{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# El oscilador armónico\n", "Consideremos el oscilador armónico, es decir, $\\ddot x = - k x$. Mediante un cambio de variables en el tiempo podemos suponer que $k=1$. Las soluciones de este sistema son de la forma $x(t) = a \\cos(t) + b \\sin (t)$ o, equivalentemente, $x(t) = A \\cos(t-\\phi)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Podemos escribir la ecuación como un sistema plano introduciendo una variable $y=\\dot x$. Entonces\n", "$$x' = y,\\quad y' = - x.$$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X(x,y) = [y,-x]\n", "cv = plot_vector_field(X(x,y),(x,-1.5,1.5),(y,-1.5,1.5),axes=false)\n", "cv" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos a hacer una pequeña animación relacionando la solución del sistema determinada por la condición inicial $(1,0)$, es decir, $(\\cos(-t),\\sin(-t))$ con una simulación del oscilador." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def muelle(t):\n", " xt = cos(t)\n", " dibujo = point((xt,-2),axes=false,size=50,color='red') + point(([2,2],[-2,-3]),size=0)\n", " dibujo += line([(-2,-2)] + [(-2+k*(xt+2)/10,-2+(-1)^k/10) for k in [1 .. 9]] + [(xt,-2)])\n", " dibujo += cv\n", " dibujo += implicit_plot(x^2+y^2==1,(x,-2,2),(y,-2,2),color=[0.8,0.8,0.8])\n", " dibujo += point((cos(-t),sin(-t)),axes=false,size=50,color='green')\n", " dibujo += line([ (cos(-t),sin(-t)) , (xt,-2) ],color='gray',linestyle='--')\n", " return dibujo" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "animacion = animate([muelle(t) for t in [0, 0.1 .. 2*pi]])" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Animation with 63 frames" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(animacion)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Animation with 42 frames" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# ============================================================\n", "# FONDO Y ELEMENTOS ESTÁTICOS\n", "# ============================================================\n", "\n", "base = Graphics()\n", "\n", "# Fondo degradado\n", "for k in range(25):\n", " y0 = -3.2 + k*(4.7/25)\n", " y1 = -3.2 + (k+1)*(4.7/25)\n", "\n", " gris = 0.98 - 0.18*k/25\n", "\n", " base += polygon(\n", " [(-2.5,y0),(2.5,y0),(2.5,y1),(-2.5,y1)],\n", " fill=True,\n", " rgbcolor=(gris,gris,gris)\n", " )\n", "\n", "# Campo de vectores (densidad moderada para no ralentizar demasiado)\n", "cv = plot_vector_field(\n", " (y, -x),\n", " (x,-2.5,2.5),\n", " (y,-3.2,1.5),\n", " plot_points=10,\n", " color=(0.75,0.75,0.75)\n", ")\n", "\n", "base += cv\n", "\n", "# Trayectoria horizontal de la masa\n", "base += line(\n", " [(-1.2,-2),(1.2,-2)],\n", " linestyle=':',\n", " color='gray'\n", ")\n", "\n", "base.axes(False)\n", "base.set_axes_range(-2.5,2.5,-3.2,1.5)\n", "\n", "# ============================================================\n", "# FRAME DE LA ANIMACIÓN\n", "# ============================================================\n", "\n", "def muelle(t):\n", "\n", " g = base + Graphics()\n", "\n", " # Punto de la rueda\n", " xg = cos(t)\n", " yg = -sin(t)\n", "\n", " # Posición de la masa\n", " xt = cos(t)\n", "\n", " # Trayectoria circular\n", " g += circle(\n", " (0,0),\n", " 1,\n", " linestyle='--',\n", " color='black'\n", " )\n", "\n", " # --------------------------------------------------------\n", " # MUELLE SINUSOIDAL\n", " # --------------------------------------------------------\n", "\n", " pts = [\n", " (\n", " -2 + (xt+2)*u,\n", " -2 + 0.14*sin(12*pi*u)\n", " )\n", " for u in srange(0,1.001,0.02)\n", " ]\n", "\n", " g += line(\n", " pts,\n", " color=(0.1,0.3,0.9),\n", " thickness=4\n", " )\n", "\n", " # --------------------------------------------------------\n", " # BIELA METÁLICA\n", " # --------------------------------------------------------\n", "\n", " g += line(\n", " [(xg,yg),(xt,-2)],\n", " color=(0.45,0.45,0.45),\n", " thickness=6\n", " )\n", "\n", " g += line(\n", " [(xg,yg),(xt,-2)],\n", " color='white',\n", " thickness=2\n", " )\n", "\n", " # --------------------------------------------------------\n", " # SOMBRA DE LA MASA\n", " # --------------------------------------------------------\n", "\n", " g += circle(\n", " (xt+0.05,-2.05),\n", " 0.15,\n", " fill=True,\n", " facecolor=(0.40,0.40,0.40),\n", " edgecolor=(0.40,0.40,0.40)\n", " )\n", "\n", " # --------------------------------------------------------\n", " # MASA ROJA\n", " # --------------------------------------------------------\n", "\n", " g += circle(\n", " (xt,-2),\n", " 0.15,\n", " fill=True,\n", " facecolor=(0.9,0.1,0.1),\n", " edgecolor=(0.5,0,0),\n", " thickness=2\n", " )\n", "\n", " # Brillo de la masa\n", " g += point(\n", " (xt-0.05,-1.95),\n", " size=80,\n", " color='white'\n", " )\n", "\n", " # --------------------------------------------------------\n", " # PUNTO VERDE\n", " # --------------------------------------------------------\n", "\n", " g += circle(\n", " (xg,yg),\n", " 0.10,\n", " fill=True,\n", " facecolor=(0.1,0.9,0.1),\n", " edgecolor='darkgreen',\n", " thickness=2\n", " )\n", "\n", " # Reflejo\n", " g += point(\n", " (xg-0.03,yg+0.03),\n", " size=50,\n", " color='white'\n", " )\n", "\n", " return g\n", "\n", "\n", "# ============================================================\n", "# ANIMACIÓN\n", "# ============================================================\n", "\n", "animacion = animate(\n", " [muelle(t) for t in srange(0,2*pi,0.15)]\n", ")\n", "\n", "animacion.show()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "ename": "ValueError", "evalue": "plot start point and end point must be different", "output_type": "error", "traceback": [ "\u001b[31m---------------------------------------------------------------------------\u001b[39m", "\u001b[31mValueError\u001b[39m Traceback (most recent call last)", "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[7]\u001b[39m\u001b[32m, line 59\u001b[39m\n\u001b[32m 55\u001b[39m \n\u001b[32m 56\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m g\n\u001b[32m 57\u001b[39m \n\u001b[32m 58\u001b[39m animacion = animate(\n\u001b[32m---> \u001b[39m\u001b[32m59\u001b[39m [frame(t0) \u001b[38;5;28;01mfor\u001b[39;00m t0 \u001b[38;5;28;01min\u001b[39;00m srange(Integer(\u001b[32m0\u001b[39m),Integer(\u001b[32m8\u001b[39m)*pi,RealNumber(\u001b[33m'0.2'\u001b[39m))]\n\u001b[32m 60\u001b[39m )\n\u001b[32m 61\u001b[39m \n\u001b[32m 62\u001b[39m animacion.show()\n", "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[7]\u001b[39m\u001b[32m, line 39\u001b[39m, in \u001b[36mframe\u001b[39m\u001b[34m(t0)\u001b[39m\n\u001b[32m 35\u001b[39m yt = x0*sin(t0)+y0*cos(t0)\n\u001b[32m 36\u001b[39m \n\u001b[32m 37\u001b[39m \u001b[38;5;66;03m# trayectoria recorrida\u001b[39;00m\n\u001b[32m 38\u001b[39m \n\u001b[32m---> \u001b[39m\u001b[32m39\u001b[39m trayectoria = parametric_plot(\n\u001b[32m 40\u001b[39m (\n\u001b[32m 41\u001b[39m x0*cos(s)-y0*sin(s),\n\u001b[32m 42\u001b[39m x0*sin(s)+y0*cos(s)\n", "\u001b[36mFile \u001b[39m\u001b[32m/opt/miniforge3/envs/sage/lib/python3.13/site-packages/sage/misc/decorators.py:495\u001b[39m, in \u001b[36moptions.__call__..wrapper\u001b[39m\u001b[34m(*args, **kwds)\u001b[39m\n\u001b[32m 493\u001b[39m options[\u001b[33m'\u001b[39m\u001b[33m__original_opts\u001b[39m\u001b[33m'\u001b[39m] = kwds\n\u001b[32m 494\u001b[39m options.update(kwds)\n\u001b[32m--> \u001b[39m\u001b[32m495\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[30;43mfunc\u001b[39;49m\u001b[30;43m(\u001b[39;49m\u001b[30;43m*\u001b[39;49m\u001b[30;43margs\u001b[39;49m\u001b[30;43m,\u001b[39;49m\u001b[30;43m \u001b[39;49m\u001b[30;43m*\u001b[39;49m\u001b[30;43m*\u001b[39;49m\u001b[30;43moptions\u001b[39;49m\u001b[30;43m)\u001b[39;49m\n", "\u001b[36mFile \u001b[39m\u001b[32m/opt/miniforge3/envs/sage/lib/python3.13/site-packages/sage/plot/plot.py:2765\u001b[39m, in \u001b[36mparametric_plot\u001b[39m\u001b[34m(funcs, *args, **kwargs)\u001b[39m\n\u001b[32m 2763\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m num_funcs == \u001b[32m2\u001b[39m \u001b[38;5;129;01mand\u001b[39;00m num_ranges == \u001b[32m1\u001b[39m:\n\u001b[32m 2764\u001b[39m kwargs[\u001b[33m'\u001b[39m\u001b[33mparametric\u001b[39m\u001b[33m'\u001b[39m] = \u001b[38;5;28;01mTrue\u001b[39;00m\n\u001b[32m-> \u001b[39m\u001b[32m2765\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[30;43mplot\u001b[39;49m\u001b[30;43m(\u001b[39;49m\u001b[30;43mfuncs\u001b[39;49m\u001b[30;43m,\u001b[39;49m\u001b[30;43m \u001b[39;49m\u001b[30;43m*\u001b[39;49m\u001b[30;43margs\u001b[39;49m\u001b[30;43m,\u001b[39;49m\u001b[30;43m \u001b[39;49m\u001b[30;43m*\u001b[39;49m\u001b[30;43m*\u001b[39;49m\u001b[30;43mkwargs\u001b[39;49m\u001b[30;43m)\u001b[39;49m\n\u001b[32m 2766\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m (num_funcs == \u001b[32m3\u001b[39m \u001b[38;5;129;01mand\u001b[39;00m num_ranges <= \u001b[32m2\u001b[39m):\n\u001b[32m 2767\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m sage.plot.plot3d.parametric_plot3d.parametric_plot3d(funcs, *args, **kwargs)\n", "\u001b[36mFile \u001b[39m\u001b[32m/opt/miniforge3/envs/sage/lib/python3.13/site-packages/sage/misc/decorators.py:495\u001b[39m, in \u001b[36moptions.__call__..wrapper\u001b[39m\u001b[34m(*args, **kwds)\u001b[39m\n\u001b[32m 493\u001b[39m options[\u001b[33m'\u001b[39m\u001b[33m__original_opts\u001b[39m\u001b[33m'\u001b[39m] = kwds\n\u001b[32m 494\u001b[39m options.update(kwds)\n\u001b[32m--> \u001b[39m\u001b[32m495\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[30;43mfunc\u001b[39;49m\u001b[30;43m(\u001b[39;49m\u001b[30;43m*\u001b[39;49m\u001b[30;43margs\u001b[39;49m\u001b[30;43m,\u001b[39;49m\u001b[30;43m \u001b[39;49m\u001b[30;43m*\u001b[39;49m\u001b[30;43m*\u001b[39;49m\u001b[30;43moptions\u001b[39;49m\u001b[30;43m)\u001b[39;49m\n", "\u001b[36mFile \u001b[39m\u001b[32m/opt/miniforge3/envs/sage/lib/python3.13/site-packages/sage/plot/plot.py:2051\u001b[39m, in \u001b[36mplot\u001b[39m\u001b[34m(funcs, *args, **kwds)\u001b[39m\n\u001b[32m 2049\u001b[39m \u001b[38;5;66;03m# if there is one extra arg, then it had better be a tuple\u001b[39;00m\n\u001b[32m 2050\u001b[39m \u001b[38;5;28;01melif\u001b[39;00m n == \u001b[32m1\u001b[39m:\n\u001b[32m-> \u001b[39m\u001b[32m2051\u001b[39m G = \u001b[30;43m_plot\u001b[39;49m\u001b[30;43m(\u001b[39;49m\u001b[30;43mfuncs\u001b[39;49m\u001b[30;43m,\u001b[39;49m\u001b[30;43m \u001b[39;49m\u001b[30;43m*\u001b[39;49m\u001b[30;43margs\u001b[39;49m\u001b[30;43m,\u001b[39;49m\u001b[30;43m \u001b[39;49m\u001b[30;43m*\u001b[39;49m\u001b[30;43m*\u001b[39;49m\u001b[30;43mkwds\u001b[39;49m\u001b[30;43m)\u001b[39;49m\n\u001b[32m 2052\u001b[39m \u001b[38;5;28;01melif\u001b[39;00m n == \u001b[32m2\u001b[39m:\n\u001b[32m 2053\u001b[39m \u001b[38;5;66;03m# if there are two extra args, then pull them out\u001b[39;00m\n\u001b[32m 2054\u001b[39m \u001b[38;5;66;03m# and pass them as a tuple\u001b[39;00m\n\u001b[32m 2055\u001b[39m xmin = args[\u001b[32m0\u001b[39m]\n", "\u001b[36mFile \u001b[39m\u001b[32m/opt/miniforge3/envs/sage/lib/python3.13/site-packages/sage/plot/plot.py:2176\u001b[39m, in \u001b[36m_plot\u001b[39m\u001b[34m(funcs, xrange, parametric, polar, fill, label, randomize, **options)\u001b[39m\n\u001b[32m 2174\u001b[39m excluded_points = []\n\u001b[32m 2175\u001b[39m imag_tol = options[\u001b[33m\"\u001b[39m\u001b[33mimaginary_tolerance\u001b[39m\u001b[33m\"\u001b[39m]\n\u001b[32m-> \u001b[39m\u001b[32m2176\u001b[39m funcs, ranges = \u001b[30;43msetup_for_eval_on_grid\u001b[39;49m\u001b[30;43m(\u001b[39;49m\u001b[30;43mfuncs\u001b[39;49m\u001b[30;43m,\u001b[39;49m\n\u001b[32m 2177\u001b[39m \u001b[30;43m \u001b[39;49m\u001b[30;43m[\u001b[39;49m\u001b[30;43mxrange\u001b[39;49m\u001b[30;43m]\u001b[39;49m\u001b[30;43m,\u001b[39;49m\n\u001b[32m 2178\u001b[39m \u001b[30;43m \u001b[39;49m\u001b[30;43moptions\u001b[39;49m\u001b[30;43m[\u001b[39;49m\u001b[30;43m'\u001b[39;49m\u001b[30;43mplot_points\u001b[39;49m\u001b[30;43m'\u001b[39;49m\u001b[30;43m]\u001b[39;49m\u001b[30;43m,\u001b[39;49m\n\u001b[32m 2179\u001b[39m \u001b[30;43m \u001b[39;49m\u001b[30;43mimaginary_tolerance\u001b[39;49m\u001b[30;43m=\u001b[39;49m\u001b[30;43mimag_tol\u001b[39;49m\u001b[30;43m)\u001b[39;49m\n\u001b[32m 2180\u001b[39m xmin, xmax, delta = ranges[\u001b[32m0\u001b[39m]\n\u001b[32m 2181\u001b[39m xrange = ranges[\u001b[32m0\u001b[39m][:\u001b[32m2\u001b[39m]\n", "\u001b[36mFile \u001b[39m\u001b[32m/opt/miniforge3/envs/sage/lib/python3.13/site-packages/sage/plot/misc.py:168\u001b[39m, in \u001b[36msetup_for_eval_on_grid\u001b[39m\u001b[34m(funcs, ranges, plot_points, return_vars, imaginary_tolerance)\u001b[39m\n\u001b[32m 165\u001b[39m range_steps = [\u001b[38;5;28mabs\u001b[39m(\u001b[38;5;28mrange\u001b[39m[\u001b[32m1\u001b[39m] - \u001b[38;5;28mrange\u001b[39m[\u001b[32m0\u001b[39m]) / (p - \u001b[32m1\u001b[39m)\n\u001b[32m 166\u001b[39m \u001b[38;5;28;01mfor\u001b[39;00m \u001b[38;5;28mrange\u001b[39m, p \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mzip\u001b[39m(ranges, plot_points)]\n\u001b[32m 167\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mmin\u001b[39m(range_steps) == \u001b[38;5;28mfloat\u001b[39m(\u001b[32m0\u001b[39m):\n\u001b[32m--> \u001b[39m\u001b[32m168\u001b[39m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[33m\"\u001b[39m\u001b[33mplot start point and end point must be different\u001b[39m\u001b[33m\"\u001b[39m)\n\u001b[32m 170\u001b[39m eov = \u001b[38;5;28;01mFalse\u001b[39;00m \u001b[38;5;66;03m# eov = \"expect one value\"\u001b[39;00m\n\u001b[32m 171\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m nargs == \u001b[32m1\u001b[39m:\n", "\u001b[31mValueError\u001b[39m: plot start point and end point must be different" ] } ], "source": [ "var('s,t')\n", "\n", "# Solución exacta del sistema\n", "#\n", "# x'=-y\n", "# y'= x\n", "#\n", "# x(t)=x0 cos(t)-y0 sin(t)\n", "# y(t)=x0 sin(t)+y0 cos(t)\n", "\n", "condiciones = [\n", " (1,0),\n", " (1/2,0),\n", " (3/2,0),\n", " (0,1),\n", " (0,-1),\n", " (-1,0)\n", "]\n", "\n", "cv = plot_vector_field(\n", " (-y,x),\n", " (x,-2,2),\n", " (y,-2,2),\n", " plot_points=12,\n", " color='gray'\n", ")\n", "\n", "def frame(t0):\n", "\n", " g = cv\n", "\n", " for x0,y0 in condiciones:\n", "\n", " xt = x0*cos(t0)-y0*sin(t0)\n", " yt = x0*sin(t0)+y0*cos(t0)\n", "\n", " # trayectoria recorrida\n", "\n", " trayectoria = parametric_plot(\n", " (\n", " x0*cos(s)-y0*sin(s),\n", " x0*sin(s)+y0*cos(s)\n", " ),\n", " (s,0,t0),\n", " color='blue'\n", " )\n", "\n", " g += trayectoria\n", " g += point((xt,yt),\n", " size=50,\n", " color='red')\n", "\n", " g.axes(False)\n", " g.set_axes_range(-2.1,2.1,-2.1,2.1)\n", "\n", " return g\n", "\n", "animacion = animate(\n", " [frame(t0) for t0 in srange(0,8*pi,0.2)]\n", ")\n", "\n", "animacion.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath", "language": "python", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.14" } }, "nbformat": 4, "nbformat_minor": 4 }