{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0af92ef8-4aa5-4623-b305-d63524af030b",
   "metadata": {},
   "source": [
    "### Задача 1: Линеаризованное уравнение на магнитный момент \n",
    "\n",
    "Рассмотрим частный случай, когда уравнение на магнитный момент Ландау–Лифшица–Гильберта может быть сведено к решению уравнения на одну компоненту $m_y$ (линейный осциллятор).\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    " \\frac{d^2 m_y}{dt^2} + 2\\alpha \\omega_J \\frac{d m_y}{dt} +\\omega_F^2 m_y = \\omega_F^2 G r \\sin(\\omega_J t)\n",
    "\\label{eq4}\n",
    "\\tag{4}\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "\n",
    "с параметрами модели:\n",
    "* G - отношение энергии Джозефсона к энергии магнитной анизотропии;\n",
    "* r - константа спин-орбитального взаимодействия;\n",
    "* $\\alpha$ - диссипация Гилберта;\n",
    "* $\\omega_F$ - частота ферромагнитного резонанса.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad08ff58-126a-45e0-b04d-26ce01f82b62",
   "metadata": {},
   "source": [
    "Для проведения исследования динамики перейдем от одного дифференциального уравнения второго порядка к системе двух уравнений и разрешим их относительно производных, полагая $ m_y = y_1$: \n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "\\begin{cases}\n",
    "   \\frac{d y_1}{dt} = y_2, \\\\\n",
    "    \\frac{d y_2}{dt} =  - 2\\alpha \\omega_J y_2 -\\omega_F^2 y_1 + \\omega_F^2 G r \\sin(\\omega_J t).\n",
    "\\end{cases}\n",
    "\\label{eq5}\n",
    "\\tag{5}\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "\n",
    "Начальные условия:\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    " y_1(0)=0.1, y_2(0)=0.\n",
    "\\tag{6}\n",
    "\\end{eqnarray}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d737667d-fb80-4458-925d-9131c683c7df",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from functools import partial\n",
    "from scipy.integrate import solve_ivp\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "sns.set(style=\"whitegrid\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d7f0182-6618-403f-a145-ae6a3fcf3014",
   "metadata": {},
   "source": [
    "__Опредляем значения параметров модели и численного решения__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "d31a5e4f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Параметры модели\n",
    "G = 0.1\n",
    "r = 0.1\n",
    "omegaF = 0.5\n",
    "alpha = 0.1\n",
    "omegaJ = 1\n",
    "# Параметры численного счета\n",
    "t0 = 0\n",
    "tf = 100\n",
    "nt = 1000\n",
    "# Массив точек (сетка) в которых будет находится решение\n",
    "t_e = np.linspace(t0, tf, nt)\n",
    "# Начальное условие\n",
    "y0 = np.array([0.01, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "d265062d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def my_t(t, S, G, r, alpha, omegaF, omegaJ):\n",
    "    ''' Определяет правые части ДУ Задачи 1.\n",
    "    G, r, alpha, omegaF,omegaJ - параметры модели\n",
    "    S=[y1, y2] - вектор-фунция'''\n",
    "    y1 = S[0]\n",
    "    y2 = S[1]\n",
    "    dy1 = y2\n",
    "    dy2 = -2*alpha*omegaF*y2 - omegaF*omegaF*y1 + \\\n",
    "        omegaF*omegaF*G*r*np.sin(omegaJ*t)\n",
    "    dS = [dy1, dy2]\n",
    "    return dS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "72df6ac1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.0, -0.025]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = np.array([0.1, 0])\n",
    "dS = my_t(0, s,  0.1, 0.1, 0.1, 0.5, 1)\n",
    "\n",
    "dS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "092436dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "f = partial(my_t, G=G, r=r, alpha=alpha,\n",
    "            omegaF=omegaF, omegaJ=omegaJ)\n",
    "t_e = np.linspace(t0, tf, nt)\n",
    "s0 = np.array([0.0, 0])\n",
    "sol_lin = solve_ivp(f, [t0, tf], s0, t_eval=t_e, method='RK45')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "31937447",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(sol_lin.t, sol_lin.y[0],\n",
    "         label='Численное решение задачи (5,6) $m_y(t)$', linewidth=3.0)\n",
    "plt.xlabel('t', size=16)\n",
    "plt.ylabel('$m_y(t)$', size=12)\n",
    "plt.legend(fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "52b37104-4481-475a-8d2c-505bbea68b4b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.9.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
