From f1c65965c06d6524e9082af421d8b124f059010c Mon Sep 17 00:00:00 2001 From: Sergio Andres Fajardo Reyes <sergio2230661@correo.uis.edu.co> Date: Tue, 25 Jul 2023 02:03:11 +0000 Subject: [PATCH] Upload New File --- pendulo2.ipynb | 513 +++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 513 insertions(+) create mode 100644 pendulo2.ipynb diff --git a/pendulo2.ipynb b/pendulo2.ipynb new file mode 100644 index 0000000..127ce15 --- /dev/null +++ b/pendulo2.ipynb @@ -0,0 +1,513 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "031d4995-54a9-4fb4-9196-fd2b7cc8bad5", + "metadata": {}, + "source": [ + "# Ecuaciones a partir del ángulo de un péndulo" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "ef7b6e1c-3e21-42c2-a0a5-20546aa96891", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.integrate import ode" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "bd57c5c5-24db-4f4c-a398-fa69323b22e7", + "metadata": {}, + "outputs": [], + "source": [ + "def rhs_small_osc(t, X, g, L):\n", + " \"\"\"Ecuación para ángulos pequeños en un péndulo\"\"\"\n", + " th, w = X\n", + " dth = w\n", + " dw = -(g/L)*th\n", + " return [dth, dw]\n", + "\n", + "def rhs_osc(t, X, g, L):\n", + " \"\"\"Ecuación para todo ángulo en un péndulo\"\"\"\n", + " th, w = X\n", + " dth = w\n", + " dw = -(g/L)*np.sin(th)\n", + " return [dth, dw]" + ] + }, + { + "cell_type": "markdown", + "id": "17e427c2-0ad0-4e19-a96b-8e2c53df2d05", + "metadata": {}, + "source": [ + "## Datos de tracker" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "54e08211-29ce-4918-a2db-5f98be66323f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0. , -0.40291159],\n", + " [ 0.03332222, -0.40048976],\n", + " [ 0.06665556, -0.4013717 ],\n", + " [ 0.09997778, -0.40117184],\n", + " [ 0.1333 , -0.41584454],\n", + " [ 0.16663333, -0.46822631],\n", + " [ 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"execute_result" + } + ], + "source": [ + "Data1 = np.genfromtxt('Pendulo2rad.txt')\n", + "Data1" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "ce3e416d-ad71-4e97-a10b-479d2e4c97bb", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "plt.plot(Data1[:,0], Data1[:,1], '.')\n", + "plt.xlabel('t(s)')\n", + "plt.ylabel('θ(rad)')\n", + "plt.savefig('pendulo2data.pdf', bbox_inches = 'tight')" + ] + }, + { + "cell_type": "markdown", + "id": "dc8d0764-79c7-4eb8-83d7-d7b4c502de99", + "metadata": {}, + "source": [ + "## Uso de las ecuaciones a partir de los datos" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "cec3fb66-f07a-463d-a1bb-8eb20d52993c", + "metadata": {}, + "outputs": [], + "source": [ + "ti = Data1[0,0]\n", + "tf = Data1[-1,0]\n", + "dt = 0.01\n", + "\n", + "# Parameters\n", + "g = 9.8\n", + "L = 0.7\n", + "\n", + "# Initial conditions\n", + "th_i = Data1[0,1]\n", + "w_i = 0\n", + "X_i = [th_i, w_i]\n", + "\n", + "t = [ti]\n", + "th = [th_i]\n", + "w = [w_i]\n", + "\n", + "\n", + "solver_small = ode(rhs_small_osc)\n", + "method = \"dopri5\"\n", + "solver_small.set_integrator(method)\n", + "solver_small.set_initial_value(X_i, ti)\n", + "solver_small.set_f_params(g, L)\n", + "\n", + "while solver_small.t < tf and solver_small.successful():\n", + " th.append(solver_small.integrate(solver_small.t + dt)[0])\n", + " w.append(solver_small.integrate(solver_small.t + dt)[1])\n", + " t.append(solver_small.t + dt)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "e262c194-ac97-4928-b025-285bba65f3a1", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "plt.plot(t, th)\n", + "plt.xlabel('t(s)')\n", + "plt.ylabel('θ(rad)')\n", + "plt.savefig('pendulo2_smallosc.pdf', bbox_inches = 'tight')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "ecd0afc2-06d4-4efa-9984-a9e6894cc61b", + "metadata": {}, + "outputs": [], + "source": [ + "ti = Data1[0,0]\n", + "tf = Data1[-1,0]\n", + "dt = 0.01\n", + "\n", + "# Parameters\n", + "g = 9.8\n", + "L = 0.7\n", + "\n", + "# Initial conditions\n", + "th_i2 = Data1[0,1]\n", + "w_i = 0\n", + "X_i2 = [th_i2, w_i]\n", + "\n", + "t2 = [ti]\n", + "th2 = [th_i2]\n", + "w2 = [w_i]\n", + "\n", + "solver_osc = ode(rhs_osc)\n", + "method = \"dopri5\"\n", + "solver_osc.set_integrator(method)\n", + "solver_osc.set_initial_value(X_i2, ti)\n", + "solver_osc.set_f_params(g, L)\n", + "\n", + "while solver_osc.t < tf and solver_osc.successful():\n", + " th2.append(solver_osc.integrate(solver_osc.t + dt)[0])\n", + " w2.append(solver_osc.integrate(solver_osc.t + dt)[1])\n", + " t2.append(solver_osc.t + dt)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "4f696f8f-198c-4061-900f-da489eb5e0df", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "plt.plot(t2,th2)\n", + "plt.xlabel('t(s)')\n", + "plt.ylabel('θ(rad)')\n", + "plt.savefig('pendulo2_osc.pdf', bbox_inches = 'tight')" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "67d3eb96-9378-45fa-b751-d8487cfac0c5", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "plt.plot(t, th, t2, th2)\n", + "plt.xlabel('t(s)')\n", + "plt.ylabel('θ(rad)')\n", + "plt.savefig('pendulo2_comparing.pdf', bbox_inches = 'tight')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9f840f78-94d0-4f3d-85af-2ec3d6fe4583", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.10.9" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} -- GitLab