extra_terrestrial_brachistochrone_en.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "<div style=\"display: flex; align-items: center;\">\n",
        "    <img src=\"https://github.com/nagelt/Teaching_Scripts/raw/9d9e29ecca4b04eaf7397938eacbf116d37ddc93/Images/TUBAF_Logo_blau.png\" width=\"500\" height=\"auto\" height=\"auto\" style=\"margin-right: 100px;\" />\n",
        "    <div>\n",
        "        <p><strong>Prof. Dr. Thomas Nagel</strong></p>\n",
        "        <p>Chair of Soil Mechanics and Foundation Engineering<br>Geotechnical Institute<br>Technische Universität Bergakademie Freiberg.</p>\n",
        "        <p><a href=\"https://tu-freiberg.de/en/soilmechanics\">https://tu-freiberg.de/en/soilmechanics</a></p>\n",
        "    </div>\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Paths of seismic body waves and the terrestrial brachistochrone"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The following derivation is very short -- more information can be found in the lecture material."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [],
      "source": [
        "#HIDDEN\n",
        "from IPython.display import display, Math, Latex\n",
        "import numpy as np\n",
        "import sympy as sp\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.integrate import odeint\n",
        "import plot_functions.plot_settings"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Preliminary considerations in Cartesian Coordinates (classical brachistochrone)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Following the textbook [Mark Levi: Classical Mechanics with Calculus of Variations and Optimal Control](https://www.google.de/books/edition/_/uVSYswEACAAJ?hl=de&sa=X&ved=2ahUKEwiE_I3G-ofyAhUBD-wKHdOeClUQ8fIDMBF6BAgIEAM), chapter 5.5."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The Fermat principle states, that light -- or more generally -- waves, travel along paths of shortest time.\n",
        "For the velocity of P- and S-waves in elastic media $c_\\mathrm{P}, c_\\mathrm{S} \\propto \\sqrt{\\mu}$ holds, where $\\mu$ denotes shear modulus."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "It is customary to approximate the depth-dependent shear modulus by $\\mu \\propto p \\propto z$, thus $c \\propto \\sqrt{z}$ holds.\n",
        "Consequently the path calculation of seismic waves is mathematically equivalent to the brachistochrone, since for the velocity of a point mass in a gravitational field $v\\propto \\sqrt{z}$ holds, too. \n",
        "The first solution we are going to discuss is a cycloid, the curve on a circle rolling along a straight line."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Conservation of energy of a point mass in a gravitational field leads to its height-dependent velocity\n",
        "\\begin{equation}\n",
        "v = \\sqrt{2g y},\n",
        "\\end{equation}\n",
        "where the $y$-coordinate points downwards."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The travel time for a certain path depends on the velocity\n",
        "\\begin{equation}\n",
        "T = \\int_\\mathrm{A}^\\mathrm{B} \\frac{\\mathrm{d}s}{v}  = \\int_\\mathrm{A}^\\mathrm{B} \\frac{\\mathrm{d}s}{\\sqrt{2gy}}.\n",
        "\\end{equation}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We are going to show next, that the extremals of a functional with the structure\n",
        "\\begin{equation}\n",
        "\\int_\\mathrm{A}^\\mathrm{B} F(y)\\, \\mathrm{d}s = \\int_\\mathrm{x_A}^\\mathrm{x_B} \\underbrace{F(y) \\sqrt{1+y'^2}}_{L} \\mathrm{d}x.\n",
        "\\end{equation}\n",
        "satisfy the relation\n",
        "\\begin{equation}\n",
        "F(y)\\sin\\alpha = \\mathrm{const.}\n",
        "\\end{equation}\n",
        "where the definition of the slope $\\alpha$ of the path can be read from the figure below."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Applying Noethers theorem to a Lagrangian $L(y,y')$ that does not explicitely depend on time, one can define the Hamiltonian\n",
        "\\begin{equation}\n",
        "H = y' \\frac{\\partial L}{\\partial y'} - L = \\mathrm{const.}.\n",
        "\\end{equation}\n",
        "Specifically for\n",
        "For $L(y,y')=F(y)\\sqrt{1+y'^2}$ we can write\n",
        "\\begin{equation}\n",
        "H = y'F(y)\\frac{y'}{\\sqrt{1+y'^2}}-F(y)\\sqrt{1+y'^2} = -\\frac{F(y)}{\\sqrt{1+y'^2}}\n",
        "\\end{equation}\n",
        "and by expressing the slope via the angle with the vertical $y'=\\frac{\\cos\\alpha}{\\sin\\alpha}$, we arrive at our proposition."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "For the classical brachistochrone, after factoring out the constant $1/\\sqrt{2g}$, $F(y)=\\frac{1}{\\sqrt{y}}$ remains inside the integral and\n",
        "\\begin{align}\n",
        "   \\frac{\\sin\\alpha}{\\sqrt{y}} &= \\frac{1}{\\sqrt{2r}}, \\\n",
        "   \\sqrt{y} &= \\sqrt{2r} \\sin\\alpha.\n",
        "\\end{align}\n",
        "holds for the extremal."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The next sketch illustrates this curve as a cycloid, which is generated by a circle of diameter $2r$.\n",
        "By Thales theorem, the velocity is perpendicular to the position vector. The circle radius is determined by the location of start- and end-point.\n",
        "![classical_brachistochrone.svg](https://github.com/nagelt/soil_dynamics/raw/master/Images/classical_brachistochrone.svg)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Switching to polar coordinates (terrestrial brachistochrone)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Inspired by [Matthew Van Koevering: Terrestrial Brachistochrone](https://www.youtube.com/watch?v=_KIvpr3X_bU)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Considering earth a sphere and working on grand circles we switch to polar coordinates for convenience. The travel time is once again determined by the functional\n",
        "\\begin{equation}\n",
        "T=\\int_\\mathrm{A}^\\mathrm{B} \\frac{\\mathrm{d} s}{v(r)}.\n",
        "\\end{equation}\n",
        "In comparison to the previous case, arc-length and depth-dependent velocity differ\n",
        "\\begin{align}\n",
        "\\mathrm{d} s &= \\sqrt{(\\mathrm{d} r)^2+(r\\mathrm{d}\\theta)^2}, \\\n",
        "v &= C\\sqrt{R^2 - r^2},\n",
        "\\end{align}\n",
        "where $C=\\sqrt{g/R}$ inserts gravitational acceleration $g$ and earth radius $R$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "As before, the Lagrangian in the functional\n",
        "\\begin{equation}\n",
        "T=\\frac{1}{C}\\int_{\\theta_\\mathrm{A}}^{\\theta_\\mathrm{B}} \\underbrace{\\sqrt{\\frac{ (\\mathrm{d} r/\\mathrm{d} \\theta)^2 +r^2}{R^2-r^2}}}_{L} \\mathrm{d} \\theta\n",
        "\\end{equation}\n",
        "is of structure $L(r,r')$. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**Remark:** The velocity dependence on depth of a point mass inside a heavy sphere is the same as for depth-dependent waves in an elastic medium with depth-dependent stiffness."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "For the terrestrial brachistochrone we obtain the force on the point mass from [Newtons shell theorem](https://doi.org/10.1080/07468342.2018.1411655)\n",
        "\\begin{equation}\n",
        "F_g = \\frac{mgr}{R}\n",
        "\\end{equation}\n",
        "where $r$ denotes the radius from earth center to the point mass."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "By conservation of energy and the potential energy of a point mass $V=\\frac{1}{2}\\frac{mg}{R}r^2$ initially at rest at the earth surface $r=R$, we obtain the velocity\n",
        "\\begin{equation}\n",
        "v(r) = \\sqrt{\\frac{g}{R}}\\sqrt{R^2 - r^2}.\n",
        "\\end{equation}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Assuming a constant mass density $\\rho$, the depth-dependent hydrostatic pressure follows\n",
        "\\begin{equation}\n",
        "p = \\int_r^R \\frac{4\\pi}{3} G \\rho^2r\\,\\mathrm{d}r = \\frac{2\\pi}{3}G\\rho^2(R^2 - r^2),\n",
        "\\end{equation}\n",
        "where $G$ denotes the gravitational constant.\n",
        "Further assuming a linear relation between pressure and shear modulus $\\mu=\\frac{1}{2}C_1 p$ we obtain for the velocity of S-wave\n",
        "\\begin{equation}\n",
        "c_\\mathrm{S} = \\sqrt{\\frac{\\mu}{\\rho}} = \\sqrt{C_1 \\frac{\\pi}{3}G\\rho}\\,\\sqrt{R^2 - r^2},\n",
        "\\end{equation}\n",
        "which is of different value, but of same structure as in the terrestrial brachistochrone problem.\n",
        "The velocity of P-waves $c_\\mathrm{P}$ differs from $c_\\mathrm{S}$ only by a constant factor."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "r, rt, r0, R, psi = sp.symbols('r rt r0 R psi')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We start with the integrand of the time functional, where the constants have been excluded, since they do not affect the paths"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [],
      "source": [
        "L = sp.sqrt((rt**2 + r**2)/(R**2 - r**2))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Instead of evaluating the Euler-Lagrange equations, we take advantage of the first integral\n",
        "$H=r' \\frac{\\partial L}{\\partial r'} - L$ and choose the lowest point $r=r_0$ as reference.\n",
        "Since the lowest point is a minimum, we have $r'(r_0)=0$. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "scrolled": true
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle H-H_0=0=\\frac{- r^{2} \\sqrt{\\frac{r^{2} + rt^{2}}{R^{2} - r^{2}}} + \\sqrt{\\frac{r_{0}^{2}}{R^{2} - r_{0}^{2}}} \\left(r^{2} + rt^{2}\\right)}{r^{2} + rt^{2}}$"
            ],
            "text/plain": [
              "<IPython.core.display.Math object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "H = sp.simplify( rt*L.diff(rt) - L )\n",
        "H0 = H.subs([(r, r0), (rt, 0)])\n",
        "TB_condition = sp.simplify( H - H0 )   # equals zero\n",
        "display(Math('H-H_0=0=' + sp.latex(TB_condition)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We can rearrange this condition as an ordinary differential equation"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle r'=- \\sqrt{\\frac{R^{2} r^{2} \\left(r^{2} - r_{0}^{2}\\right)}{r_{0}^{2} \\left(R^{2} - r^{2}\\right)}}$"
            ],
            "text/plain": [
              "<IPython.core.display.Math object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "text/latex": [
              "$\\displaystyle r'=\\sqrt{\\frac{R^{2} r^{2} \\left(- r^{2} + r_{0}^{2}\\right)}{r_{0}^{2} \\left(- R^{2} + r^{2}\\right)}}$"
            ],
            "text/plain": [
              "<IPython.core.display.Math object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "TB_ode = sp.solve(TB_condition, rt)   # quadratic equation has two solutions \n",
        "TB_ode_backward = sp.simplify(TB_ode[0])\n",
        "TB_ode_forward = sp.simplify(TB_ode[1])\n",
        "display(Math(\"r'=\" + sp.latex(TB_ode_backward)))\n",
        "display(Math(\"r'=\" + sp.latex(TB_ode_forward)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Formally, we could solve these ODEs by separation of variables.\n",
        "However, we would have to solve difficult integrals. In contrast, numerical integrators are easily to run.\n",
        "So we give _experimental numerics_ a try hoping it leads us to a qualified guess for the sought function."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Experimental numerics"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let's re-iterate three thoughts on the solution, before running the ODE-solver\n",
        "- by time symmetry we expect a symmetric path with the lowest point $r=r_0$ in the middle,\n",
        "- for $r_0=0$ we expect a straight line through earth center and for $0<r_0<R$ an angle difference $0<|\\theta_A-\\theta_B|<\\pi$,\n",
        "- for $r\\to R$ the slope approaches infinity, meaning a vertical path on start and arrival, we start or stop close to this point to avoid division by zero."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "For the ODE-solver we need to provide the ODE as a function"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [],
      "source": [
        "def tb_ode(r, t):   \n",
        "    if r < Rn:\n",
        "       dr = (Rn*r/r0n)*np.sqrt((r**2 - r0n**2)/(Rn**2 - r**2))\n",
        "    else:\n",
        "       dr = 0   # prevent division by zero\n",
        "    return dr"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The numerical values are indexed by _n_ to distinguish them from the symbolic variables."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [],
      "source": [
        "Rn = 1.0   "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The span of the independent variable (angle) is set to zero at $r=r_0$ as well as an upper bound of $\\pi/2$ for the first half of the path. The second half of the path follows by symmetry. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [],
      "source": [
        "theta_grid = np.linspace(0, np.pi/2,1000)   "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Numerical solutions can now be obtained for different values of the lowest point of the path and plotted in a polar diagramme."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "fig, ax = plt.subplots(subplot_kw={'projection': 'polar'},figsize=(10,10))\n",
        "ax.set_rlabel_position(180) \n",
        "for r0n in np.linspace(0.001, 0.9, 10):\n",
        "    initial_r = 1.001*r0n  # start slightly above r0, otherwise circle does not reach the surface\n",
        "    r_sol = odeint(tb_ode, initial_r, theta_grid) \n",
        "    last = np.count_nonzero(r_sol < Rn) + 1  # discard values after reaching the surface\n",
        "    r_real = r_sol[0:last]\n",
        "    theta_real = theta_grid[0:last]\n",
        "    ax.plot(np.concatenate((-np.flip(theta_real), theta_real)), np.concatenate((np.flip(r_real), r_real)))  # symmetry "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The numerical results and the limit case of $R=\\infty$ (classical brachistochrone) give rise to the assumption that the time-optimal path is given by a hypocycloid, the curve generated by a circle rolling inside another circle."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Verification of the guess\n",
        "![terrestrial_brachistochrone.svg](https://github.com/nagelt/soil_dynamics/raw/master/Images/terrestrial_brachistochrone.svg)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let us check wether the hypocycloid of a circle of radius $a=\\frac{R-r_0}{2}$ rolling inside the circle with radius $R$ satisfies the ODE for the optimal path."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [],
      "source": [
        "a = (R-r0)/2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The dependency of $\\theta$ on $\\psi$ is given by the rolling condition $R\\varphi=a\\psi$, the common height (opposite $\\psi$ and $\\theta-\\varphi$) of the triangle with sides $r$, $a$ and the line connecting the centerpoints."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle \\frac{\\mathrm{d} \\theta}{\\mathrm{d} \\psi}=\\frac{r_{0} \\left(R - r_{0}\\right) \\left(R^{2} \\sin^{2}{\\left(\\psi \\right)} + 2 R r_{0} \\cos{\\left(\\psi \\right)} + 2 R r_{0} - r_{0}^{2} \\sin^{2}{\\left(\\psi \\right)} + 2 r_{0}^{2} \\cos{\\left(\\psi \\right)} + 2 r_{0}^{2}\\right)}{2 R \\left(R + r_{0} + \\left(- R + r_{0}\\right) \\cos{\\left(\\psi \\right)}\\right) \\left(- R^{2} \\cos{\\left(\\psi \\right)} + R^{2} + r_{0}^{2} \\cos{\\left(\\psi \\right)} + r_{0}^{2}\\right)}$"
            ],
            "text/plain": [
              "<IPython.core.display.Math object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "THETA = (a/R)*psi + sp.atan(a*sp.sin(psi)/(R-a-a*sp.cos(psi)))\n",
        "d_theta_d_psi_tmp = sp.simplify( THETA.diff(psi) )\n",
        "display(Math(r'\\frac{\\mathrm{d} \\theta}{\\mathrm{d} \\psi}=' + sp.latex(d_theta_d_psi_tmp))) \n",
        "#print(sp.latex(d_theta_d_psi_tmp))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "To formulate $\\cos\\psi$ and $\\sin^2\\psi$ as functions of radial position $r$ we use the law of cosines"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {},
      "outputs": [],
      "source": [
        "cospsi = (R**2 + 2*a**2 - 2*R*a - r**2)/(2*(R-a)*a)\n",
        "sin2psi = 1-cospsi**2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle \\frac{\\mathrm{d} \\theta}{\\mathrm{d} \\psi}=\\frac{R r_{0}}{2 r^{2}} - \\frac{r_{0}}{2 R}$"
            ],
            "text/plain": [
              "<IPython.core.display.Math object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "d_theta_d_psi = sp.simplify( d_theta_d_psi_tmp.subs([ (sp.cos(psi), cospsi), (sp.sin(psi)**2, sin2psi)]) ) \n",
        "display(Math(r'\\frac{\\mathrm{d} \\theta}{\\mathrm{d} \\psi}=' + sp.latex(d_theta_d_psi))) \n",
        "#print(sp.latex(d_theta_d_psi))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "One feels tempted to differentiate the law of cosines $r^2 = (R-a)^2 + a^2 - 2(R-a)a\\cos\\psi$\n",
        "to resolve for $\\psi(r)$, however then $\\sin\\psi$ pops up, while we have $\\cos\\psi$ readily available.\n",
        "So we start from the tangent half-angle formula $\\tan\\frac{\\psi}{2}=\\sqrt{\\frac{1-\\cos\\psi}{1+\\cos\\psi}}$ where we eliminate $\\cos\\psi$ by the law of cosines and then differentiate with respect to $r$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle \\frac{\\mathrm{d} \\psi}{\\mathrm{d} r}=\\frac{2 r \\sqrt{\\frac{r^{2} - r_{0}^{2}}{R^{2} - r^{2}}}}{r^{2} - r_{0}^{2}}$"
            ],
            "text/plain": [
              "<IPython.core.display.Math object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "PSI = 2*sp.atan(sp.sqrt((r**2 - r0**2)/(R**2 - r**2)))\n",
        "d_psi_d_r = sp.simplify( PSI.diff(r) )\n",
        "display(Math(r'\\frac{\\mathrm{d} \\psi}{\\mathrm{d} r}=' + sp.latex(d_psi_d_r)))\n",
        "#print(sp.latex(d_psi_d_r))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "It seems hard to find $r(\\theta)$, however to find its derivative we make take advantage of the chain rule \n",
        "$\\frac{\\mathrm{d}r}{\\mathrm{d}\\theta} = \\frac{\\mathrm{d}r}{\\mathrm{d}\\psi} \\frac{\\mathrm{d}\\psi}{\\mathrm{d}\\theta}$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle \\frac{\\mathrm{d} r}{\\mathrm{d} \\theta}=\\frac{R r \\sqrt{\\frac{r^{2} - r_{0}^{2}}{R^{2} - r^{2}}}}{r_{0}}$"
            ],
            "text/plain": [
              "<IPython.core.display.Math object>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "d_r_d_theta = sp.simplify( (1/d_psi_d_r)*(1/d_theta_d_psi) )\n",
        "display(Math(r'\\frac{\\mathrm{d} r}{\\mathrm{d} \\theta}=' + sp.latex(d_r_d_theta)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "That is exactly the optimaly condition (forward), so our guess turns out correct."
      ]
    }
  ],
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