{
 "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 Orbit\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": [],
   "source": [
    "from ipywidgets.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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pYhgGoVBom+3eRH3RaDQVDnZFJBJB07Rdfswdx2HLli3UqVNnl67Da2m3LCsVhna0z0if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\n1106PXuGaNvWS8uWOk88EWLiRBe//CIzf76fxx7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1kpQUIBAIEAwGTxMwiqKgaRputxuv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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8b8c05fba8>"
      ]
     },
     "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": [
       "[<mpl_toolkits.mplot3d.art3d.Line3D at 0x7f8b887affd0>]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.plot_iss>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4JiAFU9IuyVbMEl1XqY8VNGTFNeSyFL+LOkyv19tERy+pD+GaNQwDXddRVTVpGLTIJk2k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\nI1CvhffQQz7mzo1QVLTPpenxeHjySS9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JOl4vrF5d/2fq88GECTEWL25cix673W6VdXTv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\ngpABCSZBEARByOD/ABtLJlfj2jH6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8b8c089978>"
      ]
     },
     "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 = Orbit.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": [
    {
     "data": {
      "text/plain": [
       "(<Quantity [ -835.92296213, 4151.61612901,-5303.61604874] km>,\n",
       " <Quantity [ -835.92296213, 4151.61612901,-5303.61604874] km>)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iss_f_num.r, iss_f_kep.r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "assert np.allclose(iss_f_num.r, iss_f_kep.r, rtol=rtol, atol=1e-08 * u.km)\n",
    "assert np.allclose(iss_f_num.v, iss_f_kep.v, rtol=rtol, atol=1e-08 * u.km / u.s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "assert np.allclose(iss_f_num.a, iss_f_kep.a, rtol=rtol, atol=1e-08 * u.km)\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, atol=1e-08 * u.rad)\n",
    "assert np.allclose(iss_f_num.raan, iss_f_kep.raan, rtol=rtol, atol=1e-08 * u.rad)\n",
    "assert np.allclose(iss_f_num.argp, iss_f_kep.argp, rtol=rtol, atol=1e-08 * u.rad)\n",
    "assert np.allclose(iss_f_num.nu, iss_f_kep.nu, rtol=rtol, atol=1e-08 * u.rad)"
   ]
  },
  {
   "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": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/juanlu/.miniconda3/envs/poliastro35/lib/python3.5/site-packages/scipy/integrate/_ode.py:1035: 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": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8b862cc128>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+b8O0g0d2vxQZSArCCkkHWTTbFnt/Cs5J2zD41rnwFbVzcyTbJskoog/4olOx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\n/wf0eI2ur5e4GAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8b8637e438>"
      ]
     },
     "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": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ss = Orbit.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 = Orbit.from_vectors(Earth, r * u.km, v * u.km / u.s, ss.epoch + rr.t * u.s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.0029896237 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity 0.0029896236825125828>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "da_a0 = (ss_final.a - ss.a) / ss.a\n",
    "da_a0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.0029960565 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity 0.002996056527838881>"
      ]
     },
     "execution_count": 26,
     "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": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(da_a0, 2 * dv_v0, rtol=1e-2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.011403897 \\; \\mathrm{\\frac{km}{s}}$"
      ],
      "text/plain": [
       "<Quantity 0.011403896714710093 km / s>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dv = abs(norm(ss_final.v) - norm(ss.v))\n",
    "dv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.5556982 \\; \\mathrm{\\frac{km}{s}}$"
      ],
      "text/plain": [
       "<Quantity 0.5556982036247617 km / s>"
      ]
     },
     "execution_count": 29,
     "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": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(dv, accel_dt, rtol=1e-2, atol=1e-8 * u.km / u.s)"
   ]
  },
  {
   "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": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$6.6621548 \\times 10^{-6} \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity 6.662154787513252e-06>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss_final.ecc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "* [Edelbaum, 1961] \"Propulsion requirements for controllable satellites\""
   ]
  }
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