOT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1KnaXVGr0rLQKzsfbi/E3tCc40J//Lo7l2NlUJtzWxe6ylFKW6Sv2sWDbUZ68JoLuzYLsLqdU6RqIBxARHooK47URHVgZn8jISSs5laprIkrZbf3+U7w8fydRreszqp9n7PfISwPEg9zYrQnT7urOwaQUXliVys4jZ+0uSalK63hyKvd/up7gWlV5c2SnCn2+R0E0QDxMv7B6zBrTB2Ng5KSV/PL7CbtLUqrSSc/MZuxnG0hOzeTDO7pSq1rFPt+jIBogHqhNo5o83dufJtZtcj9ffcDukpSqVF6ev5O1+07x6ogOtA6uaXc5ZUYDxEMF+Xsxa0xv+obW5V/fbuWV+Tv1viJKlYOv1ycwfcU+7r2iOUM6NrK7nDKlAeLBqlfxYcqd3bij12V8+Osexny6npT0TLvLUspjbThwiie/2UrvFnV44pqKc2taZ7kUICISJCKLRCTW+unw3HwRibb6xIpIdJ72riKyVUTiRORdsfYyicjrIrJLRLaIyLciEuhKnZWZj7cXzw9tyzP/14bFO49x44crOXY21e6ylPI4R85cYPQn62lQqwoTbutSIe/vUVKufsIngCXGmFBgiTX9JyISBDwD9AR6AM/kCZqJwCgg1HoMttoXAe2MMR2A34EnXayzUhMR/np5c6ZEd2PvifMMeX85WxPO2F2WUh4jNSOLUR+vJyUtk6nR3akd4Gd3SeXC1QAZCsywns8AhjnoMwhYZIxJMsacIiccBotIMFDTGLPS5FyD4+OL8xtjfjLGXNzWsgoIcbFOBVwV0YDZ9/fBx8uLkR+uYP7WI3aXpFSFZ4zhsdlb2Hb4DO/c3JmwBjXsLqncuHomegNjzBEAY8wREanvoE9j4GCe6QSrrbH1PH97fncDXxVUgIiMImcthnr16hETE1OS+j3WuXPnChyLf3YW3tsIf/tsA9e38mVIS1+PPEb9osLGorLRschVWmPxbWw638VnMCLMF5/jO4k5vtP14iqIIgNERBYDDR289FQx38PRN5MppD3vez8FZAKfFbRwY8xkYDJAeHi4iYyMLGZZni0mJobCxmLQVVn865utfLPxEOlV6/L6yA4ee7/1osaiMtGxyFUaY/H1+gTmxm/mxm4hvHpDB4/+Q8yRIr8xjDFRBb0mIsdEJNha+wgGjjvolgBE5pkOAWKs9pB87YfzLDsauA4YYPQys6XO39ebN2/sSERwDV5ZsIt9ieeZfGc3GgdWtbs0pSqEVXsSeeKbLfRpWYeXrq/YdxZ0lqv7QOYBF4+qigbmOuizEBgoIrWtnecDgYXWpq9kEellHX1158X5RWQw8DgwxBiT4mKNqgAiwqh+LZkW3Z0DiSkMfX85a/bqXQ6VKkrc8XOM/mQ9l9UJYOLtXfGtBEdcOeLqpx4PXC0iscDV1jQi0k1EpgAYY5KAF4C11uN5qw3gfmAKEAfEAwus9veBGsAiEdkkIpNcrFMVon9Efb4d24ca/r7c+tEqPl21X+8tolQBjp1NJXraGny9hf/d1Z1aVT3zMiXF4dJGb2NMIjDAQfs64N4809OAaQX0a+egvZUrdamSa1W/BnPGXs5DX27k33O2se3QGZ4b2pYqPt52l6aU2zibmsFd/1vL6ZR0vhzVmyZB1ewuyVaVc71LOVSrqi9TorvzQP9WfLn2IDd9uIojZy7YXZZSbiEtM4sxn6wn9lgyE2/vSvuQWnaXZDsNEPUn3l7Co4PCmXR7F2KPJfN/7y1n1Z5Eu8tSylZZ2YZ/zNzMivhEXhvRgX5h9ewuyS1ogCiHBrcLZu4Dl1Ozqi+3TVnNlGV7dL+IqpSMMfx7zlZ+2HKEf10bwfAuel7zRRogqkCt6tdg7tjLiWpdnxd/2MnYzzeQnJphd1lKlavxP+7iizUHGdu/JaP6tbS7HLeiAaIKVcPfl0m3d+XJayJYuP0YQz/4jd+PJdtdllLlYkJMHB/+soc7el3GowPD7S7H7WiAqCKJCKOvbMln9/bk7IVMhr7/G1+vTyh6RqUqsKnL9/Laj7sZ2qkRzw1pWylPFCyKBogqtl4t6jB/3BV0CKnFI7M28/jsLaRmZNldllKl7uOV+3jh+x1c064hb4zsiJeXhocjGiCqROrX9Oeze3vyQP9WfLXuIMM++I244+fsLkupUvP56gP8Z+52olo34J2bO1fas8yLQ0dGlZiPtxePDgpnxt09OJ6cxv+9t5zZuklLeYAv1xzgX99upX94PT64rTN+PvoVWRgdHeW0K8PqMX9cXzo2qcWjszbzj682cS5Nb5mrKqZPVu7jiW+2Ehlej4m3d9WrMBSDBohyScNa/nx2by8ejgpjzqZDXPfuMjYfPG13WUqVyNTle3l67naiWtfnwzu64u+r4VEcGiDKZd5ewoNRoXxxXy/SMrO5YeIKJv0ST3a2nnio3N/EmHhe+H4Hg9s2ZMJtuuZREhogqtT0bFGHBQ/2ZWDbBoxfsIvbp67Wa2kpt2WM4ZUFO3n1x10M6diI927VfR4lpaOlSlVgNT8+uLULr97Qno0HTjPo7V+Zt/lw0TMqVY6ysg3Tt6fz4S97uK1nU96+qZMebeUEHTFV6kSEm7o3ZcGDfWlRrzrjvtjIg19u5MwFvQyKsl9aZhbjvtjILwmZjO3fkheHtcNbz/NwigaIKjPN6gYwe0xvHo4K4/stRxj09q/8+vsJu8tSldiZlAzunLqGH7Ye4aZwPx4bFKFnmLtAA0SVKR9vLx6MCuXbv/Whur8Pd05bw1PfbuW8Hu6rytmh0xcY+eEKNhw4xTs3d+Ka5pX3ToKlRQNElYsOIYF8//crGNWvBZ+vOcDgd35lRdxJu8tSlcT2w2cYPuE3jpxOZcbdPRjaqbHdJXkEDRBVbvx9vfnXta2ZObo33iLcOmU1T327VU8+VGVq4fajjJi4Ei8RZt3fmz4t69pdksfQAFHlrnuzIBY82I/7+jbn8zUHGPT2ryzdfdzuspSHMcYw6Zd4xny6nrCGOfe2iWhY0+6yPIoGiLJFVT9vnvpLG76+vw9V/bz56//W8uCXG0k8l2Z3acoDpGZk8ciszYxfsIu/tA/mq1G9qF/T3+6yPI4GiLJVl6a1+WHcFTwUFcr8rUcY8NYvzFp3UG+fq5yWcCqFEZNW8M2GQzwcFcZ7t3TWS5OUEQ0QZbsqPt48FBXGD+P60rJedR6bvYWbJq8i7rje+VCVzIq4kwx5/zf2n0xhanQ3HowK1cN0y5AGiHIbYQ1qMGt0b8YPb8/uo8lc884yXvtxFynpupNdFS472/D+z7HcPnU1dQL8mPvA5Qxo3cDusjyej90FKJWXl5dwc4+mRLVpwMvzdzIhJp45Gw/x7+vacE27hvrXpLrEyXNpPPzVJpbFnmRop0a8dH17qlfRr7byoGsgyi3VrV6Ft27sxKwxvalZ1Ze/fbaBO6auIfaYbtZSuVbEneTad5axZm8S44e35783ddLwKEcaIMqtdW8WxPd/v4LnhrRlS8JpBr+zjGfmbuPU+XS7S1M2SsvM4qUfdnDrlNVU9/dhztjLublHU11DLWcuBYiIBInIIhGJtX7WLqBftNUnVkSi87R3FZGtIhInIu+K9a8vIi+IyBYR2SQiP4lII1fqVBWbj7cX0X2aEfNYf27t0ZRPVu0n8o0Ypi7fS3pmtt3lqXL2+7Fkhn2wgo+W7eX2Xk354e99aR2s53fYwdU1kCeAJcaYUGCJNf0nIhIEPAP0BHoAz+QJmonAKCDUegy22l83xnQwxnQCvgf+42KdygMEBfjxwrB2LHiwH+0b1+KF73cQ9dYv/LDliB72WwlkZmXzwdI4rnt3OcfPpjLlzm68OKw9Vf30EF27uBogQ4EZ1vMZwDAHfQYBi4wxScaYU8AiYLCIBAM1jTErTc5v/8cX5zfGnM0zfwCg3w7qD+ENa/DJPT2Y/tfuVPX1ZuznG7h+wgpWxOu1tTzV78eSGT5xBa8v3M2A1vVZ+HA/otroUVZ2E1f+chOR08aYwDzTp4wxtfP1eRTwN8a8aE0/DVwAYoDxxpgoq70v8Lgx5jpr+iXgTuAM0N8Y4/A64CIyipy1GOrVq9d15syZTn8eT3Lu3DmqV69udxllLtsYlh3KZE5sBqfSDG3reDEizI/mtXL/Kq0sY1EcFW0s0rMM3+3JYP6eDKr5wB1tq9CjYensJK9oY1GW+vfvv94Y062k8xX5LyEii4GGDl56qpjv4WivlimkPeeJMU8BT4nIk8AD5GwGu3QGYyYDkwHCw8NNZGRkMcvybDExMVSWsbgKeDwji09W7mdCTBzPrUxlYJsGPBQVRptGNSvVWBSlIo3FstgTvDRnG/sTMxjWqRH/vq4NdatXKbXlV6SxcFdFBsjFNQRHROSYiAQbY45Ym6QcXREvAYjMMx1CztpHgvU8b7uje59+DvxAAQGiFORc6fe+fi24uUcTpizby7Tle/lpxzIGt23I5YG6o70iSTiVwivzd/HD1iM0q1ONT+/pyRWhegVdd+TquuA8IBoYb/2c66DPQuDlPDvOBwJPGmOSRCRZRHoBq8nZXPUegIiEGmNirf5DgF0u1qkqiRr+vjx8dRh3X96cqcv3MO23ffyYlskvSWsZ278VnZs6PFBQuYEL6VlM/CWeD3+JRwQeigplzJUt9TpWbszVABkPzBSRe4ADwEgAEekGjDHG3GsFxQvAWmue540xSdbz+4HpQFVggfUAGC8i4UA2sB8Y42KdqpKpVc2XfwwM554rWvDs50tZuv8U109YQZ+WdRh9ZUv6hdbVcwbcRGZWNrPXJ/DfxbEcPZvK/3VsxBPXRNA4sKrdpakiuBQgxphEYICD9nXAvXmmpwHTCujXzkH7Da7UpdRFtar5MrSVHy/ccQWfr97P1OV7iZ62hoiGNbi3bwv+r2MwVXz0L1w7GGNYuP0Yry/cRfyJ83RuGsh7t3ame7Mgu0tTxaTn/KtKoXoVH0b1a8ldfZozb/NhPvp1D49a94u4rWdTbuvVlPo19H4R5cEYw087jvHukli2Hz5Ly3oBfHhHVwa2aaBrhRWMBoiqVPx8vBjRNYQbujRmWexJpq/YxztLYpkQE8c17YK5rWdTejQP0i+yMpCZlc2P248yYWk8O46cpVmdarwxsiPDOjXCx1uvqlQRaYCoSklE6BdWj35h9dh78jwfr9zH1+sTmLf5MK3qV+eWHk0Z1qkRdUrxsNHKKiU9k1nrEpiyfA8Hky7QvG4Ab47syFANjgpPA0RVes3rBvDM/7Xln4Mi+H7LYT5bfYAXvt/B+AU7uSqiPiO6NiEyvB6++mVXIvtOnueTVfuZte4gZ1Mz6dI0kKeubcPVbRrg7aVreJ5AA0QpS1U/b0Z2a8LIbk3YfTSZ2esP8u3GQyzcfozAar5c2z6YoR0b0b1ZEF76BehQWmYWi3cc56t1B/n19xP4eAmD2zXkrj7N6KY7xz2OBohSDoQ3rMFTf2nDPwdH8OvvJ5i3+TDfbjjE56sP0KBmFQa1bcjgdg3p0Syo0m+GMcaw6eBp5mw8xNzNhzmdkkHDmv48HBXGLT2aUL+mHpzgqTRAlCqEr7cXA1o3YEDrBqSkZ7JoxzEWbD3KzHUH+XjlfmpX86V/eH36R9SnX1g9alX1tbvkcpGdbdh66Azztx7h+y1HOHT6An4+Xgxq25CRXUO4vFVd3UxVCWiAKFVM1fx8GNqpMUM7NSYlPZNffz/Bwu3HWLr7ON9sPIS3l9CpSSBXtKrLFaF16dQk0KP2m5xLy2RlfCI/7zrGkp3HOZ6cho+X0De0Lv+4Ooyr2zagpn/lCFCVQwNEKSdU8/NhcLtgBrcLJivbsOngKX7edZzlcYm893Ms7yyJxd/Xi85NatO9eRDdLqtNx5BAalWrOF+w59Iy2XzwNKv3JPJbfCKbD54mM9tQvYoPV4bVY0Dr+lwVUZ/Aan52l6psogGilIu8vYSulwXR9bIgHhsEZ1IyWLknkdV7E1m7L4n3f44l27rOdLM61egQEkibRjWJaFiDiIY1aVCziu3nnaRmZLHraDI7Dp9l++EzbDxwml1Hz5JtwEugfUggo/q14PJWdeneLAg/H89Zs1LO0wBRqpTVqubL4HY5O9kBklMz2HTwNFsSzrD54GnW7E1i3tEftoYAABLFSURBVObcC0/X8Pehed0AmtcN4LI6AYQEViU40J9GgVWpV6MKNar4uBww2dmGMxcyOHA2i8U7jnH4zAUOJKYQf+Ice06e52BSyh8hV8Pfhw4htXjgqlC6Xlabzk0DddOUckgDRKkyVsPfl76h9egbWu+PttMp6ew6msyuI2eJP3GevSfPs27fKeZtPkz+e7z5eXsRFOBHYDVfqlfxIaCKD9X8vPH19sLHW/D18sJgyMw2ZGUb0jKyOZ+eyfm0TM6lZZJ0Pp1TKRlkXUyIFesA8Pf1onnd6rRvXIuhnRrTJrgGbRvVIqR2VdvXiFTFoAGilA0Cq/nRq0UderWo86f29Mxsjp1N5dDpCxw+fYGT59JIPJ9O0rl0Tl/I4HxaJqdT0jl0OovMrGwysgyZ2dl4ieDtJfh4Cb7eXgRU8SGgijd1q1eh62W1qRNQhaAAPxIT4hl4eTcaBValToCfns+iXKIBopQb8fPxoklQNZoEVSuT5cfE7Kdjk8CiOypVDLonTCmllFM0QJRSSjlFA0QppZRTNECUUko5RQNEKaWUUzRAlFJKOUUDRCmllFM0QJRSSjlFA0QppZRTNECUUko5RQNEKaWUUzRAlFJKOUUDRCmllFNcChARCRKRRSISa/2sXUC/aKtPrIhE52nvKiJbRSRORN6VfDchEJFHRcSISF1X6lRKKVX6XF0DeQJYYowJBZZY038iIkHAM0BPoAfwTJ6gmQiMAkKtx+A88zUBrgYOuFijUkqpMuBqgAwFZljPZwDDHPQZBCwyxiQZY04Bi4DBIhIM1DTGrDTGGODjfPO/DfwTMJcsUSmllO1cvaFUA2PMEQBjzBERqe+gT2PgYJ7pBKutsfU8fzsiMgQ4ZIzZXNStNUVkFDlrMdSrV4+YmBjnPomHOXfunI6FRccil45FLh0L1xUZICKyGGjo4KWnivkejhLAFNQuItWsZQ8szsKNMZOByQDh4eEmMjKymGV5tpiYGHQscuhY5NKxyKVj4boiA8QYE1XQayJyTESCrbWPYOC4g24JQGSe6RAgxmoPydd+GGgJNAcurn2EABtEpIcx5mhR9SqllCofru4DmQdcPKoqGpjroM9CYKCI1LZ2ng8EFlqbvpJFpJd19NWdwFxjzFZjTH1jTDNjTDNygqaLhodSSrkXVwNkPHC1iMSSc8TUeAAR6SYiUwCMMUnAC8Ba6/G81QZwPzAFiAPigQUu1qOUUqqcuLQT3RiTCAxw0L4OuDfP9DRgWgH92hXxHs1cqVEppVTZ0DPRlVJKOUUDRCmllFM0QJRSSjlFA0QppZRTNECUUko5RQNEKaWUUzRAlFJKOUUDRCmllFM0QJRSSjlFA0QppZRTNECUUko5RQNEKaWUUzRAlFJKOUUDRCmllFM0QJRSSjlFA0QppZRTNECUUko5RQNEKaWUUzRAlFJKOUUDRCmllFM0QJRSSjlFA0QppZRTNECUUko5RQNEKaWUUzRAlFJKOUUDRCmllFM0QJRSSjnFpQARkSARWSQisdbP2gX0i7b6xIpIdJ72riKyVUTiRORdERGr/VkROSQim6zHta7UqZRSqvS5ugbyBLDEGBMKLLGm/0REgoBngJ5AD+CZPEEzERgFhFqPwXlmfdsY08l6zHexTqWUUqXM1QAZCsywns8AhjnoMwhYZIxJMsacAhYBg0UkGKhpjFlpjDHAxwXMr5RSyg25GiANjDFHAKyf9R30aQwczDOdYLU1tp7nb7/oARHZIiLTCto0ppRSyj4+RXUQkcVAQwcvPVXM9xAHbaaQdsjZtPWCNf0C8CZwdwH1jSJnMxj16tUjJiammGV5tnPnzulYWHQsculY5NKxcF2RAWKMiSroNRE5JiLBxpgj1iap4w66JQCReaZDgBirPSRf+2HrPY/leY+PgO8LqW8yMBkgPDzcREZGFtS1UomJiUHHIoeORS4di1w6Fq5zdRPWPODiUVXRwFwHfRYCA0WktrUpaiCw0NrklSwivayjr+68OL8VRhddD2xzsU6llFKlrMg1kCKMB2aKyD3AAWAkgIh0A8YYY+41xiSJyAvAWmue540xSdbz+4HpQFVggfUAeE1EOpGzCWsfMNrFOpVSSpUylwLEGJMIDHDQvg64N8/0NGBaAf3aOWi/w5W6lFJKlT09E10ppZRTXN2E5fYyMjJISEggNTXV7lLKVa1atdi5c6fdZbgFHYsc/v7+WBd7UKpUeHyAJCQkUKNGDZo1a1apfnmSk5OpUaOG3WW4BR0LMMaQmJhIQECA3aUoD+Lxm7BSU1OpU6dOpQoPpfITEerUqYO3t7fdpSgP4vEBAmh4KIX+HqjSVykCRCmlVOnTAFFKKeUUDRCllFJO0QBRyklz5szhvvvuY+jQofz000+21rJz507GjBnDiBEjmDhxoq21qMpDA8TNXLhwgSuvvJKsrKwSzZeenk6/fv3IzMx06f1nzZpFz5496dChA61ateK5555zaXnlvfzyrGXYsGF89NFHTJ8+na+++srWWlq3bs2kSZOYOXMm69atc6kWpYpLA8TNTJs2jeHDh5f4cEs/Pz8GDBjg0hfZjBkzePXVV/n666/ZsmULmzZtolq1asWePyYmhrvuuqvMll8S5VnLiy++yNixY22vZd68eVxxxRUMGHDJ1YWUKhvGGI95hIWFmfx27NhxSVt527Jli+nTp88f0+vXrzf9+/d32Ld3795m7969f0xHRkaan376yRhjzFNPPWX+/ve/F/g+mzZtMtdcc40xxpizZ8+WqMYzZ86YoKAgEx8fX6L58lq6dKmJjo4uteWX5LMXVkv+sSitWrKzs80///lPs2jRomLXkl9ZjMu1115b4LwbNmwo9vt4uqVLl9pdgtsA1hknvnM9/kz0vJ77bjs7Dp8t1WW2aVSTZ/6vbaF92rZtS3x8PFlZWXh7e/PII4/w5ptvXtIvPT2dPXv20KxZs9yan3uO//znPxw/fpyNGzcyb968At+nXbt2rF279pL2vn37kpycfEn7G2+8QVRUzu1evv32W3r27EmLFi0K/SzOcmb5JfnsdtTy3nvvsXjxYs6cOUNcXBxjxoyxrZaYmBi++eYb0tLSuPbaa0tch1LOqFQBYhcvLy/atm3L9u3biY2NpWnTpnTp0uWSfidPniQwMPBPbf369cMYw1tvvUVMTEyhm7a8vb3x8/O7JCyWLVtWZI3bt2+nU6dOxfxEf9azZ0/S0tI4d+4cSUlJfyzn1VdfZdCgQU4vvySfvbBasrOzef3110u9lnHjxjFu3LgS1QJlMy6RkZF6cyRV7ipVgBS1plCWevXqxW+//caECRP48ccfAdizZw8vvfQSZ86cYfbs2VStWvWSiz5u3bqVI0eOULdu3T+u55R/vrzS0tLw9/f/03KKswYSEBDAhQsXHNZe2PsBrF69GsjZ1j99+nSmT59+SZ/Clj9nzhx++OEHjh8/ztixYxk4cKBTn72gWvJfC6uwWnbu3Mk777zDyZMnGTBgAPfff3+BtRTF1XEBOH/+PP369eO5557juuuuc7oWpcqEM9u93PXhrvtAjDFm3rx5JigoyDz99NOXvHbDDTf88TwkJMRcuHDBGGPM4cOHTfv27c2OHTtMVFSU+fHHHwuczxhjTp48aSIiIowxJd8HsmbNGtOiRQtz9OhRY4wxqampZvLkyYW+X36FbesvzvKTkpLM3XffbYwp+WcvrJb8Y1GcWrKysoqsJT4+3tx9991lOi5PP/20GT9+vPnuu+9KpRbdB5JL94Hkwsl9IHoUVjmJiIigSpUqPP7444X2GzhwIMuXLyclJYXhw4fz5ptv0rp1a55++mmeffbZQuddunSp09u/u3fvzrPPPsugQYNo3749nTp14vhxR7e4d05xln/xaCZnPntp1pL3aKbCamnRogVTp04ts1oWL15MmzZtaNCgAUCZ16JUiTmTOu76cOc1kLFjx5rp06c7fC3vX40bNmwwt99+e7GWmf+vzeuvv97s2rXLGFPyNRBn3q+0FPdoJmdrcXYsCjuaydlaSuJf//qXefDBB83VV19thgwZYrKyslyuRddAcukaSC50DcQ9xcfHExERwYULF4iOjv7Ta4mJiYwZM4aNGzfyyiuvANC5c2f69+9f6ImEjuZLT09n2LBhhIeHl/pncPR+peni0UyzZ89m0qRJttYSExPDuHHjGD16tO1HM7300kv897//5dZbb+W+++7Dy0t/XZWbcSZ13PXhzmsg5a0s1kAqqrIai5MnT5rRo0ebFi1amJdffrlM3qO0a9E1kFy6BpILPQ9EqfJVp06dIteYyos71aIqD10nVkop5RQNEKWUUk7RAFFKKeWUShEgOfuIlKrc9PdAlTaPDxB/f38SExP1l0dVasYYEhMTS3yfGaUK4/FHYYWEhJCQkMCJEyfsLqVcpaam4u/vb3cZbkHHIoe/vz/nz5+3uwzlQTw+QHx9fWnevLndZZS7mJgYOnfubHcZbkHHItf+/fvtLkF5EJc2YYlIkIgsEpFY62ftAvpFW31iRSQ6T3tXEdkqInEi8q6ISJ7X/i4iu0Vku4i85kqdSimlSp+r+0CeAJYYY0KBJdb0n4hIEPAM0BPoATyTJ2gmAqOAUOsx2JqnPzAU6GCMaQu84WKdSimlSpmrATIUmGE9nwEMc9BnELDIGJNkjDkFLAIGi0gwUNMYs9I6lf7jPPPfD4w3xqQBGGNK77KwSimlSoWr+0AaGGOOABhjjohIfQd9GgMH80wnWG2Nref52wHCgL4i8hKQCjxqjLn0Xq2AiIwiZy0GIE1Etjn7YTxMXeCk3UW4CR2LXDoWuXQscjl1FdYiA0REFgMNHbz0VDHfQxy0mULaL9ZVG+gFdAdmikgL4+BYXGPMZGCyVes6Y0y3Ytbl0XQsculY5NKxyKVjkUtE1jkzX5EBYoyJKuRNj4lIsLX2EQw42tSUAETmmQ4BYqz2kHzth/PM840VGGtEJJucvxYq17G4SinlxlzdBzIPuHhUVTQw10GfhcBAEalt7TwfCCy0Nn0li0gv6+irO/PMPwe4CkBEwgA/dFVTKaXciqsBMh64WkRigautaUSkm4hMATDGJAEvAGutx/NWG+TsLJ8CxAHxwAKrfRrQwtqf8SUQ7WjzlQOTXfw8nkTHIpeORS4di1w6FrmcGgvRS3wopZRyhsdfC0sppVTZ0ABRSinllAoZICIy2LrMSZyIODr7vYqIfGW9vlpEmpV/leWjGGPxDxHZISJbRGSJiFxmR53loaixyNNvhIgYEfHYQziLMxYicqP1f2O7iHxe3jWWl2L8jjQVkaUistH6PbnWjjrLmohME5HjBZ0rJznetcZpi4h0KXKhztxI3c4H4E3ODvcW5BydtRlok6/P34BJ1vObga/srtvGsegPVLOe31+Zx8LqVwP4FVgFdLO7bhv/X4QCG4Ha1nR9u+u2cSwmA/dbz9sA++yuu4zGoh/QBdhWwOvXknMgk5BzDt7qopZZEddAegBxxpg9xph0co7SGpqvT95LrMwGBuS9UKMHKXIsjDFLjTEp1uQq/nzujScpzv8LyDki8DVyrnDgqYozFvcBH5icywthPPdyQcUZCwPUtJ7XIvd8NI9ijPkVSCqky1DgY5NjFRBond9XoIoYIAVdGsVhH2NMJnAGqFMu1ZWv4oxFXveQe6i0pylyLESkM9DEGPN9eRZmg+L8vwgDwkTkNxFZJSKDy6268lWcsXgWuF1EEoD5wN/LpzS3U9Lvkwp5P5DCLoFSkj6eoNifU0RuB7oBV5ZpRfYpdCxExAt4G7irvAqyUXH+X/iQsxkrkpy10mUi0s4Yc7qMaytvxRmLW4Dpxpg3RaQ38Ik1FtllX55bKfH3ZkVcA0kAmuSZznsJlEv6iIgPOaulha26VVTFGQtEJIqca5cNMdYVjj1QUWNRA2gHxIjIPnK28c7z0B3pxf0dmWuMyTDG7AV2kxMonqY4Y3EPMBPAGLMS8Cfn0kmVTbG+T/KqiAGyFggVkeYi4kfOTvJ5+frkvcTKCOBnY+0l8jBFjoW12eZDcsLDU7dzQxFjYYw5Y4ypa4xpZoxpRs7+oCHGGKcuIufmivM7MoecAywQkbrkbNLaU65Vlo/ijMUBYACAiLQmJ0Aq43X35gF3Wkdj9QLOGOtq6wWpcJuwjDGZIvIAOdfY8gamGWO2i8jzwDpjzDxgKjmroXHkrHncbF/FZaeYY/E6UB2YZR1HcMAYM8S2ostIMceiUijmWFy8Rt0OIAt4zBiTaF/VZaOYY/EI8JGIPEzOJpu7PPEPThH5gpxNlnWt/T3PAL4AxphJ5Oz/uZacS0ulAH8tcpkeOE5KKaXKQUXchKWUUsoNaIAopZRyigaIUkopp2iAKKWUcooGiFJKKadogCillHKKBohSSimn/D99/et/xN3bzAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_range = np.arange(0.0, 1.01, 0.01)\n",
    "x_1 = list()\n",
    "y_1 = list()\n",
    "\n",
    "for i in x_range:\n",
    "    value = y1.subs([(x1, i), (E,5), (L,1), (I1,200), (I2, 50), (P,-100)])\n",
    "    x_1.append(i)\n",
    "    y_1.append(value)\n",
    "\n",
    "plt.xlim([0, 1])\n",
    "plt.ylim([-0.006, 0])\n",
    "plt.plot(x_1, y_1)\n",
    "plt.legend([\"$y_1(x_1) = C_{1} + C_{2} x_{1} + C_{3} x_{1}^{2} + C_{4} x_{1}^{3}$\"])\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}