{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyMY+10NScF/fGJa0AHnZ3AG",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/SalgadoHUB/Classical_Mechanics_II/blob/main/Problemas/Tema2/Problema_2c_1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Momento Angular de un Sistema de 3 partículas\n",
        "\n",
        "Un cuerpo rígido está formado por tres partículas de masa $m$, $2m$ y $4m$ situadas inicialmente en los puntos:\n",
        "\n",
        "- $(2a, 0, 2a)$\n",
        "- $(a, -2a, -a)$\n",
        "- $(-a, a, 0)$\n",
        "\n",
        "respectivamente. El cuerpo gira alrededor del origen con una velocidad angular:\n",
        "\n",
        "$$ \\boldsymbol{\\omega} = b(3\\hat{i} - 2\\hat{j} + 4\\hat{k}) $$\n",
        "\n",
        "### Cuestiones\n",
        "\n",
        "a). **Calcule el momento angular usando la relación matricial:**\n",
        "   $$ \\boldsymbol{J} = \\mathbb{I} \\cdot \\boldsymbol{\\omega} $$\n",
        "\n",
        "b). **Calcule el momento angular usando la definición vectorial:**\n",
        "   $$ J_i = \\mathbf{r}_i \\times m_i \\mathbf{v}_i = m_i \\mathbf{r}_i \\times (\\boldsymbol{\\omega} \\times \\mathbf{r}_i) $$\n",
        "\n",
        "c). **Calcule los ejes principales de inercia:**\n",
        "   - Encuentra una base de ejes principales de inercia.\n",
        "   - Expresa en esta base:\n",
        "     - $ \\mathbb{I} $ (tensor de inercia)\n",
        "     - $ \\boldsymbol{\\omega} $ (velocidad angular)\n",
        "     - $ \\boldsymbol{J} $ (momento angular)"
      ],
      "metadata": {
        "id": "s9TYxjqaPYAD"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Dibujamos el sistema"
      ],
      "metadata": {
        "id": "RjXn0I0dUMDz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "# Creamos una figura\n",
        "figura = plt.figure()\n",
        "\n",
        "# Creamos el eje\n",
        "eje = figura.add_subplot(111, projection='3d')\n",
        "# Utilizamos la función scatter para dibujar el vector en el eje 3D\n",
        "eje.scatter(2,0,2, c='r', marker='o', s=20)\n",
        "eje.scatter(1,-1,1, c='r', marker='o', s=2*20)\n",
        "eje.scatter(-1,1,0, c='r', marker='o', s=4*20)\n",
        "\n",
        "eje.plot([0,3],[0,-2],[0,4])\n",
        "\n",
        "# Mostramos el resultado en una ventana\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 415
        },
        "id": "vTq_EsH1UPVE",
        "outputId": "f80db57c-162f-425c-b2e1-d2e620718674"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Definimos las variables del enunciado"
      ],
      "metadata": {
        "id": "jBL4-yylS31E"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import sympy as smp\n",
        "\n",
        "m, a, b = smp.symbols('m a b')\n",
        "\n",
        "m1 = m\n",
        "m2 = 2*m\n",
        "m3 = 4*m\n",
        "\n",
        "r1 = smp.Matrix([2*a, 0, 2*a])\n",
        "r2 = smp.Matrix([a, -2*a, -a])\n",
        "r3 = smp.Matrix([-a, a, 0])\n",
        "\n",
        "w = b*smp.Matrix([3, -2, 4])"
      ],
      "metadata": {
        "id": "3ysZztfCS7Ws"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Buscamos su centro de masas, para comprobar que el eje de rotación pasa por el $CDM$ (no lo pide en el enunciado)."
      ],
      "metadata": {
        "id": "icGtkLUxd652"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "R = (m1*r1 + m2*r2 + m3*r3) / (m1+m2+m3)\n",
        "R"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 78
        },
        "id": "-XFbH9CB93jU",
        "outputId": "fa4efd30-cc8b-49dc-c162-bc9d451c3f4a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Matrix([\n",
              "[0],\n",
              "[0],\n",
              "[0]])"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## a) Usando la matriz de inercia"
      ],
      "metadata": {
        "id": "qyZ4ZQCpQeyo"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Calculamos los elementos de la matriz de inercia."
      ],
      "metadata": {
        "id": "KuZp94ncQ8jw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Ixx = m1*(r1[1]**2 + r1[2]**2) + m2*(r2[1]**2 + r2[2]**2) + m3*(r3[1]**2 + r3[2]**2)\n",
        "Iyy = m1*(r1[0]**2 + r1[2]**2) + m2*(r2[0]**2 + r2[2]**2) + m3*(r3[0]**2 + r3[2]**2)\n",
        "Izz = m1*(r1[0]**2 + r1[1]**2) + m2*(r2[0]**2 + r2[1]**2) + m3*(r3[0]**2 + r3[1]**2)\n",
        "\n",
        "Ixy = -m1*(r1[0]*r1[1]) - m2*(r2[0]*r2[1]) - m3*(r3[0]*r3[1])\n",
        "Ixz = -m1*(r1[0]*r1[2]) - m2*(r2[0]*r2[2]) - m3*(r3[0]*r3[2])\n",
        "Iyz = -m1*(r1[1]*r1[2]) - m2*(r2[1]*r2[2]) - m3*(r3[1]*r3[2])\n",
        "#\n",
        "I = smp.Matrix([[Ixx, Ixy, Ixz], [Ixy, Iyy, Iyz], [Ixz, Iyz, Izz]])\n",
        "I"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 78
        },
        "id": "zu2390LsRAb_",
        "outputId": "186fe55e-1837-430f-9f2f-7972d3784dd5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Matrix([\n",
              "[18*a**2*m,  8*a**2*m, -2*a**2*m],\n",
              "[ 8*a**2*m, 16*a**2*m, -4*a**2*m],\n",
              "[-2*a**2*m, -4*a**2*m, 22*a**2*m]])"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}18 a^{2} m & 8 a^{2} m & - 2 a^{2} m\\\\8 a^{2} m & 16 a^{2} m & - 4 a^{2} m\\\\- 2 a^{2} m & - 4 a^{2} m & 22 a^{2} m\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Calculamos $J$ como:\n",
        "$$ \\boldsymbol{J} = \\mathbb{I} \\cdot \\boldsymbol{\\omega} $$"
      ],
      "metadata": {
        "id": "Pj5x1AIqTKl7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "J = I * w\n",
        "J"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 78
        },
        "id": "j3VMamuYTOvb",
        "outputId": "fb7c10d3-e63b-4a39-9b23-f927f1830231"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Matrix([\n",
              "[ 30*a**2*b*m],\n",
              "[-24*a**2*b*m],\n",
              "[ 90*a**2*b*m]])"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}30 a^{2} b m\\\\- 24 a^{2} b m\\\\90 a^{2} b m\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## b) Usando la definición de $J$\n",
        "Ahora usamos:\n",
        "$$ J_i = \\mathbf{r}_i \\times m_i \\mathbf{v}_i = m_i \\mathbf{r}_i \\times (\\boldsymbol{\\omega} \\times \\mathbf{r}_i) $$"
      ],
      "metadata": {
        "id": "BNqRdj4xT4za"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "v1 = w.cross(r1)\n",
        "v2 = w.cross(r2)\n",
        "v3 = w.cross(r3)\n",
        "\n",
        "J1 = r1.cross(m1*v1)\n",
        "J2 = r2.cross(m2*v2)\n",
        "J3 = r3.cross(m3*v3)\n",
        "\n",
        "J = J1 + J2 + J3\n",
        "J\n",
        "#"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 78
        },
        "id": "PpM1FovzUDVx",
        "outputId": "6c9208d0-53af-40e6-d441-12bd5869d9c7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Matrix([\n",
              "[ 30*a**2*b*m],\n",
              "[-24*a**2*b*m],\n",
              "[ 90*a**2*b*m]])"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}30 a^{2} b m\\\\- 24 a^{2} b m\\\\90 a^{2} b m\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Que coincide con lo calculado en el apartado (a)."
      ],
      "metadata": {
        "id": "7EgSYfSIcanB"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## c). Cálculo de los ejes principales de inercia\n",
        "\n",
        "Tenemos que diagnoalizar nuestra matriz. Por legibilidad, vamos a extraer el factor común de todos los elementos de la matriz, $2ma²$."
      ],
      "metadata": {
        "id": "pidorqTCXfNk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "I_factor = I/(2*m*a**2)\n",
        "A, Id = I_factor.diagonalize()\n",
        "I_factor"
      ],
      "metadata": {
        "id": "tQSrnD3yXhGr",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 78
        },
        "outputId": "8a863f72-9989-4714-dad3-3596e33b35a8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Matrix([\n",
              "[ 9,  4, -1],\n",
              "[ 4,  8, -2],\n",
              "[-1, -2, 11]])"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}9 & 4 & -1\\\\4 & 8 & -2\\\\-1 & -2 & 11\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "Id.simplify()\n",
        "smp.pprint('I diagonalizada:')\n",
        "Id"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 99
        },
        "id": "Tmwy_1sZXw8j",
        "outputId": "167ff5d8-71e8-44b5-d159-5251538a339f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "I diagonalizada:\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Matrix([\n",
              "[14,           0,           0],\n",
              "[ 0, 7 - sqrt(7),           0],\n",
              "[ 0,           0, sqrt(7) + 7]])"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}14 & 0 & 0\\\\0 & 7 - \\sqrt{7} & 0\\\\0 & 0 & \\sqrt{7} + 7\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "smp.pprint('Vectores propios:')\n",
        "A"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 99
        },
        "id": "cf0GIreO9SaM",
        "outputId": "fff84541-46b7-49f3-d68a-f3871e7193e2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Vectores propios:\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Matrix([\n",
              "[-1, -sqrt(7) - 2, -2 + sqrt(7)],\n",
              "[-1,  sqrt(7) + 3,  3 - sqrt(7)],\n",
              "[ 1,            1,            1]])"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}-1 & - \\sqrt{7} - 2 & -2 + \\sqrt{7}\\\\-1 & \\sqrt{7} + 3 & 3 - \\sqrt{7}\\\\1 & 1 & 1\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    }
  ]
}