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@odarbelaeze
Created April 18, 2017 18:14
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"# Lo que queremos simular"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"image/png": 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6lqCUg5s4II6WgT5uNSeSloLFvKSao9/MgbytXDR8KM+n7aB3uzAGJ+kRR0o5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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10ddc38d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"t = np.linspace(0, 1.02)\n",
"\n",
"x_0, y_0 = 0, 0\n",
"v_0_x, v_0_y = 5, 5\n",
"\n",
"x = x_0 + v_0_x * t\n",
"y = y_0 + v_0_y * t + 0.5 * (-9.8) * t ** 2\n",
"\n",
"plt.figure()\n",
"plt.plot(x, y)\n",
"plt.xlabel('x')\n",
"plt.ylabel('y')\n",
"plt.arrow(0, 0, .5, .5, head_width=0.05, head_length=0.1)\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"image/png": 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KioK12TaD/CnRrFi3iaFt6hAT5md0IiH+pZqLA+8MiCDhXBbvrohH29hCzLPg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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10e315278>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def euler(r, v, a, delta_t):\n",
" r_new = r + delta_t * v\n",
" v_new = v + delta_t * a\n",
" return r_new, v_new\n",
"\n",
"r = np.array([x_0, y_0])\n",
"v = np.array([v_0_x, v_0_y])\n",
"a = np.array([0, -9.8])\n",
"\n",
"delta_t = 0.01\n",
"\n",
"plt.figure()\n",
"\n",
"plt.plot(x, y, label='teoria')\n",
"plt.xlabel('x')\n",
"plt.ylabel('y')\n",
"# plt.arrow(0, 0, .5, .5, head_width=0.05, head_length=0.1)\n",
"\n",
"rs = []\n",
"vs = []\n",
"for i in range(int(1.02 / delta_t)):\n",
" rs.append(r)\n",
" vs.append(v)\n",
" r, v = euler(r, v, a, delta_t)\n",
"\n",
"rs = np.array(rs)\n",
"vs = np.array(vs)\n",
"\n",
"plt.plot(rs[:,0], rs[:,1], '--', label='prediccion')\n",
"\n",
"plt.legend()\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"image/png": 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5fB7r6+toa2vb1S5vBHq+XGhnN1oMRC/JS6USlpaWyryS6dSHHte0mge23iiVSrrsL5FI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\nQqFQggQqyBQKhRIk/D+fpLfbYNgrhgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10d7b9f98>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def integracion(r_0, v_0, a, delta_t):\n",
" rs = []\n",
" vs = []\n",
" r = np.array(r_0)\n",
" v = np.array(v_0)\n",
" a = np.array(a)\n",
" while r[-1] >= 0:\n",
" rs.append(r)\n",
" vs.append(v)\n",
" r, v = euler(r, v, a, delta_t)\n",
" return np.array(rs), np.array(vs)\n",
"\n",
"\n",
"rs, vs = integracion(\n",
" [0, 0, 0],\n",
" [5, 5, 5],\n",
" [0, 0, -9.8],\n",
" delta_t=0.05\n",
")\n",
"\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
"\n",
"fig = plt.figure()\n",
"ax = plt.subplot(111, projection='3d')\n",
"ax.plot(rs[:,0], rs[:,1], rs[:,2], '.')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"source": [
"# Resorte"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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i8CEJMZEsm5NEhZ4B7VPc/oVgdS66KTWcjFZ5+UOBhh4nPUOjQf9srCtMo2dw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\nAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10482d198>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"K = 2\n",
"M = 1\n",
"\n",
"def euler_resorte(x, v, delta_t):\n",
" return (\n",
" x + v * delta_t,\n",
" v + delta_t * (- K / M) * x\n",
" )\n",
"\n",
"x = 1\n",
"v = 0\n",
"delta_t = 1e-6\n",
"\n",
"\n",
"xs = []\n",
"vs = []\n",
"ts = []\n",
"for i in range(10000000):\n",
" xs.append(x)\n",
" vs.append(v)\n",
" ts.append(i * delta_t)\n",
" x, v = euler_resorte(x, v, delta_t)\n",
"\n",
"plt.figure()\n",
"plt.plot(ts, xs)\n",
"plt.title('Err: {}'.format(np.max(xs)))\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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t+hw8hoL/nmlKyLiQsR6scaFZu8GaDsCZe/octoRu8FlSXpE5JAtrd817XiGg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\nyCCDDDLIIACZYMgggwwyyCAA/w9Uw19Kf6eo1gAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10a796710>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"K = 2\n",
"M = 1\n",
"\n",
"def verlet_uno(x, v, delta_t):\n",
" return x + v * delta_t - 0.5 * K / M * x * delta_t ** 2\n",
"\n",
"def paso_verlet(x, x_anterior, delta_t):\n",
" return 2 * x - x_anterior - K / M * x * delta_t ** 2\n",
"\n",
"x = 1\n",
"v = 0\n",
"delta_t = 1e-3\n",
"\n",
"x_anterior = x\n",
"x = verlet_uno(x, v, delta_t)\n",
"\n",
"xs = [x_anterior]\n",
"ts = [0.0]\n",
"for i in range(1, 100000):\n",
" xs.append(x)\n",
" ts.append(i * delta_t)\n",
" x_anterior, x = x, paso_verlet(x, x_anterior, delta_t)\n",
"\n",
"plt.figure()\n",
"plt.plot(ts, xs)\n",
"plt.title('Err: {}'.format(np.max(xs)))\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"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": "3.6.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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