{ "cells": [ { "cell_type": "markdown", "id": "4d16f24f", "metadata": {}, "source": [ "# The two-fixed centres elliptic billiard\n", "\n", "This example is a refinement of the [Keplerian billiard](<./The Keplerian billiard.ipynb>) described earlier in which we introduce *two* gravitational centres of attraction (rather than one) embedded in a non-rectangular billiard. Specifically, the billiard's shape is defined by the [elliptic curve](https://en.wikipedia.org/wiki/Algebraic_curve)\n", "\n", "$$\n", "y^2 = \\left(a - x \\right)\\cdot\\left(x - b\\right)\\cdot\\left(x^2 + c\\right),\n", "$$\n", "\n", "and the centres of gravity of radius $R$ are placed on the $x$ axis at coordinates $p_0$ and $p_1$. Let us pick specific numerical values for the parameters $a$, $b$, $c$, $p_0$, $p_1$ and $R$, and let us take a look at the geometry of the problem:" ] }, { "cell_type": "code", "execution_count": 1, "id": "9e385491", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib.pylab import plt\n", "import numpy as np\n", "plt.rcParams[\"figure.figsize\"] = (9, 9)\n", "\n", "# The curve's parameters.\n", "a, b, c = -1, 1.5, .01\n", "\n", "# The centres' positions on the x axis.\n", "p0 = 3.*a/5.\n", "p1 = 3.*b/5.\n", "\n", "# The centres' radiuses.\n", "R = 0.05\n", "\n", "fig, ax = plt.subplots()\n", "xrng = np.linspace(a, b, 1000)\n", "ax.axis('equal')\n", "\n", "# Plot the elliptic curve.\n", "plt.plot(xrng, np.sqrt((a - xrng)*(xrng - b)*(xrng**2 + c)), 'k-', lw=2)\n", "plt.plot(xrng, -np.sqrt((a - xrng)*(xrng - b)*(xrng**2 + c)), 'k-', lw=2)\n", "\n", "# Plot the centres.\n", "cc0 = plt.Circle((p0 , 0.), R, ec='black', fc='orange')\n", "cc1 = plt.Circle((p1 , 0.), R, ec='black', fc='orange')\n", "ax.add_artist(cc0)\n", "ax.add_artist(cc1);" ] }, { "cell_type": "markdown", "id": "7c024115", "metadata": {}, "source": [ "The elliptic curve generates on the plane a smooth, hourglass-like shape.\n", "\n", "We will begin, as usual, with the definition of the dynamics of the system:" ] }, { "cell_type": "code", "execution_count": 2, "id": "b437aca8", "metadata": {}, "outputs": [], "source": [ "import heyoka as hy\n", "\n", "# Introduce the symbolic state variables.\n", "x, y, vx, vy = hy.make_vars(\"x\", \"y\", \"vx\", \"vy\")\n", "\n", "# Cubes of the inverse of the distances\n", "# from the centres of gravity.\n", "d0_m3 = ((x - p0)**2 + y**2)**(-3/2.)\n", "d1_m3 = ((x - p1)**2 + y**2)**(-3/2.)\n", "\n", "# The ODEs.\n", "eqns = [(x, vx), (y, vy),\n", " (vx, -(x - p0)*d0_m3 -(x - p1)*d1_m3),\n", " (vy, -y*(d0_m3 + d1_m3))]" ] }, { "cell_type": "markdown", "id": "13530613", "metadata": {}, "source": [ "In order to make the test particle bounce on the walls of the billiard and on the surface of the gravitational centres of attraction, we will need to define three event equations to detect when the particle hits the walls and the centres:\n", "\n", "$$\n", "\\begin{cases}\n", "y^2 - \\left(a - x \\right)\\cdot\\left(x - b\\right)\\cdot\\left(x^2 + c\\right) = 0 \\\\\n", "\\left( x - p_0 \\right)^2 + y^2 - R^2 = 0 \\\\\n", "\\left( x - p_1 \\right)^2 + y^2 - R^2 = 0\n", "\\end{cases}.\n", "$$" ] }, { "cell_type": "code", "execution_count": 3, "id": "f062a7ae", "metadata": {}, "outputs": [], "source": [ "# Walls.\n", "eveq_curve = y**2 - (a - x)*(x - b)*(x**2 + c)\n", "\n", "# Gravitational centres.\n", "eveq_0 = (x - p0)**2 + y**2 - R**2\n", "eveq_1 = (x - p1)**2 + y**2 - R**2" ] }, { "cell_type": "markdown", "id": "679e9065", "metadata": {}, "source": [ "The next step is the definition of the callbacks that implement the bouncing behaviour. Like in the Keplerian billiard, we will be dealing with fully elastic collisions: whenever the test particle hits a surface, we flip the component of its velocity vector perpendicular to the surface. The normal to the surface can be computed via the gradient of the event equations.\n", "\n", "Let us see the code:" ] }, { "cell_type": "code", "execution_count": 4, "id": "e4b46902", "metadata": {}, "outputs": [], "source": [ "# Bouncing against the first centre.\n", "def cb_0(ta, mr, d_sgn):\n", " # Fetch the collision point\n", " # from the state vector.\n", " x, y = ta.state[0:2]\n", " \n", " # Compute the normal unit vector\n", " # using the gradient of the event\n", " # equation.\n", " grad = np.array([x-p0, y])\n", " grad_uvec = grad / np.linalg.norm(grad)\n", " \n", " # Compute the component of the velocity\n", " # across the normal vector.\n", " xy_vel = ta.state[2:4]\n", " vproj = np.dot(xy_vel, grad_uvec)\n", " \n", " # Flip it.\n", " Dv = -vproj*grad_uvec\n", " xy_vel += 2*Dv\n", "\n", " return True\n", "\n", "# Bouncing against the second centre.\n", "def cb_1(ta, mr, d_sgn):\n", " x, y = ta.state[0:2]\n", " grad = np.array([x-p1, y])\n", " grad_uvec = grad / np.linalg.norm(grad)\n", " xy_vel = ta.state[2:4]\n", " vproj = np.dot(xy_vel, grad_uvec)\n", " Dv = -vproj*grad_uvec\n", " xy_vel += 2*Dv\n", " return True\n", "\n", "# Bouncing against the walls.\n", "def cb_curve(ta, mr, d_sgn):\n", " x, y = ta.state[0:2]\n", " grad = np.array([2*x*(x - b)*(x - a) + (x - b)*(x**2 + c) + (x - a)*(x**2 + c), 2*y])\n", " grad_uvec = grad / np.linalg.norm(grad)\n", " xy_vel = ta.state[2:4]\n", " vproj = np.dot(xy_vel, grad_uvec)\n", " Dv = -vproj*grad_uvec\n", " xy_vel += 2*Dv\n", " return True" ] }, { "cell_type": "markdown", "id": "211f941e", "metadata": {}, "source": [ "We can now proceed to create the events and the integrator:" ] }, { "cell_type": "code", "execution_count": 5, "id": "121e0688", "metadata": {}, "outputs": [], "source": [ "# Construct the events.\n", "ev_0 = hy.t_event(eveq_0, callback=cb_0, direction = hy.event_direction.negative)\n", "ev_1 = hy.t_event(eveq_1, callback=cb_1, direction = hy.event_direction.negative)\n", "ev_curve = hy.t_event(eveq_curve, callback=cb_curve, direction = hy.event_direction.positive)\n", "\n", "# Construct the integrator.\n", "ta = hy.taylor_adaptive(eqns, [0., 0., -1., .8], t_events = [ev_0, ev_1, ev_curve])" ] }, { "cell_type": "markdown", "id": "f2d18fac", "metadata": {}, "source": [ "The test particle is initially placed in the neck of the billiard and moving towards the first centre of gravity. Note how, as explained in the [Keplerian billiard](<./The Keplerian billiard.ipynb>) example, we assigned specific directions to the collision events. This is done in order to avoid triggering spurious double-bounce events that would lead to the test particle exiting the box or entering one of the centres of force.\n", "\n", "We are now ready to integrate the system for a few time units:" ] }, { "cell_type": "code", "execution_count": 6, "id": "84935191", "metadata": {}, "outputs": [], "source": [ "tgrid = np.linspace(0, 20, 10000)\n", "traj = ta.propagate_grid(tgrid)[4]" ] }, { "cell_type": "markdown", "id": "acb712c2", "metadata": {}, "source": [ "Let's plot the trajectory:" ] }, { "cell_type": "code", "execution_count": 7, "id": "2ef8752e", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.axis('equal')\n", "\n", "# Setup the billiard and the centres.\n", "xrng = np.linspace(a, b, 1000)\n", "plt.plot(xrng, np.sqrt((a - xrng)*(xrng - b)*(xrng**2 + c)), 'k-', lw=2, zorder=2)\n", "plt.plot(xrng, -np.sqrt((a - xrng)*(xrng - b)*(xrng**2 + c)), 'k-', lw=2, zorder=2)\n", "cc0 = plt.Circle((p0 , 0.), R, ec='black', fc='orange', zorder=2)\n", "cc1 = plt.Circle((p1 , 0.), R, ec='black', fc='orange', zorder=2)\n", "ax.add_artist(cc0)\n", "ax.add_artist(cc1)\n", "\n", "# Plot the trajectory, color-coding\n", "# according to the velocity.\n", "vabs = np.sqrt(traj[:, 2]**2+traj[:, 3]**2)\n", "plt.scatter(traj[:, 0], traj[:, 1], c=vabs, s=1);" ] }, { "cell_type": "markdown", "id": "1f500749", "metadata": {}, "source": [ "We can see how, indeed, the test particle bounces both against the walls of the billiard and the centres of gravitational attraction.\n", "\n", "Let us now run a second integration, this time greatly increasing the initial velocity of the test particle:" ] }, { "cell_type": "code", "execution_count": 8, "id": "3a47431a", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Reset the time.\n", "ta.time = 0\n", "# Reset the state, increasing the y velocity\n", "# with respect to the previous initial conditions.\n", "ta.state[:] = [0, 0, -1, 8.]\n", "\n", "# Integrate and plot.\n", "tgrid = np.linspace(0, 20, 50000)\n", "traj = ta.propagate_grid(tgrid)[4]\n", "\n", "fig, ax = plt.subplots()\n", "ax.axis('equal')\n", "\n", "xrng = np.linspace(a, b, 1000)\n", "plt.plot(xrng, np.sqrt((a - xrng)*(xrng - b)*(xrng**2 + c)), 'k-', lw=2, zorder=2)\n", "plt.plot(xrng, -np.sqrt((a - xrng)*(xrng - b)*(xrng**2 + c)), 'k-', lw=2, zorder=2)\n", "cc0 = plt.Circle((p0 , 0.), R, ec='black', fc='orange', zorder=2)\n", "cc1 = plt.Circle((p1 , 0.), R, ec='black', fc='orange', zorder=2)\n", "ax.add_artist(cc0)\n", "ax.add_artist(cc1)\n", "\n", "vabs = np.sqrt(traj[:, 2]**2+traj[:, 3]**2)\n", "plt.scatter(traj[:, 0], traj[:, 1], c=vabs, s=0.25);" ] }, { "cell_type": "markdown", "id": "957f01cf", "metadata": {}, "source": [ "Because we increased the initial velocity, the motion of the test particle is now almost rectilinear, and it fills up in a dense fashion the simulation domain." ] } ], "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": "3.8.13" } }, "nbformat": 4, "nbformat_minor": 5 }