Gravitation simulation with Jupyter

gravitation.ipynb

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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as animation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Ball:\n",
    "    def __init__(self, m, x, y, vx, vy):\n",
    "        self.m = m\n",
    "        self.x, self.y = x, y\n",
    "        self.vx, self.vy = vx, vy\n",
    "\n",
    "    def run(self, fx, fy):\n",
    "        self.x += self.vx\n",
    "        self.y += self.vy\n",
    "        self.vx += fx / self.m\n",
    "        self.vy += fy / self.m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "%matplotlib nbagg\n",
    "\n",
    "fig = plt.figure(figsize=(4,3))\n",
    "images = []\n",
    "ball = Ball(1,0,0,1,100)\n",
    "for _ in range(22):\n",
    "    image = plt.scatter([ball.x],[ball.y])\n",
    "    images.append([image])\n",
    "    fx = 0\n",
    "    fy = -ball.m * 9.8\n",
    "    ball.run(fx,fy)\n",
    "\n",
    "ani = animation.ArtistAnimation(fig, images, interval=100, repeat_delay=1000)\n",
    "ani.save('cannon_ball.gif', writer='imagemagick', fps=25);\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib nbagg\n",
    "planet1 = Ball(10**11,0,10,-0.6,0)\n",
    "planet2 = Ball(10**11,0,-10,0.6,0)\n",
    "fig = plt.figure(figsize=(5,5))\n",
    "images = []\n",
    "plt.xlim(-50,50)\n",
    "plt.ylim(-50,50)\n",
    "\n",
    "G = 6.6*10**(-11)\n",
    "for i in range(1000):\n",
    "    if i % 2 == 1:\n",
    "        image = plt.scatter([planet1.x,planet2.x],[planet1.y,planet2.y])\n",
    "        images.append([image])\n",
    "    r2 = (planet1.x-planet2.x)**2 + (planet1.y-planet2.y)**2\n",
    "    fx = G*np.sign(planet2.x-planet1.x)*(planet1.m*planet2.m)/r2\n",
    "    fy = G*np.sign(planet2.y-planet1.y)*(planet1.m*planet2.m)/r2\n",
    "    planet1.run(fx,fy)\n",
    "    planet2.run(-fx,-fy)\n",
    "    \n",
    "ani = animation.ArtistAnimation(fig, images, interval=4, repeat_delay=1000)\n",
    "ani.save('binary_star.gif', writer='imagemagick', fps=50);\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib nbagg\n",
    "\n",
    "fig = plt.figure(figsize=(5,4.2))\n",
    "plt.xticks([])\n",
    "plt.yticks([])\n",
    "plt.xlim(-15000,15000)\n",
    "plt.ylim(-20000,5000)\n",
    "images = []\n",
    "\n",
    "balls = []\n",
    "num = 20\n",
    "for i in range(num):\n",
    "    vx = 200*np.cos(2*np.pi*i/num)\n",
    "    vy = 200*np.sin(2*np.pi*i/num)\n",
    "    balls.append(Ball(1,0,0,vx,vy))\n",
    "\n",
    "for _ in range(110):\n",
    "    xs, ys = [], []\n",
    "    for ball in balls:\n",
    "        xs.append(ball.x)\n",
    "        ys.append(ball.y)\n",
    "        fx = 0\n",
    "        fy = -ball.m * 9.8\n",
    "        ball.run(fx,fy)\n",
    "\n",
    "    image = plt.scatter(xs, ys)\n",
    "    images.append([image])\n",
    "\n",
    "ani = animation.ArtistAnimation(fig, images, interval=30, repeat_delay=1000)\n",
    "ani.save('fireworks.gif', writer='imagemagick', fps=40);\n",
    "plt.show()"
   ]
  }
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