{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Cowell's formulation\n", "\n", "For cases where we only study the gravitational forces, solving the Kepler's equation is enough to propagate the orbit forward in time. However, when we want to take perturbations that deviate from Keplerian forces into account, we need a more complex method to solve our initial value problem: one of them is **Cowell's formulation**.\n", "\n", "In this formulation we write the two body differential equation separating the Keplerian and the perturbation accelerations:\n", "\n", "$$\\ddot{\\mathbb{r}} = -\\frac{\\mu}{|\\mathbb{r}|^3} \\mathbb{r} + \\mathbb{a}_d$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## First example\n", "\n", "Let's setup a very simple example with constant acceleration to visualize the effects on the orbit." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "from astropy import units as u\n", "\n", "from matplotlib import ticker\n", "from matplotlib import pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "\n", "from scipy.integrate import ode\n", "\n", "from poliastro.bodies import Earth\n", "from poliastro.twobody import State\n", "from poliastro.examples import iss\n", "\n", "from poliastro.twobody.propagation import func_twobody\n", "\n", "from poliastro.util import norm" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ ":0: FutureWarning: IPython widgets are experimental and may change in the future.\n" ] } ], "source": [ "from IPython.html.widgets import interact, fixed" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def state_to_vector(ss):\n", " r, v = ss.rv()\n", " x, y, z = r.to(u.km).value\n", " vx, vy, vz = v.to(u.km / u.s).value\n", " return np.array([x, y, z, vx, vy, vz])" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 8.59072560e+02, -4.13720368e+03, 5.29556871e+03,\n", " 7.37289205e+00, 2.08223573e+00, 4.39999794e-01])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "u0 = state_to_vector(iss)\n", "u0" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "array([ 0. , 111.36236546, 222.72473091, 334.08709637,\n", " 445.44946182, 556.81182728, 668.17419274, 779.53655819,\n", " 890.89892365, 1002.2612891 ])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = np.linspace(0, 10 * iss.period, 500).to(u.s).value\n", "t[:10]" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "111.36236545586407" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dt = t[1] - t[0]\n", "dt" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "k = Earth.k.to(u.km**3 / u.s**2).value" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To provide an acceleration depending on an extra parameter, we can use **closures** like this one:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 9.60774274e-06, 2.71339728e-06, 5.73371317e-07])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def constant_accel_factory(accel):\n", " def constant_accel(t0, u, k):\n", " v = u[3:]\n", " norm_v = (v[0]**2 + v[1]**2 + v[2]**2)**.5\n", " return accel * v / norm_v\n", "\n", " return constant_accel\n", "\n", "constant_accel_factory(accel=1e-5)(t[0], u0, k)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on function func_twobody in module poliastro.twobody.propagation:\n", "\n", "func_twobody(t0, u, k, ad)\n", " Differential equation for the initial value two body problem.\n", " \n", " This function follows Cowell's formulation.\n", " \n", " Parameters\n", " ----------\n", " t0 : float\n", " Time.\n", " u : ndarray\n", " Six component state vector [x, y, z, vx, vy, vz] (km, km/s).\n", " k : float\n", " Standard gravitational parameter.\n", " ad : function(t0, u, k)\n", " Non Keplerian acceleration (km/s2).\n", "\n" ] } ], "source": [ "help(func_twobody)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we setup the integrator manually using `scipy.integrate.ode`. We cannot provide the Jacobian since we don't know the form of the acceleration in advance." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "array([[ 8.59072560e+02, -4.13720368e+03, 5.29556871e+03,\n", " 7.37289205e+00, 2.08223573e+00, 4.39999794e-01],\n", " [ 1.67120230e+03, -3.87307826e+03, 5.30240753e+03,\n", " 7.19314459e+00, 2.65498807e+00, -3.17311723e-01],\n", " [ 2.45692619e+03, -3.54744244e+03, 5.22508987e+03,\n", " 6.89930195e+00, 3.18546188e+00, -1.06939136e+00],\n", " [ 3.20378664e+03, -3.16547981e+03, 5.06486636e+03,\n", " 6.49612276e+00, 3.66524518e+00, -1.80427363e+00],\n", " [ 3.89995423e+03, -2.73326637e+03, 4.82430604e+03,\n", " 5.99011411e+00, 4.08674543e+00, -2.51027861e+00]])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res = np.zeros((t.size, 6))\n", "res[0] = u0\n", "ii = 1\n", "\n", "accel = 1e-5\n", "\n", "rr = ode(func_twobody).set_integrator('dop853') # All parameters by default\n", "rr.set_initial_value(u0, t[0])\n", "rr.set_f_params(k, constant_accel_factory(accel))\n", "\n", "while rr.successful() and rr.t + dt < t[-1]:\n", " rr.integrate(rr.t + dt)\n", " res[ii] = rr.y\n", " ii += 1\n", "\n", "res[:5]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And we plot the results:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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1WL1a4Y8/NPLzvbDsnkzT/Wrb7iiPqipomjvC07AhnHQSNGni0LSpTf36Dn/+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L7/XuL48cLfz8LOk8k+pkJRlAsaU2Hl8BQdluAJESyH59xUq2YQHa2zY4dMp04+Vq+206GDcHba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RiYmJuHLlil/2W1EUvP766zh69Cjeeecdmw+siKajDHahYRd4AAGdKdMVIvtcsWPHLrQipRqA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\nY8ZazDQ0NNgIGSZmKis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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "fig = plt.figure(figsize=(10, 10))\n", "ax = fig.add_subplot(111, projection='3d')\n", "\n", "ax.plot(*res[:, :3].T)\n", "\n", "ax.view_init(14, 70)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interactivity" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the last time we used `scipy.integrate.ode` directly. Instead, we can now import a convenient function from poliastro:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from poliastro.twobody.propagation import cowell" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def plot_iss(thrust=0.1, mass=2000.):\n", " r0, v0 = iss.rv()\n", " k = iss.attractor.k\n", " t = np.linspace(0, 10 * iss.period, 500).to(u.s).value\n", " u0 = state_to_vector(iss)\n", "\n", " res = np.zeros((t.size, 6))\n", " res[0] = u0\n", "\n", " accel = thrust / mass\n", "\n", " # Perform the whole integration\n", " r0 = r0.to(u.km).value\n", " v0 = v0.to(u.km / u.s).value\n", " k = k.to(u.km**3 / u.s**2).value\n", " ad = constant_accel_factory(accel)\n", " r, v = r0, v0\n", " for ii in range(1, len(t)):\n", " r, v = cowell(k, r, v, t[ii] - t[ii - 1], ad)\n", " x, y, z = r\n", " vx, vy, vz = v\n", " res[ii] = [x, y, z, vx, vy, vz]\n", "\n", " fig = plt.figure(figsize=(8, 6))\n", " ax = fig.add_subplot(111, projection='3d')\n", "\n", " ax.set_xlim(-20e3, 20e3)\n", " ax.set_ylim(-20e3, 20e3)\n", " ax.set_zlim(-20e3, 20e3)\n", "\n", " ax.view_init(14, 70)\n", "\n", " return ax.plot(*res[:, :3].T)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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JEmbMmEEwGGTs2LGMGTMGgNmzZzN16lT69+9Pjx49WLlypfXa7WEeZlu8XmcN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\ndeoUXnjhBfzyyy+4+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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "interact(plot_iss, thrust=(0.0, 0.2, 0.001), mass=fixed(2000.))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Error checking" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "rtol = 1e-13\n", "full_periods = 2" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(array([ 8.59072560e+02, -4.13720368e+03, 5.29556871e+03,\n", " 7.37289205e+00, 2.08223573e+00, 4.39999794e-01]),\n", " 13892.455090619042)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "u0 = state_to_vector(iss)\n", "tf = ((2 * full_periods + 1) * iss.period / 2).to(u.s).value\n", "\n", "u0, tf" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [], "source": [ "iss_f_kep = iss.propagate(tf * u.s, rtol=1e-18)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [], "source": [ "r0, v0 = iss.rv()\n", "r, v = cowell(k, r0.to(u.km).value, v0.to(u.km / u.s).value, tf, rtol=rtol)\n", "\n", "iss_f_num = State.from_vectors(Earth, r * u.km, v * u.km / u.s, iss.epoch + tf * u.s)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "assert np.allclose(iss_f_num.r, iss_f_kep.r, rtol=rtol)\n", "assert np.allclose(iss_f_num.v, iss_f_kep.v, rtol=rtol)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [], "source": [ "assert np.allclose(iss_f_num.a, iss_f_kep.a, rtol=rtol)\n", "assert np.allclose(iss_f_num.ecc, iss_f_kep.ecc, rtol=rtol)\n", "assert np.allclose(iss_f_num.inc, iss_f_kep.inc, rtol=rtol)\n", "assert np.allclose(iss_f_num.raan, iss_f_kep.raan, rtol=rtol)\n", "assert np.allclose(iss_f_num.argp, iss_f_kep.argp, rtol=rtol)\n", "assert np.allclose(iss_f_num.nu, iss_f_kep.nu, rtol=rtol)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Too bad I cannot access the internal state of the solver. I will have to do it in a blackbox way." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/juanlu/.miniconda3/envs/poliastro34/lib/python3.4/site-packages/scipy/integrate/_ode.py:1019: UserWarning: dop853: step size becomes too small\n", " self.messages.get(idid, 'Unexpected idid=%s' % idid))\n" ] } ], "source": [ "u0 = state_to_vector(iss)\n", "full_periods = 4\n", "\n", "tof_vector = np.linspace(0, ((2 * full_periods + 1) * iss.period / 2).to(u.s).value, num=100)\n", "rtol_vector = np.logspace(-3, -12, num=30)\n", "\n", "res_array = np.zeros((rtol_vector.size, tof_vector.size))\n", "for jj, tof in enumerate(tof_vector):\n", " rf, vf = iss.propagate(tof * u.s, rtol=1e-12).rv()\n", " for ii, rtol in enumerate(rtol_vector):\n", " rr = ode(func_twobody).set_integrator('dop853', rtol=rtol, nsteps=1000)\n", " rr.set_initial_value(u0, 0.0)\n", " rr.set_f_params(k, constant_accel_factory(0.0)) # Zero acceleration\n", "\n", " rr.integrate(rr.t + tof)\n", "\n", " if rr.successful():\n", " uf = rr.y\n", "\n", " r, v = uf[:3] * u.km, uf[3:] * u.km / u.s\n", "\n", " res = max(norm((r - rf) / rf), norm((v - vf) / vf))\n", " else:\n", " res = np.nan\n", "\n", " res_array[ii, jj] = res" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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uMDNee+01/OY3v8Grr76a6tgzZ87E6aefjueffx7PP/88Tj31VHz2s58FUJ06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\nS3vqHnT49r334D933tN0deXTCYHB0a3Tym8wsycAXDryexdXXUEnC7D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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(16, 6))\n", "\n", "xx, yy = np.meshgrid(tof_vector, rtol_vector)\n", "\n", "cs = ax.contourf(xx, yy, res_array, levels=np.logspace(-12, -1, num=12),\n", " locator=ticker.LogLocator(), cmap=plt.cm.Spectral_r)\n", "fig.colorbar(cs)\n", "\n", "for nn in range(full_periods + 1):\n", " lf = ax.axvline(nn * iss.period.to(u.s).value, color='k', ls='-')\n", " lh = ax.axvline((2 * nn + 1) * iss.period.to(u.s).value / 2, color='k', ls='--')\n", "\n", "ax.set_yscale('log')\n", "\n", "ax.set_xlabel(\"Time of flight (s)\")\n", "ax.set_ylabel(\"Relative tolerance\")\n", "\n", "ax.set_title(\"Maximum relative difference\")\n", "\n", "ax.legend((lf, lh), (\"Full period\", \"Half period\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numerical validation\n", "\n", "According to [Edelbaum, 1961], a coplanar, semimajor axis change with tangent thrust is defined by:\n", "\n", "$$\\frac{\\operatorname{d}\\!a}{a_0} = 2 \\frac{F}{m V_0}\\operatorname{d}\\!t, \\qquad \\frac{\\Delta{V}}{V_0} = \\frac{1}{2} \\frac{\\Delta{a}}{a_0}$$\n", "\n", "So let's create a new circular orbit and perform the necessary checks, assuming constant mass and thrust (i.e. constant acceleration):" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [], "source": [ "ss = State.circular(Earth, 500 * u.km)\n", "tof = 20 * ss.period\n", "\n", "ad = constant_accel_factory(1e-7)\n", "\n", "r0, v0 = ss.rv()\n", "r, v = cowell(k, r0.to(u.km).value, v0.to(u.km / u.s).value,\n", " tof.to(u.s).value, ad)\n", "\n", "ss_final = State.from_vectors(Earth, r * u.km, v * u.km / u.s, ss.epoch + rr.t * u.s)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$0.0029896237 \\; \\mathrm{}$" ], "text/plain": [ "" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "da_a0 = (ss_final.a - ss.a) / ss.a\n", "da_a0" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$0.0029960565 \\; \\mathrm{}$" ], "text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dv_v0 = abs(norm(ss_final.v) - norm(ss.v)) / norm(ss.v)\n", "2 * dv_v0" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.allclose(da_a0, 2 * dv_v0, rtol=1e-2)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$0.011403897 \\; \\mathrm{\\frac{km}{s}}$" ], "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dv = abs(norm(ss_final.v) - norm(ss.v))\n", "dv" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$0.5556982 \\; \\mathrm{\\frac{km}{s}}$" ], "text/plain": [ "" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "accel_dt = accel * u.km / u.s**2 * (t[-1] - t[0]) * u.s\n", "accel_dt" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.allclose(dv, accel_dt, rtol=1e-2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This means **we successfully validated the model against an extremely simple orbit transfer with approximate analytical solution**. Notice that the final eccentricity, as originally noticed by Edelbaum, is nonzero:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "$6.6621548 \\times 10^{-6} \\; \\mathrm{}$" ], "text/plain": [ "" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ss_final.ecc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "* [Edelbaum, 1961] \"Propulsion requirements for controllable satellites\"" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }