{ "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.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": [ "--- 4.743351936340332 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": [ "--- 0.051287174224853516 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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"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[5][:, 0], out[5][:, 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[5][:, 0], out[5][:, 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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", 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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[5][:, 0], out0[5][:, 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.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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", "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[5][:, 0], out0[5][:, 1],'r')\n", "plt.plot(out[5][:, 0], out[5][:, 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[5][0,0]:.16e}, {out[5][0,1]:.16e}, {out[5][0,2]:.16e}, {out[5][0,3]:.16e}, {out[5][0,4]:.16e}, {out[5][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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", "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[5][:, 0], out0[5][:, 1], 'r')\n", "plt.plot(out[5][:, 0], out[5][:, 1],'k')\n", "plt.plot(out2[5][:, 0], out2[5][:, 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[5][:, 0], out0[5][:, 1],'r')\n", "plt.plot(out[5][:, 0], out[5][:, 1],'k')\n", "plt.plot(out2[5][:, 0], out2[5][:, 1],'r')\n", "plt.plot(out3[5][:, 0], out3[5][:, 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);" ] }, { "cell_type": "markdown", "id": "7b093fd3", "metadata": {}, "source": [ "Found it! In order to do this in a loop, though, we will need to do better as eventually this will fail as the continuation parameter\n", "here used, i.e., the period $T$, will create issues as it is not monotonically increasng with the orbit size.\n", "\n", "The solution requires a bit more math, and it is given by the definition and use of a [pseudo arc-length](<./Pseudo arc-length continuation in the CR3BP.ipynb>)." ] } ], "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": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 5 }