{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "77c1d95e",
   "metadata": {},
   "source": [
    "# Thrust Example\n",
    "\n",
    "This program will demonstrate adding a thrust to a particle in rebound."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "818ce634",
   "metadata": {},
   "outputs": [],
   "source": [
    "import rebound\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8b6a799e",
   "metadata": {},
   "outputs": [],
   "source": [
    "sim=rebound.Simulation()\n",
    "sim.add(m=1)\n",
    "sim.add(m=1e-10,a=1)\n",
    "sim.move_to_com()\n",
    "ps=sim.particles\n",
    "\n",
    "\n",
    "#adding the additional force.\n",
    "\n",
    "A=-1./2000\n",
    "def thrust(reb_sim):\n",
    "    R=math.sqrt(ps[1].x**2+ps[1].y**2)\n",
    "    ps[1].ax+=-ps[1].y*A/R\n",
    "    ps[1].ay+=ps[1].x*A/R\n",
    "    ps[1].az+=0.0\n",
    "\n",
    "sim.additional_forces=thrust\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6827f637",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 360x360 with 1 Axes>, <AxesSubplot:xlabel='x', ylabel='y'>)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rebound.OrbitPlot(sim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bedb84da",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n",
      "0.9070297723714617\n",
      "0.8264463175250057\n",
      "0.7561446368153768\n",
      "0.6944453433501564\n",
      "0.6400005707124552\n",
      "0.5917165119305094\n",
      "0.5486973002505597\n",
      "0.5102043634913032\n",
      "0.47562462861636523\n"
     ]
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    sim.integrate(i*100)\n",
    "    print(ps[1].a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "27a47b3f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 360x360 with 1 Axes>, <AxesSubplot:xlabel='x', ylabel='y'>)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rebound.OrbitPlot(sim)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93e7c0eb",
   "metadata": {},
   "source": [
    "# reboundx\n",
    "\n",
    "In this case the additional force is running in python which will slow your simulation.  One can also add forces in c and the reboundx package already has many useful predefined forces."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b64c4e57",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}