{ "cells": [ { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "view-in-github" }, "source": [ "\"Open" ] }, { "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", 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" ] }, "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", "
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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# =========================================\n", "# Animación 3D\n", "# =========================================\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d.art3d import Poly3DCollection\n", "from matplotlib import animation\n", "from IPython.display import HTML\n", "\n", "d = 1.0\n", "\n", "# Centros respecto al CM\n", "centers = np.array([\n", " [-d, 3*d/5, 0],\n", " [0, 3*d/5, 0],\n", " [d, 3*d/5, 0],\n", " [0, -2*d/5, 0],\n", " [0, -7*d/5, 0]\n", "])\n", "\n", "def cube_vertices(center, size):\n", " cx, cy, cz = center\n", " s = size/2\n", " return np.array([\n", " [cx-s, cy-s, cz-s],\n", " [cx+s, cy-s, cz-s],\n", " [cx+s, cy+s, cz-s],\n", " [cx-s, cy+s, cz-s],\n", " [cx-s, cy-s, cz+s],\n", " [cx+s, cy-s, cz+s],\n", " [cx+s, cy+s, cz+s],\n", " [cx-s, cy+s, cz+s]\n", " ])\n", "\n", "faces_idx = [\n", " [0,1,2,3],[4,5,6,7],\n", " [0,1,5,4],[2,3,7,6],\n", " [1,2,6,5],[4,7,3,0]\n", "]\n", "\n", "cubes = [cube_vertices(c, d) for c in centers]\n", "\n", "# Momentos de inercia\n", "I1, I2, I3 = 4.0, 2.0, 6.0\n", "\n", "def euler(w):\n", " w1, w2, w3 = w\n", " return np.array([\n", " ((I2 - I3)/I1)*w2*w3,\n", " ((I3 - I1)/I2)*w3*w1,\n", " ((I1 - I2)/I3)*w1*w2\n", " ])\n", "\n", "# Simulación\n", "dt = 0.1\n", "steps = 400\n", "w = np.array([1.0, 0.01, 0.01])\n", "\n", "ws = []\n", "for _ in range(steps):\n", " ws.append(w.copy())\n", " w = w + dt * euler(w)\n", "\n", "# Rotaciones\n", "def rotation_matrix(axis, theta):\n", " norm = np.linalg.norm(axis)\n", " if norm == 0:\n", " return np.eye(3)\n", " axis = axis / norm\n", " K = np.array([\n", " [0, -axis[2], axis[1]],\n", " [axis[2], 0, -axis[0]],\n", " [-axis[1], axis[0], 0]\n", " ])\n", " return np.eye(3) + np.sin(theta)*K + (1-np.cos(theta))*(K@K)\n", "\n", "R = np.eye(3)\n", "Rs = []\n", "\n", "for w in ws:\n", " theta = np.linalg.norm(w)*dt\n", " R = rotation_matrix(w, theta) @ R\n", " Rs.append(R.copy())\n", "\n", "# Figura\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111, projection='3d')\n", "\n", "def draw_frame(i):\n", " ax.cla()\n", " R = Rs[i]\n", "\n", " for cube in cubes:\n", " rotated = (R @ cube.T).T\n", " faces = [[rotated[j] for j in face] for face in faces_idx]\n", " ax.add_collection3d(Poly3DCollection(faces))\n", "\n", " ax.set_xlim(-2,2)\n", " ax.set_ylim(-2,2)\n", " ax.set_zlim(-2,2)\n", "\n", "ani = animation.FuncAnimation(fig, draw_frame, frames=steps, interval=50)\n", "\n", "HTML(ani.to_jshtml())" ] } ], "metadata": { "colab": { "authorship_tag": "ABX9TyObwabTuc2piWbX47E72sE8", "include_colab_link": true, "provenance": [] }, "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": "3.9.7" } }, "nbformat": 4, "nbformat_minor": 1 }