{
 "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"
   ]
  },
  {
   "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./1000\n",
    "def thrust(reb_sim):\n",
    "    ps[1].ax+=ps[1].vx*A\n",
    "    ps[1].ay+=ps[1].vy*A\n",
    "    ps[1].az+=ps[1].vx*A\n",
    "\n",
    "sim.additional_forces=thrust\n",
    "sim.force_is_velocity_dependent=1"
   ]
  },
  {
   "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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ZliHEWXCiyxORiNmEiGUZIl6vFzU1NSgoKNAdhci0LBYLR5ax7syZM8jOzo6Ks9oRhQpHloTTp08jLy9PdwwiUxORiFluybIMkfPnz2PUqFG6YxCZnsViiYjRJcsyBJRSqKurQ3Z2tu4oRKbHkWUMa2pqQlJSEpdXEhnAkWUMq62t5b7gREMQCaNLlmUIsCyJhiYSdtxgWYYAy5JoaCLhQDMsyyDz+/2or6/nyh2iKMOyDLKmpiY4nU6e7pZoCLjMMgZxFpwoOrEsg6y5uRlZWVm6YxBRkLEsg6y5uRlJSUm6YxBFHLPPirMsg6yjowNOp1N3DCIKMpZlkHV0dHBkSRSFWJZB1tnZCZfLpTsGUcThbHgMcbvdUErB4XDojkIUkcy8cTrLMoi4vJJoZFiWMYJlSRS9WJZBxJU7RNGLZRlEHFkSRa/IOsu5yTmdTiQnJ+uOQUQhwJFlEE2ZMgX19fW6YxBRCGgtSxG5VUQ+E5EqEXl4gOdFRH4beP5TEblOR86h2LFjh+4IRBQC2spSRKwAngGwDMAUAHeLyJRLJlsGYHLgshrA+rCGpKjS3t6OGTNmoKOjQ3cUGoDP58PGjRvxy1/+Ehs3boTP59Md6UuuuMxSRNYAeEkp1Rzk954JoEopdSLwPq8AWAngSL9pVgL4T3Vhs/5dIpIqIqOVUueCnIViwKZNm7B3715s2rQJ3/rWt3THoX58Ph9uueUWlJWVobOzE0lJSZg1axY2b95smlNOGBlZjgKwR0ReDcw2B2ur0TEAzvS7XxN4bKjTEF3W9773PSQnJ+M73/kOAODv/u7vkJycjNWrV2tORhe9++67KCsrQ0dHB5RS6OjoQFlZGd59913d0fpcsSyVUj/BhdngFwD8LwCVIrJORCaO8L0HKt1Ldww1Ms2FCUVWi8heEdnLlSzU37/+67+ioKAANtuFGSmbzYaCggI88sgjmpPRReXl5ejs7PzSY52dnThw4ICeQAMwtMwyMBt8PnDxAkgD8JqIPD6C964BMLbf/TwAZ4cxzcWMzyulSpRSJTz4LvU3fvx4/OIXv4DH44HT6YTH48EvfvELjB8/Xnc0CiguLv7KDh1JSUkoKirSE2gAVyxLEfmxiOwD8DiAjwFMV0o9AOB6AHeM4L33AJgsIuNFxAHgLgBvXTLNWwDuDawVnw2glcsraThee+01uFwuPPbYY3A6nfjv//5v3ZGon2XLlmHWrFmw2WwQETidTsyaNQvLli3THa2PkY3SMwF8UylV3f9BpZRfRFYM942VUt7AyqPNAKwAXlRKHRaRHwSefw7AJgDLAVQB6AJw33Dfj2Lbww8/jKeffhqZmZm45557cP78ed2RqB+r1YrNmzdjzpw5mDp1Ku644w4sW7bMNCt3AANlqZT66WWeOzqSN1dKbcKFQuz/2HP9bisAPxrJexABwPTp0/tuZ2ZmIjMzU2MaGojVakVSUhK+//3vY/bs2brjfAX34AminTt3Ij09XXcMoojV3t5u2uMrsCyDyGq1Ij8/X3cMoojV2dnJsowFTqeTe4cQjUB7e7tpT8vCsgwil8uF9vZ23TGIIpaZD3PIsgwiliXR8PX29pr6HFYsyyDibDjR8DU0NOCGG24w7Xl4WJZBZLPZYLfb0d3drTsKUcQ5efIk3G637hiDYlkGGWfFiYansrISkydP1h1jUCzLIGNZEg1PVVUVJk4c6fF5QodlGWRcbkk0PBxZxpiMjAy0trbqjkEUcaqqqjBp0iTdMQbFsgyy9PR0fPHFF7pjEEUUt9uNmpoaUx82j2UZZLm5uTh7dsBDbhLRIKqrq5Gbm2vabSwBlmXQpaamwuPxcLkl0RCYfXklwLIMOhHh6JJoiMy+vBJgWYYEy5JoaBoaGnDNNdfojnFZLMsQyM3N5UoeoiHYtGkTrr32Wt0xLotlGQK5ubk4d46nCiIyoqamBm1tbSgsLNQd5bJYliGQkpICn8/HPXmIDPjoo48wb948WCzmriNzp4tQXMlDZNyOHTuwYMEC3TGuiGUZImPHjmVZEl2BUgofffQRyzKWFRQU4MiRI7pjEJladXU13G636TcbAliWITNu3Di0tLSgpaVFdxQi07o4C27WA/72x7IMEYvFgsLCQhw7dkx3FCLT+uijjzB//nzdMQxhWYbQ1772Nc6KEw1CKRUxK3cAlmVITZo0CTU1Nejp6dEdhch0PvvsM4wfPx4FBQW6oxjCsgwhh8OB8ePH4/jx47qjEJnOm2++ieuuuy4illcCLMuQKyws5Kw40SWUUnjttdewatUq3VEMY1mGWGFhISorK+Hz+XRHITKN3bt3Iz4+HtOnT9cdxTCWZYi5XC5kZWXhxIkTuqMQmcarr76KVatWRcwsOMCyDIvp06dzEyKigN7eXmzcuBF33nmn7ihDwrIMg+nTp2Pfvn1cK04E4L333sPUqVORm5urO8qQsCzDIDk5GZMnT8b+/ft1RyHSrrS0FN/61rd0xxgylmWYzJ07F5988gmUUrqjEGnT1NSEnTt3YsWKFbqjDBnLMkwKCgpgs9lQVVWlOwqRNq+//jpuvPFGOJ1O3VGGjGUZJiLSN7okikVKKezcuRN333237ijDwrIMo6KiIpw6dQrNzc26oxCF3bZt23Dy5MmI2Rf8UizLMHI4HLj++uuxa9cu3VGIwkophaeffhr/8A//YPrTRwwmMlNHsDlz5mDPnj3weDy6oxCFza5du9DY2IhvfOMbuqMMG8syzDIyMpCXl4eKigrdUYjC5umnn8aaNWtgtVp1Rxk2lqUGCxcuxI4dO+D3+3VHIQq58vJynDhxAnfccYfuKCPCstRg4sSJiI+Px+7du3VHIQq5p59+Gj/84Q9ht9t1RxkRlqUGIoIVK1Zg8+bNcLvduuMQhczRo0dRUVGBu+66S3eUEdNSliKSLiJ/E5HKwHXaINOdEpGDInJARPaGO2cojR07FhMnTsSHH36oOwpRyPz2t7/F6tWrER8frzvKiOkaWT4MYItSajKALYH7g1mslCpSSpWEJ1r4LFu2DDt27EBHR4fuKERBV1lZib179+I73/mO7ihBoassVwL4U+D2nwDcpimHVhkZGbjuuuvwt7/9TXcUoqBSSuHf/u3f8MADD0Tkro0D0VWWOUqpcwAQuM4eZDoF4D0R2Sciq8OWLoyWLl2K8vJyNDQ06I5CFDTvvPMOamtrce+99+qOEjQhK0sReV9EDg1wWTmEl5mnlLoOwDIAPxKRhZd5v9UisldE9tbX1484f7g4nU7ccMMN2LRpk+4oREHR0dGBX/7yl3jsscdgs9l0xwmakJWlUmqpUmraAJc3AdSKyGgACFzXDfIaZwPXdQBeBzDzMu/3vFKqRClVkpWVFfwPFEILFizAqVOncPr0ad1RiEbsqaeewsKFCzFjxgzdUYJK12z4WwC+G7j9XQBvXjqBiCSJiOvibQA3AzgUtoRh5HA4sHz5crz99tvcUJ0i2pEjR/DGG2/gkUce0R0l6HSV5a8B3CQilQBuCtyHiOSKyMX50RwAH4lIBYDdAN5RSv1fLWnD4Prrr4eI4P3339cdhWhY/H4/1q5di4ceegjp6em64wSdlgUKSqlGADcO8PhZAMsDt08AuDbM0bQREdxzzz34zW9+g6lTp2LMmDG6IxENyauvvgqlFL797W/rjhIS3IPHRFJTU3HbbbfhL3/5C7xer+44RIY1NTXh8ccfx7p16yL2EGxXEp2fKoKVlJQgIyMD7777ru4oRIY9++yzWLlyJaZMmaI7SsiwLE1GRPDtb38bZWVlOHXqlO44RFf0P//zP/jwww/x0EMP6Y4SUixLE3K5XFi1ahX+8pe/8EAbZGrHjx/HunXr8Pvf/x6JiYm644QUy9Kkrr32WuTn5+Ptt9/WHYVoQF1dXVizZg0eeeQRXH311brjhBzL0sTuuOMOfPrppzh27JjuKERfopTC2rVrUVxcHPEH9TWKZWliiYmJuPfee/HHP/6R+46TqfzXf/0Xjh07hp///Oe6o4QNy9LkJk6ciOXLl2P9+vXo7u7WHYcIR44cwRNPPIFnnnkGCQkJuuOEDcsyAixcuBBXX301XnjhBe4OSVq1t7djzZo1+NnPfoYJEybojhNWLMsIceeddwIAXnvtNc1JKFYppfCTn/wE8+fPj+hT2g4XyzJCWCwW3H///fjss8+wfft23XEoxiil8Pjjj8Pr9WLt2rW642jBsowgCQkJeOCBB7Bp0yauIaewev7557Fjxw6sW7cOcXFxuuNowbKMMJmZmfj7v/97bNiwAbW1tbrjUAx4+eWXUVpaig0bNiAlJUV3HG1YlhFo0qRJuO2227B+/Xq0tbXpjkNR7J133sGzzz6LDRs2INIOqh1sLMsINWfOHMyZMwdPPfUUC5NCYseOHXjsscfwwgsvYOzYsbrjaMeyjGC33HILZsyYgSeeeAItLS2641AU2b9/Px566CE888wzuOqqq3THMQWWZYT7+te/jrlz5+KJJ55AU1OT7jgUBY4dO4Y1a9bgiSeeQHFxse44psGyjAK33norFi1ahCeffJK7RdKIHD9+HD/96U/x6KOPYv78+brjmArLMkosXboUN910E5588knU1Q14skyiyyorK8P999+P++67D8uWLdMdx3RYllFk0aJFWL58OZ588kmcP39edxyKIBs3bsSDDz6Ip556ikU5iOg5AzoBuHAOcqvViqeeegr/+I//yBOf0WUppfDCCy/glVdewYYNGzBp0iTdkUyLZRmF5s6dC7vdjt/97ne45557cM011+iORCbk8/mwbt067N+/Hy+99BJycnJ0RzI1lmWUmjFjBtLS0rB+/XosXrwYX//61yEiumORSfT09ODBBx9ET08P/vznP8PpdOqOZHpcZhnFJk2ahEcffRSffvopnnnmGR4PkwBcOG3tfffdB5fLhfXr17MoDWJZRrnU1FT88z//M5KTk/HYY49xxU+MO3z4MNauXYs5c+Zg3bp1sNvtuiNFDJZlDLDZbLj33ntx880349e//jUOHDigOxKFmd/vx4YNG/CjH/0It912G3784x9zscwQcZllDFm4cCHy8vLw7LPP4vTp0/jGN77BP5gYUFdXh7Vr18Lj8eDll1/G6NGjdUeKSBxZxpgJEybg0UcfxZEjR/Af//Ef3Kc8ym3btg133XUXZsyYgRdeeIFFOQKilNKdIehKSkrU3r17dccwNa/Xi7fffhtbtmzBqlWrsHDhQo4yo0hPTw+efPJJfPTRR/jVr36FoqIi3ZEigojsU0qVDPQcR5Yxymaz4fbbb8e//Mu/YNu2bXj88ce5m2SUOH78OO6++260tbWhtLSURRkkHFkSfD4f3nvvPWzcuBErVqzAzTffDKvVqjsWDZHb7caf//xnvPbaa/jhD3+IFStWcG5hiC43suQKHoLVasWyZctw/fXX48UXX+w7oAIP+BoZlFLYunUr/v3f/73vlMm5ubm6Y0UdjizpS5RS2L59O0pLS7F48WKsXLkSNhv/TzWryspK/OY3v0FraysefPBBzJgxQ3ekiHa5kSXLkgbU0tKCl156CadPn8by5csxf/58zpqbSHNzM5577jls3boV3//+93H77bfz9wkCliUN22effYbS0lI0NzfjjjvuwOzZs2GxcL2gLl6vF6WlpfjDH/6AZcuWYfXq1UhOTtYdK2qwLGlElFI4cuQISktL0dXVhTvvvBMzZszgyoMw8vv92LZtG5577jlkZ2fjn/7pnzBhwgTdsaIOy5KCQimFiooKlJaWQimFO++8E8XFxSzNEOru7sbbb7+NV155Benp6fje976HmTNn8jsPEZYlBZVSCvv27UNpaSni4uJw++23o6ioiH/AQdTQ0IDS0lK88cYbKC4u5nFJw4RlSSGhlEJZWRm2bt2Kc+fOYfHixVi8eDHS0tJ0R4tYn3/+Of7617/iww8/xC233IK7774beXl5umPFDJYlhZRSCidPnsSWLVuwc+dOFBYW4sYbb0RRURHX0Brg9/uxZ88evPzyyzh+/DhWrVqFb37zm0hJSdEdLeawLClsenp6sGvXLmzZsgX19fVYvHgxFi1axFMWXMLv96OiogJbt27FBx98gKlTp2LevHm45ZZb4HA4dMeLWSxL0qKmpgZbtmzBjh07kJ+fjwULFqCoqAipqam6o2nh9/tx8OBBbNmyBR988AHS09Nx4403YvHixZzVNgmWJWnl8Xiwb98+fPzxx6ioqEB2djaKiopQXFyMwsLCqJ5V9/v9OHToELZu3Ypt27YhNTUVS5YswZIlS7g7qQmxLMk0fD4fKisrUV5ejvLycpw7dw7Tpk1DcXExiouLkZWVpTviiHg8HlRWVuLQoUM4ePAgGhsb0d7e3leQ+fn5uiPSZZiuLEVkFYCfA/gagJlKqQGbTURuBfA0ACuAPyilfm3k9VmWkaO1tRUVFRUoLy/HgQMH4HK5cM0112DMmDHIz89HQUEBEhMTdcccVEtLCw4fPoyDBw/i0KFDqKysRF5eHqZNm4Zp06Zh+vTpGDVqlO6YZJAZy/JrAPwA/g+ABwcqSxGxAjgO4CYANQD2ALhbKXXkSq/PsoxMSimcOHECR48exalTp3Dq1CmcOXMGTqezrzjz8/ORn5+PvLy8sB3gw+/3o7GxEefPn++7tLS0oKysDE1NTZgyZUpfMRYWFiIpKSksuSj4THeINqXUUQBX2oh5JoAqpdSJwLSvAFgJ4IplSZFJRDBx4kRMnDix7zGlFGpra3Hq1ClUV1ejrKwMr776Kurq6lBYWIje3l4kJyfD5XIhOTn5K7eTk5PhdDphsVjg8Xjg9Xrh8Xj6Ll6vF16vF263G16vFx0dHV8qxfPnz6O+vh4pKSkYNWoURo0ahZycHBQWFmL58uUYP34895WPEWY+9tYYAGf63a8BMGuwiUVkNYDVADBu3LjQJqOwEZG+kpo9e3bf4263G+fOnUNbWxva2trQ3t6O1tZWNDc3o7q6Gu3t7X2POxwO1NbWwmazwW63w263992+9LGMjAw4nU4UFhZi8eLFGDVqFLKysrg5D4WuLEXkfQADLaxZq5R608hLDPDYoMsMlFLPA3geuDAbbigkRSyHw8GVJRRWIStLpdTSEb5EDYD+21bkATg7wtckIhoWMy9s2QNgsoiMFxEHgLsAvKU5ExHFKC1lKSK3i0gNgDkA3hGRzYHHc0VkEwAopbwA1gDYDOAogFeVUod15CUi0rU2/HUArw/w+FkAy/vd3wRgUxijERENyMyz4UREpsGyJCIygGVJRGQAy5KIyACWJRGRASxLIiIDWJZERAawLImIDGBZEhEZwLIkIjKAZUlEZADLkojIAJYlEZEBLEsiIgNYlkREBrAsiYgMYFkSERnAsiQiMoBlSURkAMuSiMgAliURkQEsSyIiA1iWREQGsCyJiAxgWRIRGcCyJCIyQJRSujMEnYjUA6jW9PaZABo0vXco8POYX7R9Jp2fJ18plTXQE1FZljqJyF6lVInuHMHCz2N+0faZzPp5OBtORGQAy5KIyACWZfA9rztAkPHzmF+0fSZTfh4usyQiMoAjSyIiA1iWIyQiq0TksIj4RWTQNXgicquIfCYiVSLycDgzDoWIpIvI30SkMnCdNsh0p0TkoIgcEJG94c55JVf6vuWC3wae/1RErtOR0ygDn2eRiLQGfo8DIvJTHTmNEpEXRaRORA4N8rz5fh+lFC8juAD4GoCrAXwAoGSQaawAPgcwAYADQAWAKbqzD5L1cQAPB24/DOB/DzLdKQCZuvMO9/sGsBzAuwAEwGwAZbpzj/DzLAKwUXfWIXymhQCuA3BokOdN9/twZDlCSqmjSqnPrjDZTABVSqkTSik3gFcArAx9umFZCeBPgdt/AnCbvijDZuT7XgngP9UFuwCkisjocAc1KJL+/RiilNoOoOkyk5ju92FZhscYAGf63a8JPGZGOUqpcwAQuM4eZDoF4D0R2Sciq8OWzhgj33ck/SZGs84RkQoReVdEpoYnWsiY7vex6XzzSCEi7wMYNcBTa5VSbxp5iQEe07YZwuU+zxBeZp5S6qyIZAP4m4gcC4wWzMDI922q3+QKjGTdjwu76nWIyHIAbwCYHOpgIWS634dlaYBSaukIX6IGwNh+9/MAnB3haw7b5T6PiNSKyGil1LnAbE/dIK9xNnBdJyKv48KsolnK0sj3barf5AqumFUp1dbv9iYReVZEMpVSkbrPuOl+H86Gh8ceAJNFZLyIOADcBeAtzZkG8xaA7wZufxfAV0bOIpIkIq6LtwHcDGDAtZqaGPm+3wJwb2Ct62wArRcXP5jQFT+PiIwSEQncnokLf9uNYU8aPOb7fXSvYYr0C4DbceF/wV4AtQA2Bx7PBbCp33TLARzHhbWaa3XnvsznyQCwBUBl4Dr90s+DC2tlKwKXw2b8PAN93wB+AOAHgdsC4JnA8wcxyJYMZrkY+DxrAr9FBYBdAObqznyFz/MygHMAPIG/n/vN/vtwDx4iIgM4G05EZADLkojIAJYlEZEBLEsiIgNYlkREBrAsiYgMYFkSERnAsqSYICIzAsdFjA/sgXRYRKbpzkWRgxulU8wQkf8PQDyABAA1SqlfaY5EEYRlSTEjsF/1HgA9uLA7oE9zJIognA2nWJIOwAnAhQsjTCLDOLKkmCEib+HCUcbHAxitlFqjORJFEB7PkmKCiNwLwKuU+quIWAF8IiJLlFJbdWejyMCRJRGRAVxmSURkAMuSiMgAliURkQEsSyIiA1iWREQGsCyJiAxgWRIRGcCyJCIy4P8BRg91Y132fZ0AAAAASUVORK5CYII=\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",
      "1.224316435843165\n",
      "1.5054584365351353\n",
      "1.8574786700728483\n",
      "2.2982850231996075\n",
      "2.851433097550558\n",
      "3.5459854788258416\n",
      "4.414889626459959\n",
      "5.501873511232387\n",
      "6.866312669825766\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
}