AE-245 - Lista 01 - Q5.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bibliotecas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\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": [
    "x, y, C1, C2, C3, C4 = symbols('x y C1 C2 C3 C4')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## POLINOMIOS DE 2º GRAU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = C1 + C2*x + C3*x**2"
   ]
  },
  {
   "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_ = solve(y.subs(x,0), C1)[0]\n",
    "y = y.subs(C1,C1_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## APLICA CONDIÇÃO DE CONTORNO y(1) = 0 PARA OBTER C2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "C2_ = solve(y.subs(x,1),C2)[0]\n",
    "y = y.subs(C2,C2_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PRIMEIRA DERIVADA DE y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "dy = y.diff(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ENERGIA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "I = integrate(1/2*dy**2 - 1/2*y**2 - x*y, (x, 0, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## RESOLVER SISTEMA PARA ENCONTRAR C3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "syms = [I.diff(C3)]\n",
    "var = C3\n",
    "sol = solve(syms, var)\n",
    "C3_ = sol[C3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EQUAÇÃO DA LINHA ELASTICA FINAL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "y2 = y.subs(C3,C3_)"
   ]
  },
  {
   "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(1) = 0:  True\n"
     ]
    }
   ],
   "source": [
    "print(\"y(0) = 0: \", y2.subs(x,0).simplify() == 0)\n",
    "print(\"y(1) = 0: \", y2.subs(x,1).simplify() == 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## DECLARA SIMBOLOS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "x, y, C1, C2, C3, C4 = symbols('x y C1 C2 C3 C4')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## POLINOMIOS DE 3º GRAU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = C1 + C2*x + C3*x**2 + C4*x**3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## APLICA CONDIÇÃO DE CONTORNO y(0) = 0 PARA OBTER C1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "C1_ = solve(y.subs(x,0), C1)[0]\n",
    "y = y.subs(C1,C1_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## APLICA CONDIÇÃO DE CONTORNO y(1) = 0 PARA OBTER C2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "C2_ = solve(y.subs(x,1),C2)[0]\n",
    "y = y.subs(C2,C2_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PRIMEIRA DERIVADA DE y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "dy = y.diff(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ENERGIA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "I = integrate(1/2*dy**2 - 1/2*y**2 - x*y, (x, 0, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## RESOLVER SISTEMA PARA ENCONTRAR C3 E C4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "syms = [I.diff(C3), I.diff(C4)]\n",
    "var = [C3, C4]\n",
    "sol = solve(syms, var)\n",
    "C3_ = sol[C3]\n",
    "C4_ = sol[C4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EQUAÇÃO DA LINHA ELASTICA FINAL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "y3 = y.subs([(C3,C3_), (C4,C4_)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## VALIDA SE TODAS AS CONDIÇÕES DE CONTORNO FORAM SATISFEITAS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y(0) = 0:  True\n",
      "y(1) = 0:  True\n"
     ]
    }
   ],
   "source": [
    "print(\"y(0) = 0: \", y3.subs(x,0).simplify() == 0)\n",
    "print(\"y(1) = 0: \", y3.subs(x,1).simplify() == 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## DECLARA SIMBOLOS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "x, A, B = symbols('x A B')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## POLINOMIO SENOIDAL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = A*sin(x) + B*cos(x) - x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## APLICA CONDIÇÃO DE CONTORNO y(0) = 0 PARA OBTER B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "B_ = solve(y.subs(x,0), B)[0]\n",
    "y = y.subs(B,B_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## APLICA CONDIÇÃO DE CONTORNO y(1) = 0 PARA OBTER A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "A_ = solve(y.subs(x,1), A)[0]\n",
    "y = y.subs(A,A_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PRIMEIRA DERIVADA DE y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "dy = y.diff(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ENERGIA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "I = integrate(1/2*dy**2 - 1/2*y**2 - x*y, (x, 0, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EQUAÇÃO DA LINHA ELASTICA FINAL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "y4 = y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## VALIDA SE TODAS AS CONDIÇÕES DE CONTORNO FORAM SATISFEITAS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y(0) = 0:  True\n",
      "y(1) = 0:  True\n"
     ]
    }
   ],
   "source": [
    "print(\"y(0) = 0: \", y4.subs(x,0).simplify() == 0)\n",
    "print(\"y(1) = 0: \", y4.subs(x,1).simplify() == 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PLOT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_range = np.arange(0.0, 1.1, 0.01)\n",
    "\n",
    "x_2 = list()\n",
    "x_3 = list()\n",
    "x_4 = list()\n",
    "y_2 = list()\n",
    "y_3 = list()\n",
    "y_4 = list()\n",
    "\n",
    "for i in x_range:\n",
    "    x_2.append(i)\n",
    "    value2 = y2.subs([(x, i)])\n",
    "    y_2.append(value2)\n",
    "    \n",
    "for i in x_range:\n",
    "    x_3.append(i)\n",
    "    value3 = y3.subs([(x, i)])\n",
    "    y_3.append(value3)\n",
    "\n",
    "for i in x_range:\n",
    "    x_4.append(i)\n",
    "    value = y4.subs([(x, i)])\n",
    "    y_4.append(value)\n",
    "\n",
    "plt.plot(x_2, y_2)\n",
    "plt.plot(x_3, y_3)\n",
    "plt.plot(x_4, y_4)\n",
    "plt.xlim([0, 1])\n",
    "plt.ylim([0, 0.08])\n",
    "plt.legend([\"$y_2(x) = C_{1} + C_{2} x + C_{3} x^{2}$\", \"$y_3(x) = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} x^{3}$\", \"$y_4(x) = A \\sin(x) + B \\cos(x) - x$\"])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_2, y_2)\n",
    "plt.plot(x_2, y_3)\n",
    "plt.plot(x_2, y_4)\n",
    "plt.xlim([0.4, 0.6])\n",
    "plt.ylim([0.06, 0.08])\n",
    "plt.legend([\"$y_2(x) = C_{1} + C_{2} x + C_{3} x^{2}$\", \"$y_3(x) = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} x^{3}$\", \"$y_4(x) = A \\sin(x) + B \\cos(x) - x$\"])\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ENERGIA TOTAL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -0.333333333333333 + \\frac{0.5}{\\tan{\\left(1 \\right)}}$"
      ],
      "text/plain": [
       "-0.333333333333333 + 0.5/tan(1)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "I2 = integrate(1/2*y2.diff(x)**2 - 1/2*y2**2 - x*y2, (x, 0, 1))\n",
    "I3 = integrate(1/2*y3.diff(x)**2 - 1/2*y3**2 - x*y3, (x, 0, 1))\n",
    "I4 = integrate(1/2*y4.diff(x)**2 - 1/2*y4**2 - x*y4, (x, 0, 1)).simplify()\n",
    "min(I2, I3, I4)"
   ]
  },
  {
   "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
}