Aula_16.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "90c4a7b7-326f-4e47-8667-bfc7be79831a",
   "metadata": {},
   "source": [
    "# Aula 16\n",
    "\n",
    "Nas últimas aulas resolvemos o problema de movimento do pêndulo utilizando o método de Euler. Porém, como vimos, o método de Euler não é muito preciso, e o erro propagado ao longo da integração é muito grande. Para diminuir este problema, utilizamos passos muito pequenos e um intervalo curto de integração.\n",
    "\n",
    "Porém, existem ferramentas já disponibilizadas que permitem a realização de uma integração numérica por um intervalo muito maior de tempo com menor propagação de erro. Uma delas é o módulo **inegrate** do pacoto **scipy**. Normalmente o scipy já vem instalado com o python, mas caso este não seja o caso, basta utilizar o comando abaixo:\n",
    "\n",
    "```bash\n",
    "pip install scipy\n",
    "```\n",
    "\n",
    "O módulo integrate do scipy possui diversas funções para realizar integrações numéricas. Dêem uma olhada em sua documentação: https://docs.scipy.org/doc/scipy/tutorial/integrate.html\n",
    "\n",
    "Destes, iremos utilizar a função **solve\\_ivp**: https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html\n",
    "\n",
    "Para aprendermos a utilizá-la, vamos integrar novamente o movimento do pêndulo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0d9b31d6-215c-4542-ab07-8349dac23bba",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from scipy.integrate import solve_ivp\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "97137428-0249-4168-9f00-1f8515dd0c76",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Primeiramente definimos os valores das constantes que serão utilizadas no problema\n",
    "g = 9.81  # m/s²\n",
    "L = 5  # m\n",
    "m = 40  #kg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0c4279d0-2e5b-4029-a095-a68e40684cae",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Definimos a função que calcula as derivadas do movimento do pêndulo\n",
    "# Note que agora a função precisa receber como primeiro parâmetro o tempo, mesmo que a gente não o use,\n",
    "# e o segundo parâmetro será uma lista com os valores iniciais.\n",
    "# Isto é a forma como o solve_ivp trabalha. Outras funções ou outros pacotes\n",
    "# podem fazer as coisas de formas diferentes.\n",
    "def pendulo(t, y):\n",
    "    \"\"\" Calcula as derivadas do movimento do pêndulo com resistência do ar: Eq. 4 da Aula 12\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    t : float\n",
    "        Tempo\n",
    "    y : list\n",
    "        Lista com dois valores, o ângulo e a velocidade angular.\n",
    "    \"\"\"\n",
    "    # Agora precisamos separar os valores da lista em variáveis correspondentes\n",
    "    theta = y[0]\n",
    "    w = y[1]\n",
    "    \n",
    "    dthetadt = w  # A derivada de theta em relação ao tempo\n",
    "    dwdt = -(g/L)*np.sin(theta) # A derivada de omega em relação ao tempo desconsiderando resistência do ar\n",
    "    \n",
    "    # Agora devemos retornar uma lista com todas as derivadas\n",
    "    return [dthetadt, dwdt]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "44143f64-27e0-4a6d-a18b-d16ca88d37fd",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "t_span = [0, 50]  # Precisamos definir uma lista com dois elementos: t0 e tf.\n",
    "v0 = [60*np.pi/180, 0]  # Definimos a lista de condições iniciais.\n",
    "sol1 = solve_ivp(pendulo, t_span, v0)  # executamos o solve_ivp passando os parâmetros necessários."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "deef4c92-1442-44d9-9a18-65e63b446de2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  message: The solver successfully reached the end of the integration interval.\n",
      "  success: True\n",
      "   status: 0\n",
      "        t: [ 0.000e+00  5.880e-04 ...  4.969e+01  5.000e+01]\n",
      "        y: [[ 1.047e+00  1.047e+00 ... -5.915e-01 -8.742e-01]\n",
      "            [ 0.000e+00 -9.990e-04 ... -1.106e+00 -6.950e-01]]\n",
      "      sol: None\n",
      " t_events: None\n",
      " y_events: None\n",
      "     nfev: 566\n",
      "     njev: 0\n",
      "      nlu: 0\n"
     ]
    }
   ],
   "source": [
    "print(sol1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2a52424c-18d6-4845-9528-371e2b59c662",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "t = sol1.t  # Pegamos a lista de instantes de tempo, criada pelo próprio solve_ivp\n",
    "theta = sol1.y[0]  # Pegamos a lista de valores de theta\n",
    "w = sol1.y[1]  # Pegamos a lista de valores da velocidade angular"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "46cf949d-715b-4ee3-9e4e-8ba3c5d76c00",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fd745c0bd90>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f18b193d-5508-489a-b907-6d8a7730ee40",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Verificamos a solução utilizando a energia\n",
    "K = (m*(L*w)**2)/2\n",
    "U = m*g*L*(1-np.cos(theta))\n",
    "E = K + U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f9a83f47-a10b-471c-bd0f-c04674ae687d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd73da6f520>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, K, label='cinética')\n",
    "plt.plot(t, U, label='potencial')\n",
    "plt.plot(t, E, label='mecânica')\n",
    "plt.xlabel('Tempo (s)')\n",
    "plt.ylabel('Energia (J)')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "891e6c05-1276-4a08-928e-c4548646d8dc",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fd73d9c4c70>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, E)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eacc9960-b119-4dc8-9c49-05c13d41348b",
   "metadata": {},
   "source": [
    "Note que a energia mecânica está variando significativamente ao longo da integração, mostrando que a integração não está sendo realizada de forma adequada. Isso se deve à função **solve_ivp** não permitir que o usuário defina o passo da integração. Podemos, no entanto, fornecer um passo máximo, assim controlando um pouco mais a integração."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "19904c1a-a56c-4169-8001-e62f60ca9ce3",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "t_span = [0,1000]  # Vamos fazer agora a integração ao longo de mil segundos.\n",
    "sol2 = solve_ivp(pendulo, t_span, v0, method='RK45', max_step=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f43b42fc-891f-4266-8ffe-cac76dd088ce",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "t2 = sol2.t\n",
    "theta2 = sol2.y[0]\n",
    "w2 = sol2.y[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "907c037f-d978-4c46-b619-499bf1bc2b2c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fd73d9747c0>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t2, theta2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c4adf764-719d-4318-a274-d6b69bd104f8",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Verificamos a energia\n",
    "K2 = (m*(L*w2)**2)/2\n",
    "U2 = m*g*L*(1-np.cos(theta2))\n",
    "E2 = K2 + U2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "dd480243-2a30-480e-a667-3b6db676dea8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fd737451ae0>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plt.plot(t, E)\n",
    "plt.plot(t2, E2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b9ff4adf-029c-477e-9a34-bb42a4d3dd8f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.502521954527387e-10\n"
     ]
    }
   ],
   "source": [
    "print((E2[0] - E2[-1])/E[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6ed4448-2c73-4403-b614-bb075d9b06a0",
   "metadata": {},
   "source": [
    "Limitando o passo, mesmo sendo um passo maior que o utilizando com o método de Euler, e integrando por mil segundos, a energia variou muito pouco, 0.00000002%. Ou seja, provê um resultado confiável."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4dfc2b9-760b-4077-8c9f-95d8e6920664",
   "metadata": {},
   "source": [
    "## Movimento de Dois Corpos\n",
    "\n",
    "Agora que sabemos utilizar o solve_ivp, vamos realizar a integração de um problema diferente, o movimento planetário de dois corpos.\n",
    "\n",
    "Suponha dois corpos, com massas $m_1$ e $m_2$ no espaço como mostrado na figura abaixo. A posição deles em relação a um referencial inercial é $\\vec{r}_1$ e $\\vec{r}_2$, sendo a posição do corpo 2 em relação ao corpo 1 dado pelo vetor $\\vec{r} = \\vec{r}_2 - \\vec{r}_1$.\n",
    "\n",
    "![Movimendo de dois corpo](figuras/2-body-system.png)\n",
    "\n",
    "Se procurarmos descrever o movimento do corpo 2, a única força atuando será a força gravitacional do corpo 1. Esta força terá a direção do corpo 2 para o corpo 1, já que é uma força atrativa. Sendo assim, utilizando a segunda lei de Newton, a aceleração do corpo 2 será:\n",
    "\n",
    "$$m_2\\vec{a}_2 = -\\frac{Gm_1m_2}{r^2}\\hat{r}$$\n",
    "\n",
    "Onde $\\hat{r}$ denota que a direção da força está na direção do vetor $\\vec{r}$ e o sinal negativo indica que o sentido da força está no sentido oposto a $\\hat{r}$. Simplificando, obtemos:\n",
    "\n",
    "$$\\vec{a}_2 = -\\frac{Gm_1}{r^3}\\vec{r}$$\n",
    "\n",
    "Fazendo a mesma conta para obter a acelaração do objeto $m_2$, e separando em coordenadas  para um movimento apenas no plano x,y, temos:\n",
    "\n",
    "$$a_{1x} = \\frac{Gm_2}{r^3}(x_2 - x_1)$$\n",
    "$$a_{1y} = \\frac{Gm_2}{r^3}(y_2 - y_1)$$\n",
    "$$a_{2x} = -\\frac{Gm_1}{r^3}(x_2 - x_1)$$\n",
    "$$a_{2y} = -\\frac{Gm_1}{r^3}(y_2 - y_1)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2555d356-b276-45ab-ba53-6260b7da9e32",
   "metadata": {},
   "source": [
    "Para implementar essas equações na integração, precisamos notar que a aceleração é a segunda derivada da posição. Sendo uma equação diferencial ordinária de segunda ordem precisamos fornecer as posições e velocidades iniciais como condições iniciais do problema. Assim, para as posições, precisamos retornar suas derivadas, que são as velocidades, e para as velocidades precisamos retornar suas derivadas, que são as acelerações."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d5f88118-255c-4d6d-9723-3f53decea9ab",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Definimos a função \n",
    "def orbita(t, state_vector):\n",
    "    \"\"\"  Calcula as derivadas do movimento orbital de dois corpos\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    t: float\n",
    "        Tempo\n",
    "    state_vector : list\n",
    "        Lista com 8 valores. Para cada corpo, as posições x,y e as velocidades vx,vy.\n",
    "    \"\"\"\n",
    "    x1 = state_vector[0]\n",
    "    y1 = state_vector[1]\n",
    "    vx1 = state_vector[2]\n",
    "    vy1 = state_vector[3]\n",
    "    x2 = state_vector[4]\n",
    "    y2 = state_vector[5]\n",
    "    vx2 = state_vector[6]\n",
    "    vy2 = state_vector[7]\n",
    "    \n",
    "    # Calcula a distância entre os dois corpos\n",
    "    dx = (x2-x1)\n",
    "    dy = (y2-y1)\n",
    "    r = np.sqrt(dx**2+dy**2)\n",
    "    r3 = r**3\n",
    "    \n",
    "    # Calcula a aceleração dos dois corpos.\n",
    "    ax1 = (G*m2/r3)*dx\n",
    "    ay1 = (G*m2/r3)*dy\n",
    "    ax2 = -(G*m1/r3)*dx\n",
    "    ay2 = -(G*m1/r3)*dy\n",
    "    \n",
    "    # Retorna as velocidade e acelerações como uma lista\n",
    "    return [vx1, vy1, ax1, ay1, vx2, vy2, ax2, ay2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f9f7aa33-d84d-4f51-be7b-ee814bf98aa2",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Definimos as constantes necessárias\n",
    "G = 6.674184e-11 # m^3/(kg.s))\n",
    "ua = 1.495978707e11 # m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7e7fa61b-cd9c-4359-b825-cab3421d2f01",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Definimos as massas de cada corpo\n",
    "m1 = 1.989e30 # Massa do Sol em kg\n",
    "m2 = 5.972e24 # Massa da Terra em kg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "a22fc8dd-b3d1-4e1d-853b-e35cbabf133b",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Vamos definir as condições iniciais, colocando o Sol parado na origem e a Terra a uma distância de 1ua\n",
    "# com velocidade inicial de 30 km/s perpendicular à direção do Sol.\n",
    "z0 = [0, 0, 0, 0, 1*ua, 0, 0, 30000]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "baf9d73d-354e-409b-8b7a-088a223b8723",
   "metadata": {},
   "source": [
    "Com isso já é possível realizar a integração numérica, porém, ao considerarmos o centro de massa, pode-se verificar que existe uma velocidade do Centro de Massa que, se não for removida, fará com que todo o sistema se desloque a uma velocidade constante. Para corrigir isso e acompanharmos melhor o movimento dos corpos, precisamos considerar tudo em relação ao centro de massa, ou seja, colocar o centro de massa na origem e subtrair do sistema a velocidade do centro de massa."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "861cf29b-05ab-4a43-9fd0-94b54f3d6fb4",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def corrige_cm(state_vector, massas):\n",
    "    \"\"\" Corrige o vetor de estado do Centro de Massa.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    state_vector : list\n",
    "        Lista com 8 valores. Para cada corpo, as posições x,y e as velocidades vx,vy.\n",
    "    massas : list\n",
    "        Lista com as massas.\n",
    "    \"\"\"\n",
    "    # Obtem as componentes das posições e velocidades\n",
    "    x1 = state_vector[0]\n",
    "    y1 = state_vector[1]\n",
    "    vx1 = state_vector[2]\n",
    "    vy1 = state_vector[3]\n",
    "    x2 = state_vector[4]\n",
    "    y2 = state_vector[5]\n",
    "    vx2 = state_vector[6]\n",
    "    vy2 = state_vector[7]\n",
    "    \n",
    "    m1 = massas[0]\n",
    "    m2 = massas[1]\n",
    "    mt = m1+m2  # Massa Total\n",
    "    \n",
    "    # Posição do Centro de Massa\n",
    "    xcm = (x1*m1+x2*m2)/mt\n",
    "    ycm = (y1*m1+y2*m2)/mt\n",
    "    \n",
    "    # Velocidade do Centro de Massa\n",
    "    vxcm = (vx1*m1+vx2*m2)/mt\n",
    "    vycm = (vy1*m1+vy2*m2)/mt\n",
    "    \n",
    "    # Vetor de Estado Corrigido\n",
    "    sv_corr = [x1 - xcm, y1 - ycm, vx1 - vxcm, vy1-vycm, x2-xcm, y2-ycm, vx2-vxcm, vy2-vycm]\n",
    "    return sv_corr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "6c387e6c-34d0-4a89-be15-df1141c33826",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "z0_corr = corrige_cm(z0, [m1, m2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "c002948f-3ab7-4907-99ba-d0b1ec2bd24c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Vamos integrar por 40_000_000 de segundos com um passao máximo de 10_000 segundos\n",
    "t_span=[0, 4e7]\n",
    "sol = solve_ivp(orbita, t_span, z0_corr, max_step=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "244b035f-1127-472c-a041-d08568abca6c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  message: The solver successfully reached the end of the integration interval.\n",
      "  success: True\n",
      "   status: 0\n",
      "        t: [ 0.000e+00  6.648e-08 ...  4.000e+07  4.000e+07]\n",
      "        y: [[-4.492e+05 -4.492e+05 ... -1.381e+04 -1.358e+04]\n",
      "            [ 0.000e+00 -5.989e-09 ... -4.552e+05 -4.552e+05]\n",
      "            ...\n",
      "            [ 0.000e+00 -3.944e-10 ... -2.957e+04 -2.957e+04]\n",
      "            [ 3.000e+04  3.000e+04 ...  1.318e+03  1.303e+03]]\n",
      "      sol: None\n",
      " t_events: None\n",
      " y_events: None\n",
      "     nfev: 24074\n",
      "     njev: 0\n",
      "      nlu: 0\n"
     ]
    }
   ],
   "source": [
    "print(sol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "a9619840-7cc5-4a69-b6d0-2acdb371553a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Obtemos os tempos e posições da integração\n",
    "t = sol.t\n",
    "x1 = sol.y[0]\n",
    "y1 = sol.y[1]\n",
    "x2 = sol.y[4]\n",
    "y2 = sol.y[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "30b1bdcb-1858-4b4c-840e-f0a2d348bdac",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-169089992821.48257,\n",
       " 164773012691.34763,\n",
       " -166914549788.5479,\n",
       " 166914618887.5792)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x1, y1)\n",
    "plt.plot(x2, y2)\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdd8f892-fe4d-4d5a-945b-485be9a708cd",
   "metadata": {},
   "source": [
    "Vamos agora fazer a animação da órbita"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "c0a8fe5e-11cb-44ee-9bd3-5b8c591873bf",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_10752/344350493.py:47: MatplotlibDeprecationWarning: Setting data with a non sequence type is deprecated since 3.7 and will be remove two minor releases later\n",
      "  sun.set_data(x1[j]/ua, y1[j]/ua)\n",
      "/tmp/ipykernel_10752/344350493.py:48: MatplotlibDeprecationWarning: Setting data with a non sequence type is deprecated since 3.7 and will be remove two minor releases later\n",
      "  terra.set_data(x2[j]/ua, y2[j]/ua)\n"
     ]
    },
    {
     "data": {
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       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# importamos do matplotlib o módulo de animação\n",
    "# e importamos do Ipython a ferramenta para que a animação possa ser apresentada em HTML e visualizada no navegador\n",
    "from matplotlib import animation\n",
    "from IPython.display import HTML\n",
    "\n",
    "# Quantos frames por segundo a animação deve apresentar\n",
    "FPS=30  #\n",
    "#plt.style.use('default')\n",
    "\n",
    "# Cria o quadro onde a figura será desenhada no matplotlib e pega um ponteiro para o objeto deste quadro.\n",
    "fig = plt.figure(figsize=(8, 8), dpi=100)\n",
    "\n",
    "# Modifica os limites da figura para cobrir o quadro inteiro\n",
    "ax = plt.axes(xlim=(-1.1, 1.1), ylim=(-1.1, 1.1))\n",
    "\n",
    "# Garante que o eixo x e o eixo y possuam a mesma escala\n",
    "ax.set_aspect('equal')\n",
    "\n",
    "# remove os eixos que normalmente aparecem\n",
    "ax.axis('off')\n",
    "\n",
    "# Define os elementos da animação\n",
    "terra, = ax.plot([], [], 'bo')  # Cria um ponto para a Terra e pega um ponteiro para o objeto deste ponto\n",
    "sun, = ax.plot([], [], 'ro')  # Cria um ponto para o Sol e pega um ponteiro para o objeto deste ponto\n",
    "orbit, = ax.plot([], [], 'b')  # Cria uma linha para a órbita da Terra e pega um ponteiro para o objeto desta linha\n",
    "\n",
    "# Define de quantos em quantos pontos da integração será o intervalo entre os frames.\n",
    "step = 5  # O primeiro frame será a posição no tempo t[0], o segundo frame será a posição no tempo t[5] ...\n",
    "\n",
    "# Pega o último valor do tempo para calcular o número de frames total\n",
    "framesNum = int(len(t)/step)\n",
    "\n",
    "def animate(j):\n",
    "    \"\"\" Função de animação. Ela será chamada para cada frame\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    j : int\n",
    "        Número do frame\n",
    "    \"\"\"\n",
    "    # Calcula qual a posição da órbita será usada para o frame j\n",
    "    # Isto é necessário porque não precisamos plotar todos os instantes de tempo.\n",
    "    j = step*j\n",
    "    \n",
    "    # Em cada frame atualizamos a posição do círculo e da linha.\n",
    "    # Isso é necessário porque consome mais processamento fazer plots diferentes para cada frame\n",
    "    sun.set_data(x1[j]/ua, y1[j]/ua)\n",
    "    terra.set_data(x2[j]/ua, y2[j]/ua)\n",
    "    \n",
    "    # Note que para a órbita, plotamos apenas os 100 valores antes do ponto atual, para fazer um rastro da órbita\n",
    "    orbit.set_data(x2[np.max([0, j-100]):j]/ua, y2[np.max([0, j-100]):j]/ua)\n",
    "\n",
    "# Cria a animação\n",
    "anim = animation.FuncAnimation(fig, animate, frames=framesNum, interval=1000/FPS)\n",
    "\n",
    "plt.close(anim._fig)\n",
    "\n",
    "# Mostra a animação\n",
    "# Pode demorar um pouco para aparecer.\n",
    "HTML(anim.to_html5_video())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "72c438c7-8a97-4b02-a8c6-d0f7b9366e12",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1dd72f12-588d-434e-bf1f-12bc9786ee67",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "e29c99f2-f5e2-43b4-a676-74b2eeb026ab",
   "metadata": {},
   "source": [
    "Vamos fazer uma nova integração, agora modificando a velocidade inicial da Terra pela metade para ver o movimento elíptico."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "1cf13c1a-050c-410b-8aab-43f221917d37",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "z0 = [0, 0, 0, 0, 1*ua, 0, 0, 15000]\n",
    "z0_corr = corrige_cm(z0, [m1, m2])\n",
    "t_span=[0, 4e7]\n",
    "sol = solve_ivp(orbita, t_span, z0_corr, max_step=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "be91ba50-a315-4b29-8048-b2af29265c69",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "t = sol.t\n",
    "x1 = sol.y[0]\n",
    "y1 = sol.y[1]\n",
    "x2 = sol.y[4]\n",
    "y2 = sol.y[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "68ecf162-6fff-4855-8def-0d4935536e01",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_10752/344350493.py:47: MatplotlibDeprecationWarning: Setting data with a non sequence type is deprecated since 3.7 and will be remove two minor releases later\n",
      "  sun.set_data(x1[j]/ua, y1[j]/ua)\n",
      "/tmp/ipykernel_10752/344350493.py:48: MatplotlibDeprecationWarning: Setting data with a non sequence type is deprecated since 3.7 and will be remove two minor releases later\n",
      "  terra.set_data(x2[j]/ua, y2[j]/ua)\n"
     ]
    },
    {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
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      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# importamos do matplotlib o módulo de animação\n",
    "# e importamos do Ipython a ferramenta para que a animação possa ser apresentada em HTML e visualizada no navegador\n",
    "from matplotlib import animation\n",
    "from IPython.display import HTML\n",
    "\n",
    "# Quantos frames por segundo a animação deve apresentar\n",
    "FPS=30  #\n",
    "#plt.style.use('default')\n",
    "\n",
    "# Cria o quadro onde a figura será desenhada no matplotlib e pega um ponteiro para o objeto deste quadro.\n",
    "fig = plt.figure(figsize=(8, 8), dpi=100)\n",
    "\n",
    "# Modifica os limites da figura para cobrir o quadro inteiro\n",
    "ax = plt.axes(xlim=(-1.1, 1.1), ylim=(-1.1, 1.1))\n",
    "\n",
    "# Garante que o eixo x e o eixo y possuam a mesma escala\n",
    "ax.set_aspect('equal')\n",
    "\n",
    "# remove os eixos que normalmente aparecem\n",
    "ax.axis('off')\n",
    "\n",
    "# Define os elementos da animação\n",
    "terra, = ax.plot([], [], 'bo')  # Cria um ponto para a Terra e pega um ponteiro para o objeto deste ponto\n",
    "sun, = ax.plot([], [], 'ro')  # Cria um ponto para o Sol e pega um ponteiro para o objeto deste ponto\n",
    "orbit, = ax.plot([], [], 'b')  # Cria uma linha para a órbita da Terra e pega um ponteiro para o objeto desta linha\n",
    "\n",
    "# Define de quantos em quantos pontos da integração será o intervalo entre os frames.\n",
    "step = 5  # O primeiro frame será a posição no tempo t[0], o segundo frame será a posição no tempo t[5] ...\n",
    "\n",
    "# Pega o último valor do tempo para calcular o número de frames total\n",
    "framesNum = int(len(t)/step)\n",
    "\n",
    "def animate(j):\n",
    "    \"\"\" Função de animação. Ela será chamada para cada frame\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    j : int\n",
    "        Número do frame\n",
    "    \"\"\"\n",
    "    # Calcula qual a posição da órbita será usada para o frame j\n",
    "    # Isto é necessário porque não precisamos plotar todos os instantes de tempo.\n",
    "    j = step*j\n",
    "    \n",
    "    # Em cada frame atualizamos a posição do círculo e da linha.\n",
    "    # Isso é necessário porque consome mais processamento fazer plots diferentes para cada frame\n",
    "    sun.set_data(x1[j]/ua, y1[j]/ua)\n",
    "    terra.set_data(x2[j]/ua, y2[j]/ua)\n",
    "    \n",
    "    # Note que para a órbita, plotamos apenas os 100 valores antes do ponto atual, para fazer um rastro da órbita\n",
    "    orbit.set_data(x2[np.max([0, j-100]):j]/ua, y2[np.max([0, j-100]):j]/ua)\n",
    "\n",
    "# Cria a animação\n",
    "anim = animation.FuncAnimation(fig, animate, frames=framesNum, interval=1000/FPS)\n",
    "\n",
    "plt.close(anim._fig)\n",
    "\n",
    "# Mostra a animação\n",
    "# Pode demorar um pouco para aparecer.\n",
    "HTML(anim.to_html5_video())"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "id": "2be6ec28-278f-4bf2-b8b0-86d9238ed23f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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