{ "cells": [ { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "view-in-github" }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "id": "PSS7a80VIKYV" }, "source": [ "# Resolución de la ecuaciones de Euler para un Sólido Rígido\n", "\n", "Tenemos 5 cubos idénticos, cada uno de lado 𝑑, masa 𝑀. Se sueldan formando una T: 3 cubos en horizontal (centrados en la parte superior), 2 cubos en vertical desde el cubo central.\n", "\n", "El centro de masas se encuentra sobre el eje vertical de simetría, a una altura $\\frac{3d}{5}$ por debajo del centro del cubo central de la base.\n", "\n", "Respecto al CDM, la triz de inercia es:\n", "\n", "\n", "$\n", "\\mathbf{I}_{CM} =\n", "\\begin{pmatrix}\n", "\\frac{121}{30}Md^2 & 0 & 0 \\\\\n", "0 & \\frac{17}{6}Md^2 & 0 \\\\\n", "0 & 0 & \\frac{103}{15}Md^2\n", "\\end{pmatrix}\n", "$\n", "\n", "donde los ejes principaleson el longitudinal paralelo al lado vertical, el transversal paralelo al lado horizontal, y el perpendicular al plano de la T (todos ellos pasando por su CDM).\n", "\n", "Generamos ahora la matriz de inercia como objeto de SymPy." ] }, { "cell_type": "markdown", "metadata": { "id": "maVWmuI6LxEs" }, "source": [ "## Ecuaciones de Euler para un Sólido Rígido\n", "\n", "Las ecuaciones de Euler describen el movimiento de rotación de un **sólido rígido** alrededor de su centro de masas, en un sistema de referencia ligado al cuerpo (es decir, que gira con él). Estas ecuaciones son fundamentales en la dinámica de cuerpos rígidos y se expresan en términos de los momentos principales de inercia y las componentes de la velocidad angular.\n", "\n", "Sean $( I_1, I_2, I_3)$ los momentos principales de inercia del cuerpo respecto a sus ejes principales, y $ (\\omega_1, \\omega_2, \\omega_3) $ las componentes de la velocidad angular $( \\boldsymbol{\\omega} )$ en dichos ejes. Las ecuaciones de Euler son:\n", "\n", "\\\n", "\\begin{aligned}\n", "I_1 \\frac{d\\omega_1}{dt} + (I_3 - I_2)\\omega_2 \\omega_3 &= M_1 \\\\\n", "I_2 \\frac{d\\omega_2}{dt} + (I_1 - I_3)\\omega_3 \\omega_1 &= M_2 \\\\\n", "I_3 \\frac{d\\omega_3}{dt} + (I_2 - I_1)\\omega_1 \\omega_2 &= M_3\n", "\\end{aligned}\n", "\n", "\n", "donde $( M_1, M_2, M_3 )$ son las componentes del momento externo (torque) aplicado al cuerpo respecto a los mismos ejes.\n", "\n", "Estas ecuaciones se derivan de la segunda ley de Newton para la rotación,\n", "\n", "$ \\mathbf{M} = \\frac{d\\mathbf{L}}{dt} $,\n", "\n", "considerando que el sistema de referencia está en rotación con el cuerpo. La aparición de los productos cruzados entre las componentes de $\\boldsymbol{\\omega} $ se debe al efecto giroscópico, que es crucial en muchos sistemas físicos, como satélites, giróscopos o vehículos en rotación.\n", "\n", "En el caso especial en que no hay torques externos $( \\mathbf{M} = \\mathbf{0} )$, el sistema describe la **dinámica libre** del sólido rígido, donde pueden aparecer fenómenos como la **inestabilidad de Dzhanibekov**." ] }, { "cell_type": "markdown", "metadata": { "id": "bZn4caCmhGt2" }, "source": [ "# Ecuaciones del movimiento\n", "Escribos las ecuaciones de Euler utilizando SimPy." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 122 }, "id": "OqTyBcYLhCee", "outputId": "7d57dcb1-9171-4310-a552-b4d5eeda11af" }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle I_{1} \\frac{d}{d t} \\omega_{1}{\\left(t \\right)} + \\left(- I_{2} + I_{3}\\right) \\omega_{2}{\\left(t \\right)} \\omega_{3}{\\left(t \\right)} = M_{1}$" ], "text/plain": [ "Eq(I1*Derivative(omega1(t), t) + (-I2 + I3)*omega2(t)*omega3(t), M1)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle I_{2} \\frac{d}{d t} \\omega_{2}{\\left(t \\right)} + \\left(I_{1} - I_{3}\\right) \\omega_{1}{\\left(t \\right)} \\omega_{3}{\\left(t \\right)} = M_{2}$" ], "text/plain": [ "Eq(I2*Derivative(omega2(t), t) + (I1 - I3)*omega1(t)*omega3(t), M2)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle I_{3} \\frac{d}{d t} \\omega_{3}{\\left(t \\right)} + \\left(- I_{1} + I_{2}\\right) \\omega_{1}{\\left(t \\right)} \\omega_{2}{\\left(t \\right)} = M_{3}$" ], "text/plain": [ "Eq(I3*Derivative(omega3(t), t) + (-I1 + I2)*omega1(t)*omega2(t), M3)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import sympy as sp\n", "\n", "# Definir variables\n", "I1, I2, I3 = sp.symbols('I1 I2 I3') # Momentos de inercia\n", "M1, M2, M3 = sp.symbols('M1 M2 M3') # Momentos externos\n", "omega1, omega2, omega3 = sp.symbols('omega1 omega2 omega3', cls=sp.Function)\n", "t = sp.Symbol('t') # Variable de tiempo\n", "\n", "# Definir funciones de velocidad angular\n", "omega1 = omega1(t)\n", "omega2 = omega2(t)\n", "omega3 = omega3(t)\n", "\n", "# Definir ecuaciones de Euler\n", "omega1_dot = sp.diff(omega1, t)\n", "omega2_dot = sp.diff(omega2, t)\n", "omega3_dot = sp.diff(omega3, t)\n", "\n", "Euler1 = sp.Eq(I1 * omega1_dot + (I3 - I2) * omega2 * omega3, M1)\n", "Euler2 = sp.Eq(I2 * omega2_dot + (I1 - I3) * omega3 * omega1, M2)\n", "Euler3 = sp.Eq(I3 * omega3_dot + (I2 - I1) * omega1 * omega2, M3)\n", "\n", "# Mostrar ecuaciones\n", "display(Euler1, Euler2, Euler3)\n" ] }, { "cell_type": "markdown", "metadata": { "id": "PmFswynrhVFm" }, "source": [ "Las únicas reacciones son las que aparecen en el punto de apoyo, que no pueden general momento. Por lo tanto, imponemos las condiciones\n", "\n", "$M1=M2=M3=0 $\n", "\n", "Además, los momentos de inercia los hemos definido previamente. Escribimos las ecuaciones y les damos nombre, para poder resolverlas más adelante." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 122 }, "id": "H8NBzu3MhRV3", "outputId": "31c0bbfc-5747-455e-ca42-7eebd9c76709" }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle I_{1} \\frac{d}{d t} \\omega_{1}{\\left(t \\right)} + \\left(- I_{2} + I_{3}\\right) \\omega_{2}{\\left(t \\right)} \\omega_{3}{\\left(t \\right)} = 0$" ], "text/plain": [ "Eq(I1*Derivative(omega1(t), t) + (-I2 + I3)*omega2(t)*omega3(t), 0)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle I_{2} \\frac{d}{d t} \\omega_{2}{\\left(t \\right)} + \\left(I_{1} - I_{3}\\right) \\omega_{1}{\\left(t \\right)} \\omega_{3}{\\left(t \\right)} = 0$" ], "text/plain": [ "Eq(I2*Derivative(omega2(t), t) + (I1 - I3)*omega1(t)*omega3(t), 0)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle I_{3} \\frac{d}{d t} \\omega_{3}{\\left(t \\right)} + \\left(- I_{1} + I_{2}\\right) \\omega_{1}{\\left(t \\right)} \\omega_{3}{\\left(t \\right)} = 0$" ], "text/plain": [ "Eq(I3*Derivative(omega3(t), t) + (-I1 + I2)*omega1(t)*omega3(t), 0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Euler1 = sp.Eq(I1 * omega1_dot + (I3 - I2) * omega2 * omega3, 0)\n", "Euler2 = sp.Eq(I2 * omega2_dot + (I1 - I3) * omega3 * omega1, 0)\n", "Euler3 = sp.Eq(I3 * omega3_dot + (I2 - I1) * omega3 * omega1, 0)\n", "\n", "# Mostrar ecuaciones\n", "display(Euler1, Euler2, Euler3)\n" ] }, { "cell_type": "markdown", "metadata": { "id": "Np-wYW1MiCDg" }, "source": [ "Para resolver el sistema de ecuaciones anterior de forma analítica, usamos la función \"dsolve\" de SimPy. Como argumentos de entrada, tenemos que meter las ecuaciones que hemos escrito anteriormente." ] }, { "cell_type": "markdown", "metadata": { "id": "Jr6Jstb0jsUW" }, "source": [ "El sistema es integrable porque conserva la energía cinética y el módulo del momento angular. Esto nos ayudará a reducir la complejidad de las ecuaciones diferenciales.\n", "* Energía cinética\n", "\n", "$$\n", "T = \\frac{1}{2}(I_1 \\omega_1^2 + I_2 \\omega_2^2 + I_3 \\omega_3^2)\n", "$$\n", "\n", "* Momento angular total\n", "\n", "$$\n", "L^2 = (I_1 \\omega_1)^2 + (I_2 \\omega_2)^2 + (I_3 \\omega_3)^2\n", "$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "a0r6UXJimy_m" }, "outputs": [], "source": [ "# Definición en SymPy\n", "T = sp.Rational(1, 2)*(I1*omega1**2 + I2*omega2**2 + I3*omega3**2)\n", "L2 = (I1*omega1)**2 + (I2*omega2)**2 + (I3*omega3)**2" ] }, { "cell_type": "markdown", "metadata": { "id": "pOs1D4aWm8vm" }, "source": [ "Usamos las constantes para eliminar variables." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "ADmtIPXum9U-", "outputId": "56f92655-3b5d-4aa2-9a39-3ee709eaab1b" }, "outputs": [ { "data": { "text/plain": [ "{omega2_sq: omega2(t)**2, omega3_sq: omega3(t)**2}" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "omega2_sq, omega3_sq = sp.symbols('omega2_sq omega3_sq')\n", "\n", "eq_energy = sp.Eq(I1*omega1**2 + I2*omega2_sq + I3*omega3_sq, 2*T)\n", "eq_momentum = sp.Eq((I1*omega1)**2 + (I2**2)*omega2_sq + (I3**2)*omega3_sq, L2)\n", "\n", "sol = sp.solve([eq_energy, eq_momentum], (omega2_sq, omega3_sq))\n", "sol" ] }, { "cell_type": "markdown", "metadata": { "id": "92A9wbCPnNW2" }, "source": [ "Sustituyendo en la ecuación de $\\dot{\\omega}_1$, obtenemos una ecuación de la forma:\n", "\n", "$$\n", "\\dot{\\omega}_1^2 = f(\\omega_1)\n", "$$\n", "\n", "lo que implica que la dinámica se reduce a una ecuación diferencial de tipo elíptico. Para encontrar la solución analítica, habría que utilizar funciones elípticas.\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 61 }, "id": "ZmUtoC5ciDZ2", "outputId": "392e86c7-4a36-4705-9b19-075400c19077" }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left(\\frac{d}{d t} \\omega_{1}{\\left(t \\right)}\\right)^{2} = \\frac{\\left(I_{2} - I_{3}\\right)^{2} \\omega_{2}^{2}{\\left(t \\right)} \\omega_{3}^{2}{\\left(t \\right)}}{I_{1}^{2}}$" ], "text/plain": [ "Eq(Derivative(omega1(t), t)**2, (I2 - I3)**2*omega2(t)**2*omega3(t)**2/I1**2)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Sustituimos las soluciones de w2^2 y w3^2\n", "omega2_sq_expr = sol[omega2_sq]\n", "omega3_sq_expr = sol[omega3_sq]\n", "\n", "# Ecuación de Euler para w1\n", "domega1 = ((I2 - I3)/(I1)) * sp.sqrt(omega2_sq_expr * omega3_sq_expr)\n", "\n", "# Elevamos al cuadrado para evitar raíces\n", "eq_reduced = sp.simplify(domega1**2)\n", "\n", "solucion = sp.Eq(omega1_dot**2, eq_reduced)\n", "\n", "# Mostrar ecuaciones\n", "display(solucion)" ] }, { "cell_type": "markdown", "metadata": { "id": "XJ1MsNAxf48Y" }, "source": [ "Esta solución puede ser bastante complicada de interpretar. Por eso vamos a hacer una evaluación numérica." ] }, { "cell_type": "markdown", "metadata": { "id": "BXaDmMwQo-yR" }, "source": [ "## Resolución numérica\n", "Usamos numpy para evaluar numéricamente la evolución de w1, w2 y w3.\n", "Por simplicidad, tomamos $M=1$ kg, $d=1$ m. Sustituímos los valores que tenemos para los momentos principales:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "ReuTvZi_hCrq" }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "\n", "# Valores arbitrarios (importante: que sean distintos)\n", "I1 = 121/30 # eje intermedio\n", "I2 = 17/6 # eje menor\n", "I3 = 103/15 # eje mayor\n" ] }, { "cell_type": "markdown", "metadata": { "id": "2qtx7XdlhTKn" }, "source": [ "## Ecuaciones de Euler\n", "Plantemaos las ecuaciones para resolverlas numéricamente. Las resolvemos mediante el método de Euler." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "1HGbx1HJhfS3" }, "outputs": [], "source": [ "def euler_equations(w, t):\n", " w1, w2, w3 = w\n", "\n", " dw1 = ((I2 - I3)/I1) * w2 * w3\n", " dw2 = ((I3 - I1)/I2) * w3 * w1\n", " dw3 = ((I1 - I2)/I3) * w1 * w2\n", "\n", " return np.array([dw1, dw2, dw3])\n", "\n", "# -----------------------------\n", "# Integración (método simple)\n", "# -----------------------------\n", "dt = 0.01\n", "T = 80\n", "N = int(T/dt)" ] }, { "cell_type": "markdown", "metadata": { "id": "aQ1E7wjYhkbX" }, "source": [ "## Valores para $\\omega$\n", "Probamos con un valor inicial, donde la velocidad en el eje $\\vec{e}_1$:\n", "\n", "$\\omega = (\\omega_1, \\omega_1/100, \\omega_1/100)$\n", "\n", "Este eje es el intermedio de los momentos de inercia. Esperamos una oscilación inestable." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "KnNJQZTMjMIg" }, "outputs": [], "source": [ "# Velocidad angular inicial:\n", "# giro principalmente alrededor del eje intermedio + pequeña perturbación\n", "w = np.array([1.0, 0.01, 0.01])" ] }, { "cell_type": "markdown", "metadata": { "id": "ND9XYsv1ja1X" }, "source": [ "Resolvemos numéricamente las ecuaciones de Euler:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 472 }, "id": "_Vn9CGAjLe5Y", "outputId": "f231e29d-d12c-479e-d85c-cfc7256bb202" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "trajectory1 = []\n", "\n", "for _ in range(N):\n", " trajectory1.append(w.copy())\n", "\n", " # método de Euler explícito\n", " w = w + dt * euler_equations(w, 0)\n", "\n", "trajectory1 = np.array(trajectory1)\n", "\n", "# -----------------------------\n", "# 5. Visualización\n", "# -----------------------------\n", "t_vals = np.linspace(0, T, N)\n", "\n", "plt.figure()\n", "plt.plot(t_vals, trajectory1[:,0], label='ω1')\n", "plt.plot(t_vals, trajectory1[:,1], label='ω2')\n", "plt.plot(t_vals, trajectory1[:,2], label='ω3')\n", "\n", "plt.xlabel(\"Tiempo\")\n", "plt.ylabel(\"Velocidad angular\")\n", "plt.legend()\n", "plt.title(\"Efecto Dzhanibekov (inestabilidad del eje intermedio)\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "rx1469KRjlNn" }, "source": [ "Por comparar, probamos con una velocidad inicial dominante en alguno de los otros ejes:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 472 }, "id": "lPWIYHYCjtko", "outputId": "9066eebe-6cde-4965-d156-c5f74bc30439" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Velocidad angular inicial:\n", "# giro principalmente alrededor del eje menor + pequeña perturbación\n", "w = np.array([0.01, 1.0, 0.01])\n", "\n", "trajectory2 = []\n", "\n", "for _ in range(N):\n", " trajectory2.append(w.copy())\n", "\n", " # método de Euler explícito\n", " w = w + dt * euler_equations(w, 0)\n", "\n", "trajectory2 = np.array(trajectory2)\n", "\n", "# -----------------------------\n", "# 5. Visualización\n", "# -----------------------------\n", "t_vals = np.linspace(0, T, N)\n", "\n", "plt.figure()\n", "plt.plot(t_vals, trajectory2[:,0], label='ω1')\n", "plt.plot(t_vals, trajectory2[:,1], label='ω2')\n", "plt.plot(t_vals, trajectory2[:,2], label='ω3')\n", "\n", "plt.xlabel(\"Tiempo\")\n", "plt.ylabel(\"Velocidad angular\")\n", "plt.legend()\n", "plt.title(\"Efecto Dzhanibekov (estabilidad del eje menor)\")\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 472 }, "id": "FTdiZiuIkZNA", "outputId": "9773ce14-de58-4790-8ac3-86ddaf9f4376" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Velocidad angular inicial:\n", "# giro principalmente alrededor del eje menor + pequeña perturbación\n", "w = np.array([0.01, 1.0, 0.01])\n", "\n", "trajectory3 = []\n", "\n", "for _ in range(N):\n", " trajectory3.append(w.copy())\n", "\n", " # método de Euler explícito\n", " w = w + dt * euler_equations(w, 0)\n", "\n", "trajectory3 = np.array(trajectory3)\n", "\n", "# -----------------------------\n", "# 5. Visualización\n", "# -----------------------------\n", "t_vals = np.linspace(0, T, N)\n", "\n", "plt.figure()\n", "plt.plot(t_vals, trajectory3[:,0], label='ω1')\n", "plt.plot(t_vals, trajectory3[:,1], label='ω2')\n", "plt.plot(t_vals, trajectory3[:,2], label='ω3')\n", "\n", "plt.xlabel(\"Tiempo\")\n", "plt.ylabel(\"Velocidad angular\")\n", "plt.legend()\n", "plt.title(\"Efecto Dzhanibekov (estabilidad del eje mayor)\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "JzG8_Y00kmeJ" }, "source": [ "Como conclusión final, y a la vista de las gráficas, podemos decir que la rotación en torno a los ejes $\\vec{e}_2$ y $\\vec{e}_3$ (los de momentos de inercia mayor y menor) es una rotación estable, pero la rotación en torno al eje intermedio ($\\vec{e}_1$) es inestable, lo que se traduce en una transferencia de la rotación hacia los otros ejes." ] }, { "cell_type": "markdown", "metadata": { "id": "0INQmYxbLef-" }, "source": [ "# ANEXO: animación\n", "\n", "Por probar, podemos intentar hacer una animación con matplotlib del objeto rotando." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 1000 }, "id": "zzm3z97FXxmk", "outputId": "5c747a4e-8140-4fed-b734-d2c46c740897" }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING:matplotlib.animation:Animation size has reached 21010437 bytes, exceeding the limit of 20971520.0. If you're sure you want a larger animation embedded, set the animation.embed_limit rc parameter to a larger value (in MB). This and further frames will be dropped.\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " Once\n", " \n", " Loop\n", " \n", " Reflect\n", " \n", " \n", "\n", "\n", "\n", "