{ "cells": [ { "cell_type": "markdown", "id": "61d7a4e5", "metadata": {}, "source": [ "Continuation of Periodic Orbits in the CR3BP\n", "=====================================\n", "\n", "In this example, we will show how it is possible to use heyoka.py's [expression system](<./The expression system.ipynb>), to compute the state transition matrix of the [circular restricted three-body problem](<./The restricted three-body problem.ipynb>) via [variational equations](<./The variational equations.ipynb>) and outline its use to find periodic orbits via a simple continuation scheme.\n", "\n", "**NOTE**: There is quite some literature on finding periodic orbits in the CR3BP, a plethora of very clever techniques have been developed in the past. This notebook implements only a basic approach as it only aims to show the use of heyoka in this field.\n", "\n", "We make some standard imports:" ] }, { "cell_type": "code", "execution_count": 1, "id": "8b2a7edb", "metadata": {}, "outputs": [], "source": [ "import heyoka as hy\n", "import numpy as np\n", "import time \n", "\n", "from scipy.optimize import root_scalar\n", "\n", "from matplotlib.pylab import plt" ] }, { "cell_type": "markdown", "id": "b2e5665b", "metadata": {}, "source": [ "... and define some functions that will help later on to visualize our trajectories and make nice plots. (ignore them and come back to this later in case you are curious)" ] }, { "cell_type": "code", "execution_count": 2, "id": "a6309475", "metadata": {}, "outputs": [], "source": [ "def potential_function(position,mu):\n", " \"\"\"Computes the system potential\n", " Args:\n", " position (array-like): The position in Cartesian coordinates\n", " mu (float): The value of the mu parameter.\n", "\n", " Returns:\n", " The potential\n", " \"\"\"\n", " x,y,z=position\n", " r_1=np.sqrt((x-mu)**2+y**2+z**2)\n", " r_2=np.sqrt((x-mu+1)**2+y**2+z**2)\n", " Omega=1./2.*(x**2+y**2)+(1-mu)/r_1+mu/r_2\n", " return Omega\n", "\n", "def jacobi_constant(state,mu):\n", " \"\"\"Computes the system Jacobi constant\n", " Args:\n", " state (array-like): The system state (x,y,z,px,py,pz)\n", " mu (float): The value of the mu parameter.\n", "\n", " Returns:\n", " The Jacobi constant for the state\n", " \"\"\"\n", " x,y,z,px,py,pz=state\n", " vx = px + y\n", " vy = py - x\n", " vz = pz\n", " r_1=np.sqrt((x-mu)**2+y**2+z**2)\n", " r_2=np.sqrt((x-mu+1)**2+y**2+z**2)\n", " Omega=1/2*(x**2+y**2)+(1-mu)/r_1+mu/r_2\n", " T=1/2*(vx**2+vy**2+vz**2)\n", " C=Omega-T\n", " return C" ] }, { "cell_type": "markdown", "id": "5c23101e", "metadata": {}, "source": [ "## The Circular Restricted 3 Body Problem dynamics" ] }, { "cell_type": "markdown", "id": "excited-uganda", "metadata": {}, "source": [ "Let us start defining the equations of motion for the Circular Restricted 3 Body Problem (CR3BP from now on). \n", "\n", "The problem is usually formulated in a rotating reference frame in which the two massive bodies are at rest. In the rotating reference frame, the equations of motion for the massless particle's cartesian coordinates $\\left(x, y, z\\right)$ and conjugated momenta $\\left(p_x, p_y, p_z\\right)$ read:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\dot{x} & = p_x+y,\\\\\n", "\\dot{y} & = p_y-x, \\\\\n", "\\dot{z} & = p_z, \\\\\n", "\\dot{p}_x & = p_y - \\frac{1-\\mu}{r_{PS}^3}\\left( x - \\mu \\right)-\\frac{\\mu}{r_{PJ}^3}\\left( x - \\mu + 1\\right), \\\\\n", "\\dot{p}_y & = -p_x-\\left( \\frac{1-\\mu}{r_{PS}^3} + \\frac{\\mu}{r_{PJ}^3}\\right)y, \\\\\n", "\\dot{p}_z & = -\\left( \\frac{1-\\mu}{r_{PS}^3} + \\frac{\\mu}{r_{PJ}^3}\\right)z,\n", "\\end{aligned}\n", "$$\n", "\n", "where $\\mu$ is a mass parameter, $r_{PS}^2=\\left( x-\\mu \\right)^2+y^2+z^2$ and $r_{PJ}^2=\\left( x -\\mu + 1 \\right)^2+y^2+z^2$. \n", "\n", "NOTE: In these equations it is assumed that $M_1 + M_2 = 1$ and the Cavendish constant $G=1$. The biggest mass is then indicated with $1-\\mu$, while the smallest with $\\mu$. The biggest mass is placed in $x = \\mu$ and the smallest in $x = \\mu-1$ so that the distance between primaries is also 1. All remaining units are induced by these choices.\n", "\n", "We also refer to the whole state with the symbol $\\mathbf x = [x,y,z,p_x, p_y, p_z]$ and the right hand side of the dynamic equations with the symbol $\\mathbf f$ so that $\\dot{\\mathbf x} = \\mathbf f(\\mathbf x)$. In general we use bold for vectors matrices and normal fonts for their components, hence $\\mathbf M$ will, as an example, have components $M_{ij}$.\n", "\n", "With respect to the heyoka.py notebook on [circular restricted three-body problem](<./The restricted three-body problem.ipynb>), we will be here making use of numpy arrays of heyoka expressions as to simplify the notation later on when we need to compute the variational equations." ] }, { "cell_type": "code", "execution_count": 3, "id": "confused-excellence", "metadata": {}, "outputs": [], "source": [ "# Create the symbolic variables.\n", "symbols_state = [\"x\", \"y\", \"z\", \"px\", \"py\", \"pz\"]\n", "x = np.array(hy.make_vars(*symbols_state))\n", "# This will contain the r.h.s. of the equations\n", "f = []\n", "\n", "rps_32 = ((x[0] - hy.par[0])**2 + x[1]**2 + x[2]**2)**(-3/2.)\n", "rpj_32 = ((x[0] - hy.par[0] + 1.)**2 + x[1]**2 + x[2]**2)**(-3/2.)\n", "\n", "# The equations of motion.\n", "f.append(x[3] + x[1])\n", "f.append(x[4] - x[0])\n", "f.append(x[5])\n", "f.append(x[4] - (1. - hy.par[0]) * rps_32 * (x[0] - hy.par[0]) - hy.par[0] * rpj_32 * (x[0] - hy.par[0] + 1.))\n", "f.append(-x[3] -((1. - hy.par[0]) * rps_32 + hy.par[0] * rpj_32) * x[1])\n", "f.append(-((1. - hy.par[0]) * rps_32 + hy.par[0] * rpj_32) * x[2])\n", "f = np.array(f)" ] }, { "cell_type": "markdown", "id": "d04a7823-5405-447c-b133-68b19bee2494", "metadata": {}, "source": [ "Let us also define a function to compute the position of the Lagrangian points:" ] }, { "cell_type": "code", "execution_count": 4, "id": "a8416e87-6365-49d9-9f21-fae485115ae4", "metadata": {}, "outputs": [], "source": [ "# Introduce a compiled function for the evaluation\n", "# of the dynamics equation for px.\n", "px_dyn_cf = hy.make_cfunc([f[3]], vars=x)\n", "\n", "def compute_L_points(mu):\n", " \"\"\"Computes The exact position of the Lagrangian points. To do so it finds the zeros of the\n", " the dynamics equation for px.\n", " \n", " Args:\n", " mu (float): The value of the mu parameter.\n", "\n", " Returns:\n", " xL1, xL2, xL3, xL45, yL45: The coordinates of the various Lagrangian Points\n", " \"\"\"\n", " # Position of the lagrangian points approximated\n", " xL1 = (mu-1) + (mu/3/(1-mu))**(1/3)\n", " xL2 = (mu-1) - (mu/3/(1-mu))**(1/3)\n", " xL3 = -(mu-1) - 7/12 * mu / (1-mu)\n", " yL45 = np.sin(60/180*np.pi)\n", " xL45 = -0.5 + mu\n", "\n", " # Solve for the static equilibrium from the approximated solution\n", " def equilibrium(expr, x,y):\n", " return px_dyn_cf([x, y, 0., -y, x, 0.], pars=[mu])[0]\n", " xL1 = root_scalar(lambda x: equilibrium(f, x,0.), x0=xL1,x1=xL1-1e-2).root\n", " xL2 = root_scalar(lambda x: equilibrium(f, x,0.), x0=xL2,x1=xL2-1e-2).root\n", " xL3 = root_scalar(lambda x: equilibrium(f, x,0.), x0=xL3,x1=xL3-1e-2).root;\n", " return xL1, xL2, xL3, xL45, yL45" ] }, { "cell_type": "markdown", "id": "978a0065", "metadata": {}, "source": [ "## The variational equations" ] }, { "cell_type": "markdown", "id": "23fb01fa", "metadata": {}, "source": [ "We now compute the variational equations expressing the state transition matrix defined as $\\delta \\mathbf x(t) = \\mathbf \\Phi(t)\\delta \\mathbf x(0)$. We define its $ij$ component as:\n", "\n", "$$\n", "\\Phi_{ij}(t) = \\frac{d x_i(t)}{dx_j(0)}\n", "$$\n", "\n", "hence the variational equations:\n", "\n", "$$\n", "\\frac{d }{dt} \\Phi_{ij}(t) = \\frac{d}{dt}\\left(\\frac{d x_i(t)}{dx_j(0)}\\right) = \\frac{d}{dx_j(0)}\\left(\\frac{d x_i(t)}{dt}\\right) = \\frac{d f_i(x(t))}{dx_j(0)}\n", "$$\n", "\n", "expanding the total derivative in the last term we get:\n", "\n", "$$\n", "\\frac{d}{dt}\\Phi_{ij}(t) = \\sum_k \\frac{\\partial f_i}{\\partial x_k}\\frac{dx_k(t)}{dx_j(0)}=\\sum_k \\frac{\\partial f_i}{\\partial x_k} \\Phi_{kj}(t)\n", "$$\n", "\n", "which can be written in compact matrix form as:\n", "\n", "$$\n", "\\frac{d}{dt}\\mathbf \\Phi(t) = \\left[\\frac{\\partial f_i}{\\partial x_k}\\right] \\mathbf \\Phi(t)\n", "$$\n", "\n", "Note that the initial conditions are, trivially: $\\mathbf \\Phi(0) = \\mathbf I$\n", "\n", "Let us then introduce these variational equations using heyoka.\n", "\n", "First, we define the various symbols for the components of the state transition matrix" ] }, { "cell_type": "code", "execution_count": 5, "id": "76d34b7d", "metadata": {}, "outputs": [], "source": [ "symbols_phi = []\n", "for i in range(6):\n", " for j in range(6):\n", " # Here we define the symbol for the variations\n", " symbols_phi.append(\"phi_\"+str(i)+str(j)) \n", "phi = np.array(hy.make_vars(*symbols_phi)).reshape((6,6))" ] }, { "cell_type": "markdown", "id": "c03385dc", "metadata": {}, "source": [ "Then we find the various $\\left[\\frac{\\partial f_i}{\\partial x_k}\\right]$:" ] }, { "cell_type": "code", "execution_count": 6, "id": "b1bd6632", "metadata": {}, "outputs": [], "source": [ "dfdx = []\n", "for i in range(6):\n", " for j in range(6):\n", " dfdx.append(hy.diff(f[i],x[j]))\n", "dfdx = np.array(dfdx).reshape((6,6))" ] }, { "cell_type": "markdown", "id": "91426c62", "metadata": {}, "source": [ "... and finally the r.h.s. of the variational equations is:" ] }, { "cell_type": "code", "execution_count": 7, "id": "4f3f2e07", "metadata": {}, "outputs": [], "source": [ "# The (variational) equations of motion\n", "dphidt = dfdx@phi" ] }, { "cell_type": "markdown", "id": "6d27c0f5", "metadata": {}, "source": [ "how very very beautiful!\n", "\n", "**NOTE**: The variational equations are here written for a chaotic system, thus for long interation times the variations can explode and have a negative influence for the step size control. Nothing we can do about it, it's chaos! " ] }, { "cell_type": "markdown", "id": "ad47ad1a", "metadata": {}, "source": [ "## Putting all together and integrating some initial conditions\n", "Let us put all the equations 6 + 6x6 = 42 into one big Taylor integrator and perform one numerical integration.\n", "\n", "First, we create the dynamics ..." ] }, { "cell_type": "code", "execution_count": 8, "id": "65949284", "metadata": {}, "outputs": [], "source": [ "dyn = []\n", "for state, rhs in zip(x,f):\n", " dyn.append((state, rhs))\n", "for state, rhs in zip(phi.reshape((36,)),dphidt.reshape((36,))):\n", " dyn.append((state, rhs))\n", "# These are the initial conditions on the variational equations (the identity matrix)\n", "ic_var = np.eye(6).reshape((36,)).tolist()" ] }, { "cell_type": "markdown", "id": "47618ce7", "metadata": {}, "source": [ "... then we instantiate the Taylor integrator (high accuracy and no compact mode)" ] }, { "cell_type": "code", "execution_count": 9, "id": "37433a60", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--- 4.484630584716797 seconds --- to build the Taylor integrator\n" ] } ], "source": [ "start_time = time.time()\n", "ta = hy.taylor_adaptive(\n", " # The ODEs.\n", " dyn,\n", " # The initial conditions.\n", " [-0.45, 0.80, 0.00, -0.80, -0.45, 0.58] + ic_var,\n", " # Operate below machine precision\n", " # and in high-accuracy mode.\n", " tol = 1e-18, high_accuracy = True\n", ")\n", "print(\"--- %s seconds --- to build the Taylor integrator\" % (time.time() - start_time))" ] }, { "cell_type": "markdown", "id": "c4abd67d", "metadata": {}, "source": [ "... and we perform and time a numerical propagation for these conditions" ] }, { "cell_type": "code", "execution_count": 10, "id": "3acbb840", "metadata": {}, "outputs": [], "source": [ "ic = [-0.80, 0.0, 0, 0.0, -0.6276410653920693, 0.]\n", "t_final=200\n", "mu=0.01\n", "ta.pars[0] = mu\n", "# Reset the state\n", "ta.time = 0\n", "ta.state[:] = ic + ic_var\n", "# Time grid\n", "t_grid = np.linspace(0, t_final, 2000)" ] }, { "cell_type": "code", "execution_count": 11, "id": "c02c7bac", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--- 0.05100584030151367 seconds --- to propagate\n" ] } ], "source": [ "# Go ...\n", "start_time = time.time()\n", "out = ta.propagate_grid(t_grid)\n", "print(\"--- %s seconds --- to propagate\" % (time.time() - start_time))" ] }, { "cell_type": "markdown", "id": "67d3a6e3", "metadata": {}, "source": [ "To check and validate, let's plot the trajectory and some cosmetics to visualize the solution" ] }, { "cell_type": "code", "execution_count": 12, "id": "51ae7e56", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(14,14))\n", "\n", "# Lets find the postiion of the lagrangian points\n", "xL1, xL2, xL3, xL45, yL45 = compute_L_points(mu)\n", "# We also compute the Jacobi constant\n", "C_jacobi = jacobi_constant(ic, mu)\n", "\n", "# Plot the trajectory (xy)\n", "plt.subplot(1,2,1)\n", "plt.plot(out[4][:, 0], out[4][:, 1])\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "# Plot the zero velocity curve\n", "xx = np.linspace(-1.5,1.5,2000)\n", "yy = np.linspace(-1.5,1.5,2000)\n", "x_grid,y_grid = np.meshgrid(xx,yy)\n", "im = plt.imshow( ((potential_function((x_grid,y_grid,np.zeros(np.shape(x_grid))),mu=mu)<=C_jacobi)).astype(int) , \n", " extent=(x_grid.min(),x_grid.max(),y_grid.min(),y_grid.max()),origin=\"lower\", cmap=\"Greens\")\n", "# Plot the lagrangian points and primaries\n", "plt.scatter(mu, 0, c='k', s=300)\n", "plt.scatter(mu-1, 0, c='k', s=150)\n", "plt.scatter(xL1, 0, c='r')\n", "plt.scatter(xL2, 0, c='r')\n", "plt.scatter(xL3, 0, c='r')\n", "plt.scatter(-0.5+mu, yL45, c='r')\n", "plt.scatter(-0.5+mu, -yL45, c='r')\n", "\n", "# Plot the trajectory (xz)\n", "plt.subplot(1,2,2)\n", "plt.plot(out[4][:, 0], out[4][:, 2])\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"z\");\n", "# Plot the zero velocity curve\n", "xx = np.linspace(-1.5,1.5,2000)\n", "zz = np.linspace(-1.5,1.5,2000)\n", "x_grid,z_grid = np.meshgrid(xx,zz)\n", "im = plt.imshow( ((potential_function((x_grid,np.zeros(np.shape(x_grid)), z_grid),mu=mu)<=C_jacobi)).astype(int) , \n", " extent=(x_grid.min(),x_grid.max(),z_grid.min(),z_grid.max()),origin=\"lower\", cmap=\"Greens\")\n", "# Plot the lagrangian points and primaries\n", "plt.scatter(mu, 0, c='k', s=300)\n", "plt.scatter(mu-1, 0, c='k', s=150)\n", "plt.scatter(xL1, 0, c='r')\n", "plt.scatter(xL2, 0, c='r')\n", "plt.scatter(xL3, 0, c='r')\n", "plt.scatter(-0.5+mu, 0, c='r')\n", "plt.scatter(-0.5+mu, 0, c='r')" ] }, { "cell_type": "markdown", "id": "0098b9ee", "metadata": {}, "source": [ "All fine ..... at least visually! So far we have not made use of the variational equations at all, but this is about to change!" ] }, { "cell_type": "markdown", "id": "001e24d2", "metadata": {}, "source": [ "## Finding Periodic Orbits\n", "To find a periodic orbit in a dynamical system, a first step to then possibly find a whole family of them, we will proceed as follows:\n", "\n", "* Get some *decent* initial conditions, for example one can use the [Poincaré–Lindstedt method](https://en.wikipedia.org/wiki/Poincar%C3%A9%E2%80%93Lindstedt_method) or, in the specific case of the CR3BP, the work from Richardson).\n", "\n", "Richardson, D. L. (1980). Analytic construction of periodic orbits about the collinear points. Celestial mechanics, 22(3), 241-253.\n", "\n", "* Once some initial guess $\\mathbf x_0$ is available for the initial state and $T$ for the period, we write the Taylor first order expansion of the system solution as:\n", "\n", "$$\n", "\\mathbf x = \\overline {\\mathbf x} + \\mathbf \\Phi \\delta \\mathbf x_0 + \\mathbf \\Phi_T \\delta T\n", "$$\n", "\n", "where $\\mathbf \\Phi = \\left[\\frac{\\partial x_i}{\\partial x_{0_k}}\\right] $ is computed via the variational equations, $\\mathbf \\Phi_T = \\left[\\frac{\\partial x_i}{\\partial t}\\right] = \\dot{\\mathbf x} = \\mathbf f$ and $\\overline {\\mathbf x}$ is the final state reached starting from $\\mathbf x_0$ and integrating for $T$. Such an expansion tells us how much the state evaluated in $T$ would change if we move the initial conditions by $\\delta\\mathbf x_0$ and the integration time by $\\delta T$. \n", "\n", "* Now (**pay attention, as here is the whole trick**), we write the periodicity condition enforcing that after $T+\\delta T$ the state goes back to $\\mathbf x_0 + \\delta \\mathbf x_0$:\n", "\n", "$$\n", "\\overline {\\mathbf x} + \\mathbf \\Phi \\delta \\mathbf x_0 + \\mathbf f \\delta T = \\mathbf x_0 + \\delta \\mathbf x_0\n", "$$\n", "\n", "which is rearranged in the form:\n", "\n", "$$\n", "\\left(\\mathbf \\Phi -\\mathbf I\\right) \\delta \\mathbf x_0 + \\mathbf f \\delta T = \\mathbf x_0 -\\overline {\\mathbf x}\n", "$$\n", "\n", "This fundamental relation is at the basis of any numerical algorithm that wants to find a closed periodic orbit. It is a system of 6 equation in the 7 unknowns $\\delta \\mathbf x, \\delta T$: as a consequence, it is overdetermined. We then must choose among the infinitely many solutions one. We do so adding the Poincare' phasing condition, which requests that:\n", "\n", "$$\n", "\\mathbf f \\cdot \\delta \\mathbf x_0 = \\mathbf 0\n", "$$\n", "in other word we will restrict our $\\delta x$ to the hyperplane plane perpendicular to the dynamics.\n", "\n", "We now have seven equations and seven unknowns. Seems like we are done (as far as $\\mathbf \\Phi -\\mathbf I$ has full rank). \n", "\n", "Let us implement a naive iterative scheme and close some orbit. \n", "\n", "First we play to find a decent initial condition ...." ] }, { "cell_type": "code", "execution_count": 13, "id": "f98598d0", "metadata": {}, "outputs": [], "source": [ "# New mu parameter (no reason to change, just came out playing)\n", "mu = 0.01215057\n", "# Initial guess for the integration time (will eventually converge to a period)\n", "t_final = 3.\n", "# We recomupte the lagrangian points\n", "xL1, xL2, xL3, xL45, yL45 = compute_L_points(mu)\n", "\n", "# Initial conditions in the cartesian representation x,y,z,vx,vy,vz\n", "ic_cart = [ -8.36809444e-01, 0.,0.,0., -8.85435468e-04, 0.]\n", "ic = [ic_cart[0], ic_cart[1], ic_cart[2], ic_cart[3]- ic_cart[1], ic_cart[4] + ic_cart[0], ic_cart[5]]\n", "# We recompute the Jacobi constant\n", "C_jacobi = jacobi_constant(ic, mu)\n", "\n", "# Reset the state\n", "ta.time = 0.\n", "ta.state[:] = ic + ic_var\n", "ta.pars[0] = mu\n", "# Time grid\n", "t_grid = np.linspace(0, t_final, 2000)\n", "# Go ...\n", "out0 = ta.propagate_grid(t_grid)" ] }, { "cell_type": "markdown", "id": "c5fc9876", "metadata": {}, "source": [ "We plot the initial orbit (zooming in the Lagrangian point)" ] }, { "cell_type": "code", "execution_count": 14, "id": "b6c18355", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(9,9))\n", "\n", "plt.subplot(1,1,1)\n", "zoom=0.005\n", "plt.plot(out0[4][:, 0], out0[4][:, 1],'r')\n", "\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "\n", "# Plot the zero velocity curve\n", "xx = np.linspace(xL1-zoom,xL1+zoom,2000)\n", "yy = np.linspace(-zoom,zoom,2000)\n", "x_grid,y_grid = np.meshgrid(xx,yy)\n", "im = plt.imshow( ((potential_function((x_grid,y_grid,np.zeros(np.shape(x_grid))),mu=mu)<=C_jacobi)).astype(int) , \n", " extent=(x_grid.min(),x_grid.max(),y_grid.min(),y_grid.max()),origin=\"lower\", cmap=\"Greens\")\n", "\n", "# Plot the lagrangian points and primaries\n", "plt.scatter(mu, 0, c='k', s=300)\n", "plt.scatter(mu-1, 0, c='k', s=100)\n", "plt.scatter(xL1, 0, c='r')\n", "plt.scatter(xL2, 0, c='r')\n", "plt.scatter(xL3, 0, c='r')\n", "plt.scatter(-0.5+mu, yL45, c='r')\n", "plt.scatter(-0.5+mu, -yL45, c='r')\n", "\n", "\n", "plt.xlim(xL1-zoom, xL1+zoom)\n", "plt.ylim(-zoom, +zoom);" ] }, { "cell_type": "markdown", "id": "3ce34c88", "metadata": {}, "source": [ "The orbit is good but does not close! Let us build an iteration that corrects $x_0,y_0, z_0, p_{x_0}, p_{y_0}, p_{z_0}, T$ as to close the orbit." ] }, { "cell_type": "code", "execution_count": 15, "id": "b8b461e5", "metadata": {}, "outputs": [], "source": [ "# Introduce a compiled function for the evaluation\n", "# of the dynamics equations.\n", "dyn_cf = hy.make_cfunc(f, vars=x)\n", "\n", "def corrector(ta, x0):\n", " \"\"\"\n", " Performs and logs a step of a corrector algorithm that takes a numerical integration from x0 -> T -> xf. The result\n", " is a new tentative x0 that should result in a closed orbit.\n", " \"\"\"\n", " x0 = np.array(x0)\n", " mu = ta.pars[0]\n", " t_final = ta.time\n", " \n", " state_T = ta.state[:6]\n", " \n", " Phi = ta.state[6:].reshape((6,6))\n", " dynT = dyn_cf(state_T, pars=[mu]).reshape((-1,1))\n", "\n", " # We add as last state delta T\n", " A = np.concatenate((Phi-np.eye(6),dynT), axis=1)\n", " # We add the Poincare phasing condition as a last equation\n", " phasing_cond = np.insert(dynT,-1,0).reshape((1,-1))\n", "\n", " A = np.concatenate((A, phasing_cond))\n", " # We construct the r.h.s.\n", " b = (x0 - state_T).reshape(-1,1)\n", " print(\"error was:\", np.linalg.norm(b))\n", " # need to add the zero corresponding to the phasing condition\n", " b = np.insert(b,-1,0)\n", " \n", " delta = np.linalg.inv(A)@b\n", " print(\"condition number is:\", np.linalg.cond(A))\n", " \n", " x0_new = x0+delta[:6]\n", " t_final = t_final+delta[-1]\n", "\n", " # Reset the state\n", " ta.time = 0.\n", " ta.state[:] = x0_new.reshape((-1,)).tolist() + ic_var\n", " # Go ...\n", " ta.propagate_until(t_final)\n", " # New error is:\n", " b = (x0_new - ta.state[:6]).reshape(-1,1)\n", " print(\"new error is:\", np.linalg.norm(b))\n", " return ta, x0_new.tolist()" ] }, { "cell_type": "markdown", "id": "302c9d26", "metadata": {}, "source": [ "Lets do some corrector iterations (not too many since as we get near to a periodic orbit, the condition number will explode)" ] }, { "cell_type": "code", "execution_count": 16, "id": "0b026400", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "error was: 0.0012972874386999722\n", "condition number is: 16558416262.086914\n", "new error is: 0.0011268499651408712\n", "error was: 0.0011268499651408712\n", "condition number is: 112029239.50776398\n", "new error is: 0.005318388913864064\n", "error was: 0.005318388913864064\n", "condition number is: 97382195.71293469\n", "new error is: 0.0008512521429497622\n", "error was: 0.0008512521429497622\n", "condition number is: 208596161.3646372\n", "new error is: 6.615966149010238e-06\n", "error was: 6.615966149010238e-06\n", "condition number is: 33988164.714402355\n", "new error is: 6.542953225678637e-08\n", "error was: 6.542953225678637e-08\n", "condition number is: 5547007599.431791\n", "new error is: 1.771535461099794e-12\n" ] } ], "source": [ "ic_periodic = ic\n", "for i in range(6):\n", " ta, ic_periodic = corrector(ta, ic_periodic)" ] }, { "cell_type": "markdown", "id": "087ea83a", "metadata": {}, "source": [ " .... et voila'!! As expected the iterations converge to a periodic orbit, while the matrix condition number increases to infinite as $\\mathbf \\Phi$ becomes a monodromy matrix.\n", " \n", "Of course, we now visualize the orbit as to make sure its closed!" ] }, { "cell_type": "code", "execution_count": 17, "id": "9045f179", "metadata": {}, "outputs": [], "source": [ "t_final = ta.time\n", "\n", "# We compute the IC Jacobi constant\n", "C_jacobi = jacobi_constant(ic_periodic, mu)\n", "\n", "# Reset the state\n", "ta.time = 0.\n", "ta.state[:] = ic_periodic + ic_var\n", "ta.pars[0] = mu\n", "# Time grid\n", "t_grid = np.linspace(0, t_final, 2000)\n", "# Go ...\n", "out = ta.propagate_grid(t_grid)" ] }, { "cell_type": "code", "execution_count": 18, "id": "db95db14", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "mu: 0.01215057\n", "Initial condition: [-8.3660628428208705e-01, 6.8716716228516570e-05, 0.0000000000000000e+00, -2.3615601659846791e-05, -8.3919863036055131e-01, 0.0000000000000000e+00]\n", "Period: 2.6915996001661409e+00\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# We plot the initial condition (zoom in the Lagrangian point)\n", "plt.figure(figsize=(9,9))\n", "\n", "plt.subplot(1,1,1)\n", "zoom=0.005\n", "plt.plot(out0[4][:, 0], out0[4][:, 1],'r')\n", "plt.plot(out[4][:, 0], out[4][:, 1],'k')\n", "\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "\n", "# Plot the zero velocity curve\n", "xx = np.linspace(xL1-zoom,xL1+zoom,2000)\n", "yy = np.linspace(-zoom,zoom,2000)\n", "x_grid,y_grid = np.meshgrid(xx,yy)\n", "im = plt.imshow( ((potential_function((x_grid,y_grid,np.zeros(np.shape(x_grid))),mu=mu)<=C_jacobi)).astype(int) , \n", " extent=(x_grid.min(),x_grid.max(),y_grid.min(),y_grid.max()),origin=\"lower\", cmap=\"Greens\")\n", "\n", "# Plot the lagrangian points and primaries\n", "plt.scatter(mu, 0, c='k', s=300)\n", "plt.scatter(mu-1, 0, c='k', s=100)\n", "plt.scatter(xL1, 0, c='r')\n", "plt.scatter(xL2, 0, c='r')\n", "plt.scatter(xL3, 0, c='r')\n", "plt.scatter(-0.5+mu, yL45, c='r')\n", "plt.scatter(-0.5+mu, -yL45, c='r')\n", "\n", "\n", "plt.xlim(xL1-zoom, xL1+zoom)\n", "plt.ylim(-zoom, +zoom)\n", "\n", "print(\"mu: \", ta.pars[0])\n", "print(f\"Initial condition: [{out[4][0,0]:.16e}, {out[4][0,1]:.16e}, {out[4][0,2]:.16e}, {out[4][0,3]:.16e}, {out[4][0,4]:.16e}, {out[4][0,5]:.16e}]\")\n", "print(f\"Period: {t_final:.16e}\")" ] }, { "cell_type": "markdown", "id": "3a932c57", "metadata": {}, "source": [ "## Continuing into a family of periodic orbits.\n", "\n", "Since we now have initial conditions $\\mathbf x_0$ that result in a periodic orbit, necessarily $\\mathbf x_0 =\\overline {\\mathbf x}$, hence the periodicity condition becomes:\n", "\n", "$$\n", "\\left(\\mathbf \\Phi -\\mathbf I\\right) \\delta \\mathbf x_0 + \\mathbf f \\delta T = \\mathbf 0\n", "$$\n", "\n", "which is a system of 6 equations in seven unknowns. Futhermore, the monodromy matrix $\\mathbf \\Phi$ has now the eigenvalue 1, and thus $\\left(\\mathbf \\Phi -\\mathbf I\\right)$ is not invertible! \n", "\n", "This corresponds, physically, to the fact that there are infinite possibilities to choose $\\delta \\mathbf x_0$ so that $\\mathbf x_0 + \\delta \\mathbf x_0$ results in a new periodic orbit having period $T + \\delta T$.\n", "\n", "We still make use of the Poincare' phasing condition so that the overall system we actually consider is:\n", "\n", "$$\n", "\\left\\{\n", "\\begin{array}{c}\n", "\\left(\\mathbf \\Phi -\\mathbf I\\right) \\delta \\mathbf x_0 + \\mathbf f \\delta T = \\mathbf 0\\\\\n", "\\mathbf f \\cdot \\delta \\mathbf x_0 = 0\n", "\\end{array}\n", "\\right.\n", "$$\n", "\n", "which we write as:\n", "\n", "$$\n", "\\mathbf A_f \\delta {\\mathbf x_f} = \\mathbf 0\n", "$$\n", "\n", "where we considered the full state $\\delta {\\mathbf x_f}$ including both $\\delta \\mathbf x_0$ and $\\delta T$. The rank of the square 7x7 full matrix ${\\mathbf A_f}$ is only 6, thus the linear system admits non trivial solutions. To find them we fix the value of one component of $\\delta {\\mathbf x_f}$ and thus obtain a new system with a reduced state and matrix:\n", "\n", "$$\n", "\\mathbf A_r\\delta {\\mathbf x_r} = \\mathbf b\n", "$$\n", "\n", "This is an overdetermined system of seven equations in six variables, but having only one only solution which we find as:\n", "\n", "$$\n", "\\delta \\mathbf x_r = (\\mathbf A^T \\mathbf A)^{-1}\\mathbf A^T\\mathbf b\n", "$$\n", "\n", "We have thus found a new initial guess to start with to find the next closed orbit in the family." ] }, { "cell_type": "markdown", "id": "b5572ba6", "metadata": {}, "source": [ "To start with, as validation and test of what we got so far, we get the monodromy matrix (from the last numerical integrated periodic orbit) ... " ] }, { "cell_type": "code", "execution_count": 19, "id": "93aa5c06", "metadata": {}, "outputs": [], "source": [ "Phi = ta.state[6:].reshape((6,6))" ] }, { "cell_type": "markdown", "id": "deb5144a", "metadata": {}, "source": [ "And compute its eigenvalues" ] }, { "cell_type": "code", "execution_count": 20, "id": "72fad6d4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[2.67528714e+03+0.j 3.73791653e-04+0.j\n", " 9.99999893e-01+0.j 1.00000011e+00+0.j\n", " 9.84479860e-01+0.17549759j 9.84479860e-01-0.17549759j]\n" ] } ], "source": [ "eigv = np.linalg.eigvals(Phi)\n", "print(eigv)" ] }, { "cell_type": "markdown", "id": "b8a11ad2", "metadata": {}, "source": [ "As expecetd we have two eigenvalues $\\lambda_{3,4}$ equal to one, two real ones so that $\\lambda_{1}\\cdot \\lambda_2=1$ (stable and unstable manifold) and two complex conjugated ones $\\lambda_{5}\\cdot \\lambda_6=1$.\n", "\n", "We write a simple function that takes as argument the result of some numerical integration over periodic conditions and creates new tentative initial guess continuing on the state parameter indexed by *idx*, (defaults to $x$).\n", "\n", "Note that in the following function we assemble the full matrix $\\mathbf A_f$ completed with the Poincare phase condition and having we consider as state ${\\mathbf x_f} = [\\delta x,\\delta y,\\delta z,\\delta p_x,\\delta p_y,\\delta p_z,\\delta T]$. We then select a column, fix the corresponding value for the state variable, bring it to the right side and solve the resulting system which is overdetermined, but admits a unique solution since $\\mathbf \\Phi - \\mathbf I$ is singular." ] }, { "cell_type": "code", "execution_count": 21, "id": "95cd0c30", "metadata": {}, "outputs": [], "source": [ "def predictor(ta, idx=0, variation=1e-4):\n", " Phi = ta.state[6:].reshape((6,6))\n", " state_T = ta.state[:6]\n", " state_T_dict = {\"x\":state_T[0], \"y\":state_T[1], \"z\":state_T[2], \"px\":state_T[3], \"py\":state_T[4], \"pz\":state_T[5]}\n", " # Compute the dynamics from its expressions\n", " dynT = dyn_cf(state_T, pars=[mu]).reshape((-1,1))\n", " # Computing the full A\n", " A = np.concatenate((Phi-np.eye(6), dynT.T))\n", " fullA = np.concatenate((A,np.insert(dynT,-1,0).reshape((-1,1))), axis=1)\n", " # Computing the A resulting from fixing the continuation parameter to a selected state.\n", " A = fullA[:,list(set(range(7))-set([idx]))]\n", " b = - fullA[:,[idx]] * variation\n", " # We solve.\n", " dx = np.linalg.inv((A.T@A)) @ (A.T@b)\n", " # Assembling back the full state (x,y,z,px,py,pz,T)\n", " dx = np.insert(dx,idx,variation)\n", " return dx" ] }, { "cell_type": "markdown", "id": "91c20cc1", "metadata": {}, "source": [ "We can now use the function to create a new initial guess:" ] }, { "cell_type": "code", "execution_count": 22, "id": "2dd405d4", "metadata": {}, "outputs": [], "source": [ "dx = predictor(ta)\n", "ic_continued_guess = [a+b for a,b in zip(ic_periodic, dx[:6].tolist())]\n", "new_T = ta.time + dx[-1]" ] }, { "cell_type": "markdown", "id": "8f067f1b", "metadata": {}, "source": [ "Let us visualize as usual the resulting orbit .... (code is repeated for convenience, but its identical to above cells)" ] }, { "cell_type": "code", "execution_count": 23, "id": "76bdb6b4", "metadata": {}, "outputs": [], "source": [ "C_jacobi = jacobi_constant(ic_continued_guess, mu)\n", "\n", "# Reset the state\n", "ta.time = 0.\n", "ta.state[:] = ic_continued_guess + ic_var\n", "ta.pars[0] = mu\n", "# Time grid\n", "t_grid = np.linspace(0, new_T, 2000)\n", "# Go ...\n", "out2 = ta.propagate_grid(t_grid)" ] }, { "cell_type": "code", "execution_count": 24, "id": "075ae1f0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-0.005, 0.005)" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# We plot the initial condition (zoom in the Lagrangian point)\n", "plt.figure(figsize=(9,9))\n", "\n", "plt.subplot(1,1,1)\n", "zoom=0.005\n", "plt.plot(out0[4][:, 0], out0[4][:, 1], 'r')\n", "plt.plot(out[4][:, 0], out[4][:, 1],'k')\n", "plt.plot(out2[4][:, 0], out2[4][:, 1],'r')\n", "\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "\n", "# Plot the zero velocity curve\n", "xx = np.linspace(xL1-zoom,xL1+zoom,2000)\n", "yy = np.linspace(-zoom,zoom,2000)\n", "x_grid,y_grid = np.meshgrid(xx,yy)\n", "im = plt.imshow( ((potential_function((x_grid,y_grid,np.zeros(np.shape(x_grid))),mu=mu)<=C_jacobi)).astype(int) , \n", " extent=(x_grid.min(),x_grid.max(),y_grid.min(),y_grid.max()),origin=\"lower\", cmap=\"Greens\")\n", "\n", "# Plot the lagrangian points and primaries\n", "plt.scatter(mu, 0, c='k', s=300)\n", "plt.scatter(mu-1, 0, c='k', s=100)\n", "plt.scatter(xL1, 0, c='r')\n", "plt.scatter(xL2, 0, c='r')\n", "plt.scatter(xL3, 0, c='r')\n", "plt.scatter(-0.5+mu, yL45, c='r')\n", "plt.scatter(-0.5+mu, -yL45, c='r')\n", "\n", "\n", "plt.xlim(xL1-zoom, xL1+zoom)\n", "plt.ylim(-zoom, +zoom)" ] }, { "cell_type": "markdown", "id": "b35eea61", "metadata": {}, "source": [ "It's nearly closed, but not that well .... it will need a correction ... but we can call the same iterations we made previously when we closed the first initial guess, remember?" ] }, { "cell_type": "code", "execution_count": 25, "id": "b5807f39", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "error was: 0.00027713982303279586\n", "condition number is: 15773618.561420336\n", "new error is: 9.470894213691114e-07\n", "error was: 9.470894213691114e-07\n", "condition number is: 78690773437.61931\n", "new error is: 6.077500558656773e-09\n", "error was: 6.077500558656773e-09\n", "condition number is: 859354545799.8098\n", "new error is: 9.972303343724588e-14\n" ] } ], "source": [ "ic_continued = ic_continued_guess\n", "for i in range(3):\n", " ta, ic_continued = corrector(ta, ic_continued)" ] }, { "cell_type": "markdown", "id": "87200ace", "metadata": {}, "source": [ "And we visualize all the initial guesses and closed orbit found so far:" ] }, { "cell_type": "code", "execution_count": 26, "id": "849257f8", "metadata": {}, "outputs": [], "source": [ "t_final = ta.time\n", "\n", "# We compute the IC Jacobi constant\n", "C_jacobi = jacobi_constant(ic_continued, mu)\n", "\n", "# Reset the state\n", "ta.time = 0.\n", "ta.state[:] = ic_continued + ic_var\n", "ta.pars[0] = mu\n", "# Time grid\n", "t_grid = np.linspace(0, t_final, 2000)\n", "# Go ...\n", "out3 = ta.propagate_grid(t_grid)" ] }, { "cell_type": "code", "execution_count": 27, "id": "04a64a89", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# We plot the initial condition (zoom in the Lagrangian point)\n", "plt.figure(figsize=(9,9))\n", "\n", "plt.subplot(1,1,1)\n", "zoom=0.005\n", "plt.plot(out0[4][:, 0], out0[4][:, 1],'r')\n", "plt.plot(out[4][:, 0], out[4][:, 1],'k')\n", "plt.plot(out2[4][:, 0], out2[4][:, 1],'r')\n", "plt.plot(out3[4][:, 0], out3[4][:, 1],'k')\n", "\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "\n", "# Plot the zero velocity curve\n", "xx = np.linspace(xL1-zoom,xL1+zoom,2000)\n", "yy = np.linspace(-zoom,zoom,2000)\n", "x_grid,y_grid = np.meshgrid(xx,yy)\n", "im = plt.imshow( ((potential_function((x_grid,y_grid,np.zeros(np.shape(x_grid))),mu=mu)<=C_jacobi)).astype(int) , \n", " extent=(x_grid.min(),x_grid.max(),y_grid.min(),y_grid.max()),origin=\"lower\", cmap=\"Greens\")\n", "\n", "# Plot the lagrangian points and primaries\n", "plt.scatter(mu, 0, c='k', s=300)\n", "plt.scatter(mu-1, 0, c='k', s=100)\n", "plt.scatter(xL1, 0, c='r')\n", "plt.scatter(xL2, 0, c='r')\n", "plt.scatter(xL3, 0, c='r')\n", "plt.scatter(-0.5+mu, yL45, c='r')\n", "plt.scatter(-0.5+mu, -yL45, c='r')\n", "\n", "\n", "plt.xlim(xL1-zoom, xL1+zoom)\n", "plt.ylim(-zoom, +zoom);" ] } ], "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": "3.10.6" } }, "nbformat": 4, "nbformat_minor": 5 }