{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/SalgadoHUB/Classical_Mechanics_II/blob/main/Tareas/Tarea3_ecsEuler.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ebL-c3gLKSbS"
   },
   "source": [
    "# Molino en equilibrio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5kQ2YJcvxm0P"
   },
   "source": [
    "Tenemos un molino de luz, del cuál hemos calculado su matriz de inercia. Suponemos que su CDM está sobre la vertical (válido para pequeñas oscilaciones), de modo que podemos suponer que no hay fuerzas externas. Tenemos que estudiar entonces la  rotación del sólido libre. En esta situación, lo indicado es utilizar las Ecuaciones de Euler para el Sólido Rígido.\n",
    "\n",
    "\n",
    "## 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": "AVUlGp89KYwZ"
   },
   "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": "zEJ5ixY_AkHv",
    "outputId": "bd01d733-5547-4490-f90b-eea99e705972"
   },
   "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": "iNuYDU3BBY_U"
   },
   "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, el cuerpo tiene simetría de rotación en torno $e_3$, por lo que se cumple que\n",
    "\n",
    "$I_1=I_2$.\n",
    "\n",
    "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": "0eK7StcwBznA",
    "outputId": "6fd2fe9e-bcab-49a8-ad51-8eae448be522"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle I_{1} \\frac{d}{d t} \\omega_{1}{\\left(t \\right)} + \\left(- I_{1} + I_{3}\\right) \\omega_{2}{\\left(t \\right)} \\omega_{3}{\\left(t \\right)} = 0$"
      ],
      "text/plain": [
       "Eq(I1*Derivative(omega1(t), t) + (-I1 + I3)*omega2(t)*omega3(t), 0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle I_{1} \\frac{d}{d t} \\omega_{2}{\\left(t \\right)} + \\left(I_{1} - I_{3}\\right) \\omega_{1}{\\left(t \\right)} \\omega_{3}{\\left(t \\right)} = 0$"
      ],
      "text/plain": [
       "Eq(I1*Derivative(omega2(t), t) + (I1 - I3)*omega1(t)*omega3(t), 0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle I_{3} \\frac{d}{d t} \\omega_{3}{\\left(t \\right)} = 0$"
      ],
      "text/plain": [
       "Eq(I3*Derivative(omega3(t), t), 0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "Euler1 = sp.Eq(I1 * omega1_dot + (I3 - I1) * omega2 * omega3, 0)\n",
    "Euler2 = sp.Eq(I1 * omega2_dot + (I1 - I3) * omega3 * omega1, 0)\n",
    "Euler3 = sp.Eq(I3 * omega3_dot, 0)\n",
    "\n",
    "# Mostrar ecuaciones\n",
    "display(Euler1, Euler2, Euler3)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dTZ3FSX4CJz7"
   },
   "source": [
    "## Encontramos las soluciones a las ecuaciones\n",
    "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": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 72
    },
    "id": "7IjVxtAFCPXG",
    "outputId": "48a8b2db-d7e3-4efa-85ea-1302eadd2308"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Eq(omega1(t), I*C1*exp(-t*(I*C2*I1 - I*C2*I3)/I1) - I*C3*exp(t*(I*C2*I1 - I*C2*I3)/I1)),\n",
       " Eq(omega2(t), C1*exp(-t*(I*C2*I1 - I*C2*I3)/I1) + C3*exp(t*(I*C2*I1 - I*C2*I3)/I1)),\n",
       " Eq(omega3(t), C2)]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Resolver el sistema de ecuaciones\n",
    "solutions = sp.dsolve([Euler1, Euler2, Euler3])\n",
    "\n",
    "# Mostrar soluciones\n",
    "display(solutions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OgWjYCI4DHFa"
   },
   "source": [
    "Las soluciones obtenidas de las ecuaciones de Euler nos indican lo siguiente:\n",
    "\n",
    "Conservación de $ω_3$:\n",
    "La ecuación $I_3 ω_3=0$ implica que $ω_3$ es constante en el tiempo.\n",
    "Esto significa que el sólido rota alrededor del eje de inercia asociado a $I_3$ sin cambios en la velocidad angular en esa dirección.\n",
    "\n",
    "Oscilaciones en $ω_1$ y $ω_2$\n",
    " Las ecuaciones para $ω_1$ y $ω_2$ tienen la forma de ecuaciones acopladas con términos proporcionales a $ω_3$.\n",
    "Esto sugiere un comportamiento oscilatorio en estas componentes, similar a un movimiento periódico o precesión.\n",
    "Interpretación física:\n",
    "Cuando  $I_1 = I_2$, el cuerpo tiene simetría en los ejes $x$ e $y$, y su rotación en esos planos sigue una dinámica de precesión alrededor del eje $z$.\n",
    "La velocidad angular en el plano perpendicular a zz varía de manera sinusoidal con el tiempo.\n",
    "\n",
    "Conclusión\n",
    "\n",
    "El sistema describe la rotación de un sólido simétrico (con $I_1 = I_2$) en ausencia de momentos externos. La velocidad angular alrededor del eje de máxima inercia $I_3$ se conserva, mientras que las componentes perpendiculares oscilan, lo que refleja el movimiento natural de precesión del cuerpo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ftsSjPxWEWoF"
   },
   "source": [
    "## Damos los valores de $I_1$, $I_3$\n",
    "\n",
    "Utilizamos las dimensiones del molino y los momentos de inercia calculados en la actividad anterior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 122
    },
    "id": "np3klCI-EctF",
    "outputId": "340e7ac3-0be9-445d-e489-5725164c55cf"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(0.5 L^{2} M + 2 M \\left(d^{2} + 2 h^{2}\\right)\\right) \\frac{d}{d t} \\omega_{1}{\\left(t \\right)} + \\left(- 0.166666666666667 L^{2} M + 4 M d^{2} - 2 M \\left(d^{2} + 2 h^{2}\\right)\\right) \\omega_{2}{\\left(t \\right)} \\omega_{3}{\\left(t \\right)} = 0$"
      ],
      "text/plain": [
       "Eq((0.5*L**2*M + 2*M*(d**2 + 2*h**2))*Derivative(omega1(t), t) + (-0.166666666666667*L**2*M + 4*M*d**2 - 2*M*(d**2 + 2*h**2))*omega2(t)*omega3(t), 0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(0.5 L^{2} M + 2 M \\left(d^{2} + 2 h^{2}\\right)\\right) \\frac{d}{d t} \\omega_{2}{\\left(t \\right)} + \\left(0.166666666666667 L^{2} M - 4 M d^{2} + 2 M \\left(d^{2} + 2 h^{2}\\right)\\right) \\omega_{1}{\\left(t \\right)} \\omega_{3}{\\left(t \\right)} = 0$"
      ],
      "text/plain": [
       "Eq((0.5*L**2*M + 2*M*(d**2 + 2*h**2))*Derivative(omega2(t), t) + (0.166666666666667*L**2*M - 4*M*d**2 + 2*M*(d**2 + 2*h**2))*omega1(t)*omega3(t), 0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(0.333333333333333 L^{2} M + 4 M d^{2}\\right) \\frac{d}{d t} \\omega_{3}{\\left(t \\right)} = 0$"
      ],
      "text/plain": [
       "Eq((0.333333333333333*L**2*M + 4*M*d**2)*Derivative(omega3(t), t), 0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Definir variables\n",
    "M, L, d, h = sp.symbols('M L d h')  # Parámetros físicos\n",
    "I1 = 0.5 * M * L**2 + 2 * M * (d**2 + 2 * h**2)\n",
    "I3 = (1/3) * M * L**2 + 4 * M * d**2\n",
    "\n",
    "Euler1 = sp.Eq(I1 * omega1_dot + (I3 - I1) * omega2 * omega3, 0)\n",
    "Euler2 = sp.Eq(I1 * omega2_dot + (I1 - I3) * omega3 * omega1, 0)\n",
    "Euler3 = sp.Eq(I3 * omega3_dot, 0)\n",
    "\n",
    "# Mostrar ecuaciones\n",
    "display(Euler1, Euler2, Euler3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 72
    },
    "id": "FaQOXlKPEn04",
    "outputId": "d4e50e6b-6eca-4d70-df0a-0f14435e841c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Eq(omega1(t), 1.0*I*C1/exp(t*(0.333333333333333*I*C2*L**2 - 4.0*I*C2*d**2 + 8.0*I*C2*h**2)/(L**2 + 4.0*d**2 + 8.0*h**2))**1.0 - 1.0*I*C3*exp(t*(0.333333333333333*I*C2*L**2 - 4.0*I*C2*d**2 + 8.0*I*C2*h**2)/(L**2 + 4.0*d**2 + 8.0*h**2))),\n",
       " Eq(omega2(t), 1.0*C1/exp(t*(0.333333333333333*I*C2*L**2 - 4.0*I*C2*d**2 + 8.0*I*C2*h**2)/(L**2 + 4.0*d**2 + 8.0*h**2))**1.0 + 1.0*C3*exp(t*(0.333333333333333*I*C2*L**2 - 4.0*I*C2*d**2 + 8.0*I*C2*h**2)/(L**2 + 4.0*d**2 + 8.0*h**2))),\n",
       " Eq(omega3(t), C2)]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Resolver el sistema de ecuaciones\n",
    "solutions = sp.dsolve([Euler1, Euler2, Euler3])\n",
    "\n",
    "# Mostrar soluciones\n",
    "display(solutions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gp2Yvsd4ErRK"
   },
   "source": [
    "# Simulación de una perturbación sobre el molino\n",
    "Para ver más claramente cómo es el movimiento, calculamos la evolución de forma numérica. Para ello, utilizamos numpy, y la función \"solve_ivp\" del módulo scipy.integrate para resolver las ecuaciones diferenciales."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "a7JUQ4WAEw0r"
   },
   "outputs": [],
   "source": [
    "# Valores numéricos para simulación\n",
    "param_values = {M: 1, L: 2, d: 1, h: 0.2}\n",
    "I1_val = I1.subs(param_values)\n",
    "I3_val = I3.subs(param_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "sOxujLr8FNyj"
   },
   "outputs": [],
   "source": [
    "# Definir ecuaciones de Euler\n",
    "\n",
    "def euler_eqs(t, omega):\n",
    "    omega1, omega2, omega3 = omega\n",
    "    omega1_dot = -((I3_val - I1_val) / I1_val) * omega2 * omega3\n",
    "    omega2_dot = -((I1_val - I3_val) / I1_val) * omega3 * omega1\n",
    "    omega3_dot = 0  # Omega3 es constante\n",
    "    return [omega1_dot, omega2_dot, omega3_dot]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JxtbbcFJ4tO6"
   },
   "source": [
    "Como valores iniciales, hacemos que $\\omega_1 = \\omega_3 / 10$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 488
    },
    "id": "Ype75UbBFSjv",
    "outputId": "f69ceaa8-12ef-4afd-831f-5c776bd2fdcf"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import solve_ivp\n",
    "\n",
    "# Condiciones iniciales\n",
    "omega0 = [0.1, 0.0, 1]  # Valores iniciales arbitrarios\n",
    "\n",
    "# Resolver ecuaciones en el tiempo\n",
    "t_span = (0, 100)\n",
    "t_eval = np.linspace(0, 100, 300)\n",
    "sol = solve_ivp(euler_eqs, t_span, omega0, t_eval=t_eval)\n",
    "\n",
    "# Graficar soluciones\n",
    "plt.figure(figsize=(8, 5))\n",
    "plt.plot(sol.t, sol.y[0], label='$\\omega_1(t)$')\n",
    "plt.plot(sol.t, sol.y[1], label='$\\omega_2(t)$')\n",
    "plt.plot(sol.t, sol.y[2], label='$\\omega_3(t)$')\n",
    "plt.xlabel('Tiempo')\n",
    "plt.ylabel('Velocidades angulares')\n",
    "plt.legend()\n",
    "plt.title('Evolución de las velocidades angulares')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "authorship_tag": "ABX9TyOLxOZTwdsSLM9EK1KsZ1OJ",
   "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
}