Bola quicando.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation\n",
    "from IPython.display import HTML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Gravidade em m/s^2\n",
    "g = 9.81\n",
    "# Coeficiente de restituição\n",
    "α = 0.65\n",
    "\n",
    "# Passo e tempo e tmax\n",
    "tmax  = 6\n",
    "dt    = 0.01\n",
    "# Array de tempos\n",
    "tarr = np.arange(start = 0, stop = tmax+dt, step = dt)\n",
    "\n",
    "#Condições iniciais em m/s\n",
    "x0 , y0  = 0., 5.\n",
    "vx0, vy0 = 3., 2.\n",
    "\n",
    "# Arrays de pos e vel\n",
    "pos = np.zeros((tarr.size, 2)) # pos[t] = x(t) , y(t)\n",
    "vel = np.zeros((tarr.size, 2)) # vel[t] = vx(t), vy(t)\n",
    "pos[0] = x0 , y0\n",
    "vel[0] = vx0, vy0 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(1, tarr.size):\n",
    "    \n",
    "    # Movimento em x\n",
    "    vel[i,0] = vel[i-1,0]\n",
    "    pos[i,0] = pos[i-1,0] + vel[i-1,0]*dt\n",
    "\n",
    "    # Movimento em y\n",
    "    vel[i,1] = vel[i-1,1] - g*dt\n",
    "    pos[i,1] = pos[i-1,1] + vel[i-1,1]*dt\n",
    "    # Condição para a bola quicar no chão\n",
    "    if pos[i,1] <= 0.:\n",
    "        pos[i,1] = 0.\n",
    "        vel[i,0] = α*vel[i,0]\n",
    "        vel[i,1] = α*(-vel[i,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,1, figsize = (15,10))\n",
    "ax.plot(pos[:,0], pos[:,1])\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set up a new Figure, with equal aspect ratio so the ball appears round.\n",
    "fig, ax = plt.subplots(figsize = (10,10))\n",
    "\n",
    "# These are the objects we need to keep track of.\n",
    "line, = ax.plot([], [], lw=2)\n",
    "ball = plt.Circle((x0, y0), 0.08)\n",
    "ax.add_patch(ball)\n",
    "ax.grid()\n",
    "xdata, ydata = [], []\n",
    "\n",
    "def init():\n",
    "    \"\"\"Initialize the animation figure.\"\"\"\n",
    "    ax.set_xlim((0,8))\n",
    "    ax.set_ylim((0,8))\n",
    "    ax.set_xlabel('$x$ /m')\n",
    "    ax.set_ylabel('$y$ /m')\n",
    "    line.set_data(xdata, ydata)\n",
    "    ball.set_center((x0, y0))\n",
    "    return line, ball\n",
    "\n",
    "def animate(i):\n",
    "    \"\"\"For each frame, advance the animation to the new position, pos.\"\"\"\n",
    "    x, y = pos[i]\n",
    "    xdata.append(x)\n",
    "    ydata.append(y)\n",
    "    line.set_data(xdata, ydata)\n",
    "    ball.set_center((x, y))\n",
    "    return line, ball\n",
    "\n",
    "interval = 1000*dt\n",
    "anim = animation.FuncAnimation(fig, animate, frames = tarr.size,\n",
    "                               blit=True, interval=interval, repeat = False, init_func=init)\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "ACAAAAAiAAAAKQAAAB4AAAAeAAAAIAAAACoAAAAgAAAAIAAAABRzdGNvAAAAAAAAAAEAAAAwAAAA\n",
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       "dAAAACWpdG9vAAAAHWRhdGEAAAABAAAAAExhdmY1OC43Ni4xMDA=\n",
       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HTML(anim.to_html5_video())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "anim.save('test.mp4', fps=30, dpi=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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