{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c6805951",
   "metadata": {},
   "source": [
    "# Multidimensional differential equations\n",
    "\n",
    "- Börge Göbel "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "921259c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "from scipy import integrate"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29eb17ec",
   "metadata": {},
   "source": [
    "## Ball in a bowl: 2 uncoupled harmonic oscillators"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b461fb52",
   "metadata": {},
   "source": [
    "We solve the following differential equation:\n",
    "\\\\( m\\ddot{\\vec{r}} = -\\xi\\dot{\\vec{r}}-\\nabla U(\\vec{r}) + \\vec{F}_\\mathrm{ext}.\\\\)\n",
    "\n",
    "For the profile of the bowl we consider a quadratic function\n",
    "\\\\( U(\\vec{r}) = U_0 r^2 = U_0 (x^2 + y^2). \\\\)\n",
    "\n",
    "The gradient is \n",
    "\\\\( \\nabla U(\\vec{r}) = 2U_0 \\begin{pmatrix}x\\\\y\\end{pmatrix} = 2U_0\\vec{r}. \\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "34940b2b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.contour.QuadContourSet at 0x24af2a064c0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = np.meshgrid(np.linspace(-10,10,201),np.linspace(-10,10,201))\n",
    "z = x**2 + y**2\n",
    "\n",
    "plotproj = plt.axes(projection='3d')\n",
    "plotproj.contour3D(x,y,z,200)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef679d02",
   "metadata": {},
   "source": [
    "### Revisit 1d harmonic oscillator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1d3e711b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Pendulum geometry\n",
    "length = 2\n",
    "c = 9.81/length\n",
    "\n",
    "# Damping\n",
    "b = 0.1\n",
    "d = -1.0\n",
    "omega = 1.0\n",
    "\n",
    "def f_ODE(t,theta):\n",
    "    return theta[1], -b*theta[1] - c*np.sin(theta[0]) - d*np.sin(omega*t)\n",
    "\n",
    "theta00 = 2.0\n",
    "theta10 = 0.0\n",
    "\n",
    "solution_RK45 = integrate.solve_ivp(f_ODE, [0,100], [theta00, theta10], method = 'RK45', t_eval = np.linspace(0,100,201))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "87463039",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x24af7d30790>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('t')\n",
    "plt.ylabel('theta')\n",
    "\n",
    "plt.plot(solution_RK45.t, solution_RK45.y[0], 'red')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "665666cb",
   "metadata": {},
   "source": [
    "**The normal harmonic oscillator is (mathematically) already a two-dimensional example:**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2dde00d2",
   "metadata": {},
   "source": [
    "Second-order differential equation: \\\\( y''(t) = f\\left(t,y(t),y'(t)\\right)\\\\)\n",
    "\n",
    "Introduce: \\\\( z_0(t) = y(t)\\\\) and \\\\( z_1(t) = y'(t)\\\\)\n",
    "\n",
    "\\\\( \\begin{pmatrix}z_0'(t)\\\\z_1'(t)\\end{pmatrix}=\\begin{pmatrix}z_1(t)\\\\f\\left(t,z_0(t),z_1(t)\\right)\\end{pmatrix}\\\\)\n",
    "\n",
    "Therefore, we can describe the second-order differential equation by a set of two first-order differential equations. We can solve both with our Euler method\n",
    "\n",
    "\\\\( z_0^{(n+1)} = z_0^{(n)} + z_1^{(n)} h \\\\)\n",
    "\n",
    "\\\\( z_1^{(n+1)} = z_1^{(n)} + f\\left(t,z_0^{(n)},z_1^{(n)}\\right) h \\\\)\n",
    "\n",
    "Or, going back to our initial nomenclature:\n",
    "\n",
    "\\\\( y_{n+1} = y_{n} + y'_{n} h \\\\)\n",
    "\n",
    "\\\\( y'_{n+1} = y'_{n} + f\\left(t,y_{n},y'_{n}\\right) h \\\\)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "412f37a4",
   "metadata": {},
   "source": [
    "### Ball in a bowl"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bcfb25f",
   "metadata": {},
   "source": [
    "**Now we have 2 harmonic oscillators. Therefore, mathematically speaking, we have a four-dimensional system**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0be92e69",
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 1\n",
    "U0 = 1\n",
    "xi = 0.1\n",
    "\n",
    "def f_ODE(t,r):\n",
    "    x, y = r[0:2]\n",
    "    vx, vy = r[2:4]\n",
    "    return [vx, vy, -xi/m*vx -2*U0/m*x, -xi/m*vy -2*U0/m*y]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "520c1cfa",
   "metadata": {},
   "source": [
    "### Linear trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3f700a47",
   "metadata": {},
   "outputs": [],
   "source": [
    "tStart = 0\n",
    "tEnd = 100\n",
    "\n",
    "x0 = 1\n",
    "y0 = -0.5\n",
    "vx0 = 0\n",
    "vy0 = 0\n",
    "\n",
    "solution = integrate.solve_ivp(f_ODE, [tStart,tEnd], [x0, y0, vx0, vy0], method = 'RK45', t_eval = np.linspace(tStart,tEnd,1001))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "386ad41b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x24af7db7100>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('Time t')\n",
    "plt.ylabel('Coordinates x and y')\n",
    "\n",
    "plt.plot(solution.t, solution.y[0], 'red')\n",
    "plt.plot(solution.t, solution.y[1], 'blue')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "89dd2879",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x24af7e1be80>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQsAAAEGCAYAAAByy7CMAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAnnElEQVR4nO2dd3SVVdaHn53QQTo2ilgQUcAREQQbggo4WChW7DooA9bRsWJjrKPOqDMWHGyMHRRQFFRGRQSE0KWIijQFpCooxcD+/tg3HxETcpNbzi37Wetd7205ZyeQX845u4mq4jiOUxI5oQ1wHCc9cLFwHCcqXCwcx4kKFwvHcaLCxcJxnKgoF9qA0lC3bl1t3LhxaDMcJ2OZOnXqalWtV9R7aSUWjRs3Ji8vL7QZjpOxiMji4t7zbYjjOFHhYuE4TlS4WDiOExUuFo7jRIWLheM4URFMLESkkohMFpGZIjJHRO4KZYvjOCUT0nW6BeioqhtFpDwwXkTeU9VJAW1yHKcYgomFWm78xsjT8pHL8+XTAFVYtw6WLbP7xo07rg0b7P7rr1CuHJQvb/eCq2JFqFMH6tWDunXtql0bcnNDf1dOSQQNyhKRXGAqcADwb1X9vIjP9AH6ADRq1Ci5BmYx+fmwYAHMng1z58LixSYOS5fa/Zdf4jeXiAnIvvvCAQdAkyY7rgMOsPec8EgqFL8RkZrAW8CVqvpFcZ9r3bq1egRn/NmyBfLyYOJEmDXLBGLePHsdICcH9t4bGjaEBg123Bs0sF/katVgt93sXq0aVK1qK4pt20x0Cl+bNsGaNbB6NaxaZffVq2HlSvjmG/jqK1iyxFYvBdSvD23a2HXEEdC6NdSoEeZnlemIyFRVbV3UeykR7q2q60XkY6ALUKxYOPHh559h0iQYN86uSZNg82Z7r359aNECTjzR7i1aQLNmtn0oLQVbj51p2HDXX7dlCyxcaMKxYAFMnw6TJ8Nbb+34TNOmcMwxcNJJcMIJUKtW6e1zSkcwsRCResCvEaGoDJwAPBDKnkxnyRIYMQKGDzeByM+3FcNhh0HfvnDssXDUUXaWEJqKFU2gmjX77etr19oKaMoU+PxzeOMN+M9/7Pto0wY6dzbxaNOmaJFyYiPYNkREWgIvALmYC/d1Vb17V1/j25DoUbUtxfDhJhLTp9vrzZrBKafA8cdD+/ZQvXpQM2MiP99WHGPG2DVlCmzfboJ3xhlwzjn2PeZ4NFHU7GobkhJnFtHiYlEyK1fCf/8Lzz5rB5Mi9gtz2ml2HXhgaAsTx9q18MEHMGwYvP22ba0aNoSzzoKzz4ZWrezn4RSPi0WG8+uv8N57JhCjRtlf3Hbt4MIL4fTTYY89QluYfDZsgJEj4dVXYfRo+5k0bw5//jOcf74dxDq/x8UiQ1m9Gp54Ap58ElasMFG44AK4+OLf7/ezmbVrYehQePppmDbNPDcXXgj9+sFBB4W2LrXYlVigqmlzHX744eqofvONar9+qpUrq4LqySerjhypunVraMtSm+3bVSdOVO3dW7VCBfvZdeqkOnq0veeoAnlazO+fH/2kEXl5cOaZFqw0aJDtw+fMsa3HKadYbINTPCJw5JF2prN0KdxzD8yfD1262Lbtvfd+G9/h/BYXizRg3jzo0cMCkt5/H/76V1i0yM4oDj44tHXpye67wy23WCDYU0/B8uVw8skmJqNGuWgUhYtFCrNsGVx2mR3Mffgh3H23/UW87z6LqHRip2JFuPxyCwB75hn44Qfo1g3atoXx40Nbl1q4WKQg69fb6qFJExgyBK66yv4CDhhgh3NO/KlQwYR5wQIYPNgOjI85xrZ6S5aEti41cLFIIVThpZcslPmhhyyw6Msv4R//SI3IymygfHm45BI7y7jzTnO/Nm1qj+OZPJeOuFikCF99ZaHK550H++xjh5kvvgjeJiUMVarAHXeYaJx+Otx1l4lG4fyUbMPFIjBbtthZRIsWFrr8739b9merVqEtcwAaNYJXXrF8mjp17KD53HMtxiXbcLEIyPTplsh1xx3212v+fIsw9EIwqccxx1juyd13W4DXIYfAm2+Gtiq5uFgEYPt2O5No29YOM99918KS99ortGXOrihf3g6Z8/KslkfPnnYAmi2rDBeLJPP995ZKfcMN5qKbPRu6dg1tlVMaWra0GiADB9rqomVL+PTT0FYlHheLJDJ8uJ1NTJhgPv1hw7xkXLpSvjzcdpudM1Wtain/Dz6Y2cFcLhZJYPt2uPVW6N7d6kxOm2Y+fU+XTn/+8AeYOtX+bW+80c6e1q0LbVVicLFIMD/+aHUk7r0X/vQn+Owzc8E5mUP16vD66/Doo5Zf0qqVCUim4WKRQBYssFyD0aMtlfzpp8tWy9JJfUQs0vbTT20lecwxVqEsk3CxSBCjR1styNWrLa+jb1/fdmQDbduai7VFC9uaPPpoaIvih4tFAhgyxDwdjRubm+2440Jb5CST3XeHjz6y84trroGrr7a2COmOi0WcefRRq1bVoYMtSffZJ7RFTgiqVLHq49deC489ZpGfP/8c2qrYcLGIE6pw++32l6RHD6uJ4Bmi2U1uLjzyCDz+OLzzjsXTbNgQ2qqy42IRB7Zvh/79LUjnssvsZNwPMp0C+veHl1+2+JouXeCnn0JbVDZcLGJk+3YTiCeeMD/7oEGe2+H8nrPOgtdesyCuk04yl3q64WIRA6p2ePXcc5YMdv/97vFwiqdnTzvHmDbN2kOmW/BWMLEQkYYi8pGIzBOROSJydShbyoIq3Hwz/OtfcP31JhaOUxKnn25h/jNnmmCk0xlGyJVFPvAXVW0GHAn0E5G0KT97773wwANwxRWWE+ArCidaTjnFBGPGDFttbN0a2qLoCCYWqrpcVadFHm8A5gH1Q9lTGh57zJKIzj/fitW4UDilpVs3a+r8wQdw6aV29pXqpESvaRFpDBwGfF7Ee32APgCNGjVKrmFFMHKkuUe7d7dS/N501ykrF10E331nf3j23ttWqqlMcLEQkWrAMOAaVf2dU0lVBwGDwNoXJtm83zBjhpVUO/xwa1RTLvhPz0l3brnFWj48+CDUr2/5JalK0P/uIlIeE4qXVDWli5StWAGnngo1a9rqokqV0BY5mYCIHZKvWGEr1gMOsGZHqUhIb4gAg4F5qvpIKDuiYdMmSzNfswbeftvL3znxJTfXWkC0bAm9e8PChaEtKpqQO+6jgPOBjiIyI3KlnKaqWh2KyZNt63HYYaEtcjKRKlV2FADu0SM1e5SE9IaMV1VR1Zaq+ofI9W4oe4pj8GBT/bvvtkNNx0kU++1nYeGzZplLPtVK9PlZ/i6YM8cOnE44wcriOU6i6drVGhoNGWJu+VTCxaIYfvnF4vl3283+4dxF6iSLW2+1wK3rrjMPXKrgvwLFcO21trIYMgT23DO0NU42kZNj+UZ16ljg35YtoS0yXCyKYOhQyx696SbLEHScZFOnjp2XffGF1UlJBVwsdmLNGmsh2Lq1HWo6TihOPhn69IG//x3Gjw9tjYvF77juOksdHjzYGsk4Tkgefth6zVxwQfgMVReLQowZAy++aNuPli1DW+M4UK2a/Z9ctMhCw0PiYhFh40a4/HJrAORuUieVOOoo6NfPqrGF9I64WEQYMAAWL7a04UqVQlvjOL9l4EA79OzXL1w6u4sFMHeu1ai44go4+ujQ1jjO76lZ0zJTJ0ywbUkIXCyAG26w4KuBA0Nb4jjFc8EF0K4d/PWvsH598ufPerH48EN49107p6hbN7Q1jlM8OTkWAr5mTZjYi6wWi23brNhu48Zw5ZWhrXGckjnsMGs98dRT8O23yZ07q8ViyBCrsnzffX6o6aQPAwbYKiPZ2+asFYvNm632Ydu2ljDmOOlCgwbQty+88AIsWJC8ebNWLF54wYql3nOPV+d20o+bbrLV8J13Jm/OrBSL/HyrpNy2LXTsGNoaxyk9e+xhtVZefdWSzZJBVorFa6/Z4dDNN/uqwklfku3yzzqx2L7depIecogVGHGcdKV2bUtRGDYMlixJ/HxZJxbvvGPLtptv9upXTvrTv7/dk1GCL+t+XR56yOIq3APiZAKNGlk18EGD4OefEztXVonFvHnw6afmdvJuYk6mcM01Fv6d6JyRrBKLQYOsoM1FF4W2xHHiR7t2cMQR8Oijic1IzRqx2LzZYiu6d4fddw9tjePEDxFzo375JXz8ceLmCSoWIvKsiPwgIgn3FA8bZuXyLr880TM5TvLp2XNH24pEEXpl8TzQJRkTPf20NZ3t0CEZszlOcqlcGXr1ssr0iWp9GFQsVHUcsDbR8yxaZAebl17q7lInczn/fCsPOWJEYsZP+V8dEekjInkikrdq1aoyjTFsmN3PPDOOhjlOinHccdCwYeK2IikvFqo6SFVbq2rrevXqlWmMN96AVq2s8azjZCo5OXDeefD++7BiRQLGj/+QqcWSJfD557afc5xMp3dvK+o0fHj8x854sXjzTbv37BnWDsdJBgcfbE2JRo2K/9glioWIVBGRASLyTOR5ExHpFo/JReQVYCLQVESWicil8Ri3MEOHWsOgAw+M98iOk3qIwB//CGPHwqZN8R07mpXFc8AWoF3k+TLgb/GYXFXPUdW9VLW8qjZQ1cHxGLeAtWutdHr37vEc1XFSmz/+0YQi3gFa0YjF/qr6IPArgKpuAtKiCsTHH4MqnHhiaEscJ3l06ABVqsR/KxKNWGwVkcqAAojI/thKI+X53/+galWLm3ecbKFSJejUycRCNX7jRiMWdwKjgYYi8hIwFrgxfiYkjrFj4dhjoUKF0JY4TnLp2tWCERcujN+YJSZqq+r7IjIVOBLbflytqqvjZ0Ji+P57mD/fojYdJ9soaMM5cSLsv398xozGGzJWVdeo6ihVfUdVV4vI2PhMnzg++sjunTqFtcNxQnDwwZZYNmFC/MYsdmUhIpWAKkBdEanFjkPN6sDe8TMhMYwfDzVqwKGHhrbEcZJPbi4ceWR8xWJXK4vLganAQZF7wTUCSELFv9iYNs1CvD1xzMlW2reH2bNhw4b4jFfsr5KqPqqq+wLXq+p+qrpv5DpUVf8Vn+kTQ34+zJplfSEdJ1tp394qZ02eHJ/xojngfFxEmgMHA5UKvZ7gin9lZ/58q4zlYuFkM23b2n3y5Pic3ZUoFiJyB9ABE4t3ga7AeCBlxWL6dLu3ahXWDscJSY0aUL++FaqOB9Hs6HsBnYAVqnoxcChQMT7TJ4bp061yUNOmoS1xnLA0a5ZcsdikqtuBfBGpDvwApHRliFmzoHlzOxF2gOXLYfBgy112sopmzWxbHo9IzmjEIk9EagLPYN6QaUCcjkwSw8KFVm/TifDii3DZZdYs5dxzXTSyiGbNrNTesmWxj1WiWKjqn1V1vao+BZwIXBjZjqQk+fmwdKnl9DsRrr3WUhEBXnnFRSOLaNbM7vHYikQVhSAi9UWkPdAIqCkix8Y+dWL47jsTDBeLQlSoYE1et2xx0cgyCsTiyy9jHyuacO8HgM+A24AbItf1sU+dGL791u6NGwc1IzVx0cg66tWzLnzffx/7WNGsLE4Hmqrqyap6SuQ6NfapE8OiRXb3lcUucNHIGnJyYI894lPANxqxWAiUj32q5LBokZUWa9gwtCVpgItGVrDnnuYQi5VoxOIXYIaIPC0ijxVcsU+dGNasgZo1vYZFqXDRyGj22it5K4uRwEBgAr9NKEtJ1q+HWrVCW5GmuGhkJElbWajqC0VdsU+dGNats5WFEwMuGhnFXnvBqlXmJYyFYsVCRF6P3GeLyKydr9imTRzr17tYxA0XjYygenWL4Iy1YfKuVhZXR+7dgFOKuFIS34YkABeNtKZSJFd88+bYxtlVPYvlkfvioq7Ypk0c69ZZtp2TAFw00pKEi4WIbBCRn4q7Ypv2/+foIiJfisjXInJTPMbcunXHD8dJEC4aaUUyVha7qWp14J/ATUB9oAHWBiDmjmQikouV5+uK1co4R0QOjnVcJ4m4aKQFCReLQnRW1SdUdYOq/qSqTwLxaDPcBvhaVReq6lbgVeC0OIzrJJtdicbAgVbbzQnGggV2LygKVVaiEYttItJbRHJFJEdEegPx+JNRH1ha6PmyyGu/QUT6iEieiOStWrUqDtM6CaMo0bj9dvjDH2DYMBeNQBQ0SE6kN6SAc4EzgZWR64zIa7FSVL/U35XoUNVBqtpaVVvXq1cvDtM6CadANPLz4aWX7CCpVy8XjUAU1KJt3z62cXYpFpFzhX6qepqq1lXVeqp6uqouim1awFYShTM4GgBxyI1zUobcXDu7mDPHRSMgBSuLWA/+dykWqroNODy2KYplCtBERPYVkQrA2VhoeUyUK2f/J50UwkUjKAUHmwkViwjTRWSkiJwvIj0KrtimBVXNB/oDY4B5wOuqOifWcWvWhB9/jHUUJyG4aAQhmWJRG1gDdGRH9Ga32KY1VPVdVT1QVfdX1XviMWbNmhbF6aQwLhpJJWlioaoXF3FdEtu0iaNWLReLtMFFIyls3Gj3ypVjGyeasnoNROQtEflBRFaKyDARaRDbtImjZk0L+XbSCBeNhLJiBdSuHXuNl2i2Ic9hB497Y3EQb0deS0l8G5LGuGgkhBUrLE09VqIRi3qq+pyq5keu54GUDXioXdtWFh5pnMa4aMSV5cutAE6sRCMWq0XkvEgEZ66InIcdeKYkjRqZUHz3XWhLnJhx0YgLyVxZXIJFcK6IXL0ir6UkBVW9C6p8OxmAi0aZUTWxSMrKQlWXqOqpkejNggjOlK1nUSAWBf1DnAzCRaPUrFtnrtOkrCzSzRvSsKG1AnCxyGBcNKKmoBNZkyaxj5Vx3pCKFaF+fReLrMBFo0QKepwWtDGMhYzzhoBtRRYuDG2FkzRcNIpl3jz7AxqPDn0Z5w0BaN4cZs3K6v8j2UlxovFcyi6EE868eXDggfajiZXSekOWk+LeELD8/Z9+8q1I1lJYNF5+Gc45J7RFwZg3Lz5bEIByJX1AVZcAKdsIuSgKin1Mnw777x/WFicgublZLRS//GJ/MM8/Pz7jReMNeUFEahZ6XktEno3P9ImheXOraxFrzUHHSWemTrU4i8PjVJEmmm1IS1VdX/BEVdcBh8Vn+sRQqRIcfLCLhZPdTJhg93bt4jNeNGKRIyL/3+NLRGoTxfYlNIcdBtOmmbI6TjYyYYIdbtatG5/xohGLh4EJIjJQRO7Guqk/GJ/pE0f79rBy5Y4y6I6TTajCxImxF+ktTDTh3i9ifUJWAquAHqo6JH4mJIaOHe3+v/+FtcNxQvDNN9Y5PV5bEIhyO6Gqc4G58Zs28ey/v2Wgjh0LffuGtsZxkstnn9k9qSuLdEXEVhcffeTBWU72MWYM1KtnB/3xImPFAkws1q6FmTNDW+I4ySM/H0aPhpNPhpw4/oZHE2fRv7A3JJ0oOLcYOzasHY6TTCZNstT0gg6S8SIa3dkTmCIir4tIFxEpqu1gSlK/PrRsCSNGhLbEcZLHqFEWlHjSSfEdNxpvyG1AE2AwcBHwlYjcKyJpEUjdq5cd9nzvjRGdLGHUKDj6aKhRI77jRrWjUVVlR1m9fKAWMFREyhRvISJniMgcEdkuIq3LMka09OplPue33krkLI6TGixeDLNnx38LAtGdWVwlIlOxQKzPgBaq2hfrgdqzjPN+AfQAxpXx66OmWTM7ER46NNEzOU54Xn3V7t27x3/saOIs6mKBWL+pu6mq20WkTG0MVXUeQLKOP3r1gr/9zSI699gjKVM6TtJRhRdftNiKRGRbR3NmcXtxBXoLfukTiYj0EZE8EclbtWpVmcbo1ctiLd58M87GOU4KMX06zJ0bv5T0nUlYnIWIfCgiXxRxnVaacVR1kKq2VtXW9eqVrZpf8+bQogUMHlymL3ectGDIEGtReOaZiRk/YdmjqnpCosYuLSLQpw9ceaXl+Mcrv99xUoX8fHjlFTvYrF07MXNkdARnYc47z7pIDxoU2hLHiT9jxtiZXKK2IBBILESku4gsA9oBo0RkTKLnrFkTzjrLSjJu2JDo2RwnuTz+uDUSSoTLtIAgYqGqb6lqA1WtqKp7qGrnZMzbpw9s3LjDveQ4mcDcubay6NfPziwSRdZsQwCOPNIOOp94witoOZnDY49ZKck+fRI7T1aJhQhccw3MmAHvvx/aGseJnTVrLLbivPMsJT2RZJVYgP1QGzSAe+8NbYnjxM4zz8CmTXD11YmfK+vEokIFuOEGGDcOxo8PbY3jlJ1Nm2wL0qmTxRIlmqwTC4DLLrOKx/fdF9oSxyk7Tz4Jy5fDgAHJmS8rxaJKFbj2Wnj3XTu/cJx0Y+NGuP9+OOEEOO645MyZlWIB8Oc/W75/slTZceLJ449b9e6BA5M3Z9aKRc2acMst8M47VtTXcdKF9evhwQehWzcLB0gWWSsWAFddZe0C/vIXrwDupA+PPGKCcffdyZ03q8WiUiU75Jw+Hf7739DWOE7JLF4MDz1kmaWHJbnjcFaLBcDZZ0Pr1nDrrdai3nFSmWuvteDChx5K/txZLxY5OfDww7BsWZh/AMeJltGjrZbsgAHQsGHy5xdNoySJ1q1ba15eXkLGPussGD7cGhIddFBCpnCcMrNliwVe5eRYQd5EJYyJyFRVLbKIdtavLAp47DGoWhX+9Cc/7HRSj4cfhq+/NpdpIjNLd4WLRYQ99rBT5vHj4emnQ1vjODv48ksrON2jR/wbB5UGF4tCXHihRcTdeKOdYThOaPLz4YILrMrbv/4V1hYXi0KI2Kpi2zbo29drXjjhuf9+mDwZnnrKKmGFxMViJ/bbD+65xyI7n3oqtDVONjN1Ktx1F5x7LpxxRmhrXCyK5KqroGtX82nPnBnaGicb2bTJiu/uvnv47UcBLhZFkJMDzz9vJdXPOgt+/jm0RU62ccMNMG8ePPcc1KoV2hrDxaIYdt/dQsAXLID+/UNb42QTL74I//635SyF9H7sjIvFLujYEW67zVYZQ4aEtsbJBqZPh8svhw4d7HAzlXCxKIHbb4djj7XKyZMnh7bGyWTWrrVYijp14LXXoFzC+gWWDReLEihXDoYONbfVqafC0qWhLXIykW3bzOvx/fcwbJhtg1ONUB3J/i4i80Vkloi8JSI1Q9gRLfXqwdtv2wn1KadYSTPHiSd//as1CnrsMWjbNrQ1RRNqZfEB0FxVWwILgJsD2RE1hxxiS8PZs62dgOePOPHikUfs6t8/8Y2CYiFU+8L3VTU/8nQS0CCEHaWlSxf4xz9gxAhzbXmEpxMrr7xiXo9eveCf/7Qo4lQlFY5QLgFeK+5NEekD9AFo1KhRsmwqliuvhK++sr8EtWqZt8RxysLYsZaPdOyx5m3LzQ1t0a5JmFiIyIfAnkW8dauqjoh85lYgH3ipuHFUdRAwCKyeRQJMLRUi8Oij8NNPVoSkalWL9HSc0jBjBnTvDgceaHVUKlUKbVHJJEwsVPWEXb0vIhcC3YBOmk4VeLAIz8GDrQzfddeZYKTyXtNJLWbMsOzmGjWs+lWqRGiWRJBtiIh0AW4EjlPVtKx8Wa4cvPSSCcYVV5hg9O4d2ion1Zk6FU48EapVsxYUDdLitM4I5Q35F7Ab8IGIzBCRtMzvrFDBYjA6dLCaA889F9oiJ5WZPNn6klavDp98AvvvH9qi0hFkZaGqB4SYNxFUrmwxGD16wCWXWBTeX/4S2ion1Zg40bxpderYimKffUJbVHo8gjMOVK1qgnHmmXD99XDzze5WdXYwerQlhO2+u60o0lEoIDVcpxlBhQrw8st2WHX//bB6tRXPSXV3mJNYBg2yvrrNm1sj7r33Dm1R2XGxiCO5ufDkk1C3rlXb+uEH859Xrx7aMifZbN9uvXQfeMC2H6+/DrvtFtqq2PBtSJwRsUrMjz8Oo0ZBu3ZWwt3JHjZvhnPOMaG44grboqa7UICLRcLo3x/efx9WrIAjjrDHTuazdCkcf7ytJB58EJ54IvVSzcuKi0UC6dgRpkyxVnNdu1peiR98Zi6jR1uz4jlzzKV+ww2pnetRWlwsEsx++8GECRbae911VtNz3brQVjnxZNs2C/0/+WQ7wMzLg549Q1sVf1wskkC1arYsvf9+a2x76KHmQnPSn5UrzS36t7/BRRfBpEmW75GJuFgkiZwc63Q2YYIlDR1/vJ2W//praMucsjJ0KLRoYQFXzz5rV5Uqoa1KHC4WSeaII2DaNLj0UrjvPmjf3npZOunDqlW2nTzjDDuPmjwZLr44tFWJx8UiANWqwTPP2F+mb76Bli3hzjvN5eakNkOHWtW0t96yWJpJkyzgKhtwsQhIz54wd67d77rLRON//wttlVMUS5ZYNaszzrBw7WnTbBtZvnxoy5KHi0Vg9tzTwsTHjLGov06drG3dDz+EtswBK0Fw111w0EEWZHfPPXZGkS2ricK4WKQIJ51kxYBvu80KAzdpAvfe660TQ6Fq/w4HHWRbxFNPhfnzbTWRKUFWpcXFIoWoXBkGDoRZs+C44+DWW000nn7avSbJZOJEq4t59tmW5zNuHLz6avpmi8YLF4sU5KCDYORI+PRTC+q64go7VHvjDY8ATSTjx1sVq/btrcftf/5jEbjHHBPastTAxSKFOfpoE4yRIy0F/swzza///POwdWto6zKHTz6x0PxjjrFV3UMPwcKF5t72EgM7cLFIcUSsC9rMmZbunpNjPv1997VEpR9/DG1hepKfD2++adu9Dh1g3jxr7/Dtt1bprGrV0BamHi4WaUJurnVCmznTEpaaNbOI0IYNrTrXggWhLUwPVq600Ox99zWX9aJF1txn4UJr6ZDJEZix4mKRZohA587w4YdWKbpbN/vP3rSpbVuefRY2bAhtZWqxfbsdUvbubeI6YICdCw0fbkFxV19th8vOrnGxSGNatbIYjaVLrdDK6tW2z95rL9uqfPKJZURmI6omptdfb16M446Dd96Bvn3NBfrBB3DaadnrBi0Lkk79fVq3bq15eXmhzUhZVM3t99xz5urbuNE6wJ9yCpx+ujW2yeS/oKoWqzJ0qH3/X31lEZadO5sb9LTTLNTeKR4RmaqqrYt8z8UiM/n5ZyvnNmKEFYr96Sfbj3fubAFGHTrYX9x0L86yerWtEsaMsWpky5fb93T88VbarkcPqF07tJXpg4tFlrN1K3z8sQnHiBHw3Xf2esOGFnxUcDVtmtrioWpbrilT4PPPLY9m2jR7vXZti5E46SSrSrbXXqGtTU9STixEZCBwGrAd+AG4SFW/L+nrXCxip2Cp/umndug3bpzVCQWLVjz0UIvlKLgOOSSMh+DXX82N+dVXJgiTJ5tIrFxp75cvD23a2Eqpc2c4/HCPiYgHqSgW1VX1p8jjq4CDVfWKkr7OxSL+qFr18XHjrDDP7NlWQ/KXSAdaEWuz17ixrUQaNPjtvXZtOweoVs1iQKJh82bbPqxaZffVq00EvvnGxOHrr82lWXA4K2LeizZtrB5ImzaWoVuxYiJ+ItnNrsQiVPvCnwo9rQqkz14owxCx/JMmTcyTAvZL+u23Fs1YIB5Lluw4E9i+veixqlTZIRwVKtjqID//t9emTTuEaGeqVTM7Dj/cDiSbNIEDDrAMzxo1EvP9O9ET7MxCRO4BLgB+BI5X1VXFfK4P0AegUaNGhy9evDh5Rjq/49dfTTCWLbPzg/XrzetScG3YYPetW22rUL68uScLrgoVbLtTr57dCz+uUye1z0yygSDbEBH5ENiziLduVdURhT53M1BJVe8oaUzfhjhOYgmyDVHVE6L86MvAKKBEsXAcJxxBIjhFpEmhp6cC80PY4ThO9IQKdr1fRJpirtPFQImeEMdxwhLKG5KB/ZocJ7PxRDLHcaLCxcJxnKhwsXAcJypcLBzHiYq0yjoVkVWY96Qk6gKrE2yO2+A2pJMN0c6/j6rWK+qNtBKLaBGRvOKi0NwGtyEbbYjH/L4NcRwnKlwsHMeJikwVi0GhDcBtKMBtMELbEPP8GXlm4ThO/MnUlYXjOHHGxcJxnKjIWLEQkYEiMktEZojI+yKyd5Ln/7uIzI/Y8JaI1Ezm/BEbzhCROSKyXUSS6rYTkS4i8qWIfC0iNyVz7kI2PCsiP4jIF4HmbygiH4nIvMi/w9UBbKgkIpNFZGbEhrvKPJiqZuQFVC/0+CrgqSTPfxJQLvL4AeCBAD+DZkBT4GOgdRLnzQW+AfYDKgAzsaLMyf7+jwVaAV8ke+7I/HsBrSKPdwMWJPvnAAhQLfK4PPA5cGRZxsrYlYUGLgqsqu+ran7k6SSgQTLnj9gwT1W/TPa8QBvga1VdqKpbgVex1g9JRVXHAWuTPW+h+Zer6rTI4w3APKB+km1QVd0YeVo+cpXpdyFjxQKsKLCILAV6A7cHNOUS4L2A8yeb+sDSQs+XkeRfklRDRBoDh2F/2ZM9d66IzMB69HygqmWyIa3FQkQ+FJEvirhOA1DVW1W1IfAS0D/Z80c+cyuQH7Eh7kRjQwCKqtGdtT56EakGDAOu2WnFmxRUdZuq/gFb3bYRkeZlGSete0hr4KLAJc0vIhcC3YBOGtk0xptS/AySyTKgYaHnDYASO85lIiJSHhOKl1T1zZC2qOp6EfkY6AKU+tA3rVcWuyJ0UWAR6QLcCJyqqsW01clYpgBNRGRfEakAnA2MDGxT0hERAQYD81T1kUA21CvwxIlIZeAEyvi7kLERnCIyDPME/H9RYFX9Lonzfw1UBNZEXpqkUbRojLMN3YHHgXrAemCGqnZO0twnA//EPCPPquo9yZh3JxteATpg6dkrgTtUdXAS5z8a+BSYjf0/BLhFVd9Nog0tgRewf4cc4HVVvbtMY2WqWDiOE18ydhviOE58cbFwHCcqXCwcx4kKFwvHcaLCxcJxnKhwsXCSiohsjNz3FpGhMYxzjYhUiZ9lTkm469RJGCJSrlAyXcFrG1W1WhzGXoRl0oYu8Z81+MoiCxCRIyJ1NSqJSNVIXYPf5QeIyAWRz80UkSGR1/YRkbGR18eKSKMSXn9eRB4RkY+AByJRnBNFZIqIDCw0V+OCOhMicpGIvCkio0XkKxF5sNDnnhSRvMK1GETkKmBv4KPIPIjISZF5ponIG5F8DCeehMjz9yv5F/A34CHg38DNRbx/CPAlUDfyvHbk/jZwYeTxJcDwEl5/HngHyI08HwlcEHncD9gYedyYSJ0J4CJgIVADqIRF3DbcyY5crC5Hy8jzRYVsrQuMA6pGnt8I3B76Z55pl68ssoe7gROB1sCDRbzfERiqkWW9qhbUgWiHJeIBDAGOLuF1gDdUdVvk8VHAK4U+VxxjVfVHVd0MzAX2ibx+pohMA6ZjgnZwEV97ZOT1zyKp2BcW+nonTqR11qlTKmoD1bDiJ5WAn3d6X4gujby4zxR+feexoxl3S6HH24ByIrIvcD1whKquE5HnMdt3RrA6DedEMY9TRnxlkT0MAgZgdTUeKOL9sdhf8ToAIlI78voELGsUrIjQ+BJe35nPdvpcaaiOCc+PIrIH0LXQexuwUnVglciOEpEDIrZXEZEDSzmXUwIuFlmAiFwA5Kvqy8D9wBEi0rHwZ1R1DnAP8ImIzAQKUqqvAi4WkVnA+cDVJby+M1cD/URkCnYmETWqOhPbfswBnsWEp4BBwHsi8pGqrsLOPV6J2DMJOKg0czkl465Tx3GiwlcWjuNEhYuF4zhR4WLhOE5UuFg4jhMVLhaO40SFi4XjOFHhYuE4TlT8H9oJV7RoxQSXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "ax.set_aspect(1)\n",
    "\n",
    "plt.xlabel('x coordinate')\n",
    "plt.ylabel('y coordinate')\n",
    "\n",
    "plt.plot(solution.y[0], solution.y[1], 'red')\n",
    "\n",
    "t_array = np.linspace(0, 2*np.pi, 100)\n",
    "x_array = 3*np.cos(t_array)\n",
    "y_array = 3*np.sin(t_array)\n",
    "plt.plot(x_array,y_array, 'blue')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5232a1f",
   "metadata": {},
   "source": [
    "### Elliptical trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3f62b92d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x24af7f9fa30>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tStart = 0\n",
    "tEnd = 100\n",
    "\n",
    "x0 = 2\n",
    "y0 = 0\n",
    "vx0 = 0\n",
    "vy0 = 1\n",
    "\n",
    "solution = integrate.solve_ivp(f_ODE, [tStart,tEnd], [x0, y0, vx0, vy0], method = 'RK45', t_eval = np.linspace(tStart,tEnd,1001))\n",
    "\n",
    "plt.xlabel('Time t')\n",
    "plt.ylabel('Coordinates x and y')\n",
    "\n",
    "plt.plot(solution.t, solution.y[0], 'red')\n",
    "plt.plot(solution.t, solution.y[1], 'blue')\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "ax.set_aspect(1)\n",
    "\n",
    "plt.xlabel('x coordinate')\n",
    "plt.ylabel('y coordinate')\n",
    "\n",
    "plt.plot(solution.y[0], solution.y[1], 'red')\n",
    "\n",
    "t_array = np.linspace(0, 2*np.pi, 100)\n",
    "x_array = 3*np.cos(t_array)\n",
    "y_array = 3*np.sin(t_array)\n",
    "plt.plot(x_array,y_array, 'blue')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f36c2779",
   "metadata": {},
   "source": [
    "### External force"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b94114fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 1\n",
    "U0 = 1\n",
    "xi = 0.1\n",
    "\n",
    "A0 = 4\n",
    "tOsc = 50\n",
    "phi = 45 / 180 *np.pi \n",
    "\n",
    "def f_ODE(t,r):\n",
    "    x, y = r[0:2]\n",
    "    vx, vy = r[2:4]\n",
    "    return [vx, vy, -xi/m*vx -2*U0/m*x + A0*np.sin(2*np.pi*t/tOsc)*np.cos(phi), -xi/m*vy -2*U0/m*y + A0*np.sin(2*np.pi*t/tOsc)*np.sin(phi)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a32abd57",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x24af80811f0>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tStart = 0\n",
    "tEnd = 100\n",
    "\n",
    "x0 = 2\n",
    "y0 = 0\n",
    "vx0 = 0\n",
    "vy0 = 1\n",
    "\n",
    "solution = integrate.solve_ivp(f_ODE, [tStart,tEnd], [x0, y0, vx0, vy0], method = 'RK45', t_eval = np.linspace(tStart,tEnd,1001))\n",
    "\n",
    "plt.xlabel('Time t')\n",
    "plt.ylabel('Coordinates x and y')\n",
    "\n",
    "plt.plot(solution.t, solution.y[0], 'red')\n",
    "plt.plot(solution.t, solution.y[1], 'blue')\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "ax.set_aspect(1)\n",
    "\n",
    "plt.xlabel('x coordinate')\n",
    "plt.ylabel('y coordinate')\n",
    "\n",
    "plt.plot(solution.y[0], solution.y[1], 'red')\n",
    "\n",
    "t_array = np.linspace(0, 2*np.pi, 100)\n",
    "x_array = 3*np.cos(t_array)\n",
    "y_array = 3*np.sin(t_array)\n",
    "plt.plot(x_array,y_array, 'blue')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b2d14502",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
