{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7fb27b941602401d91542211134fc71a",
   "metadata": {
    "papermill": {
     "duration": 0.013567,
     "end_time": "2026-05-16T13:49:13.035955+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:13.022388+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# Integration and Plotting\n",
    "\n",
    "This tutorial covers integrating orbits in potentials, plotting their\n",
    "trajectories, accessing orbital quantities, and working with\n",
    "non-inertial reference frames."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "acae54e37e7d407bbb7b55eff062a284",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:13.061234Z",
     "iopub.status.busy": "2026-05-16T13:49:13.060974Z",
     "iopub.status.idle": "2026-05-16T13:49:15.477705Z",
     "shell.execute_reply": "2026-05-16T13:49:15.476865Z"
    },
    "papermill": {
     "duration": 2.431013,
     "end_time": "2026-05-16T13:49:15.479163+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:13.048150+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy\n",
    "from astropy import units\n",
    "from galpy.orbit import Orbit\n",
    "from galpy.potential import MWPotential2014, LogarithmicHaloPotential\n",
    "import warnings\n",
    "\n",
    "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n",
    "warnings.filterwarnings(\"ignore\", category=UserWarning)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a63283cbaf04dbcab1f6479b197f3a8",
   "metadata": {
    "papermill": {
     "duration": 0.012151,
     "end_time": "2026-05-16T13:49:15.506931+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:15.494780+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Basic integration\n",
    "\n",
    "Use `o.integrate(ts, pot)` to integrate an orbit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8dd0d8092fe74a7c96281538738b07e2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:15.533328Z",
     "iopub.status.busy": "2026-05-16T13:49:15.532903Z",
     "iopub.status.idle": "2026-05-16T13:49:15.555580Z",
     "shell.execute_reply": "2026-05-16T13:49:15.554370Z"
    },
    "papermill": {
     "duration": 0.036941,
     "end_time": "2026-05-16T13:49:15.556296+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:15.519355+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Integration complete. Final R = 1.0478229328266577\n"
     ]
    }
   ],
   "source": [
    "o = Orbit([1.0, 0.1, 1.0, 0.0, 0.1, 0.0])\n",
    "ts = numpy.linspace(0.0, 10.0, 10000)\n",
    "o.integrate(ts, MWPotential2014)\n",
    "print(\"Integration complete. Final R =\", o.R(ts[-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72eea5119410473aa328ad9291626812",
   "metadata": {
    "papermill": {
     "duration": 0.012081,
     "end_time": "2026-05-16T13:49:15.580957+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:15.568876+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Automatic time determination\n",
    "\n",
    "You can pass just the potential and galpy will integrate for ~10 dynamical times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8edb47106e1a46a883d545849b8ab81b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:15.606601Z",
     "iopub.status.busy": "2026-05-16T13:49:15.606364Z",
     "iopub.status.idle": "2026-05-16T13:49:15.875948Z",
     "shell.execute_reply": "2026-05-16T13:49:15.874851Z"
    },
    "papermill": {
     "duration": 0.283332,
     "end_time": "2026-05-16T13:49:15.876635+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:15.593303+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "o_auto = Orbit([1.0, 0.1, 1.0, 0.0, 0.1, 0.0])\n",
    "o_auto.integrate(MWPotential2014)\n",
    "o_auto.plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10185d26023b46108eb7d9f57d49d2b3",
   "metadata": {
    "papermill": {
     "duration": 0.012491,
     "end_time": "2026-05-16T13:49:15.902629+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:15.890138+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Physical units for time\n",
    "\n",
    "When using `ro=` and `vo=`, you can pass time arrays in physical units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8763a12b2bbd4a93a75aff182afb95dc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:15.928523Z",
     "iopub.status.busy": "2026-05-16T13:49:15.928306Z",
     "iopub.status.idle": "2026-05-16T13:49:15.980267Z",
     "shell.execute_reply": "2026-05-16T13:49:15.979324Z"
    },
    "papermill": {
     "duration": 0.066117,
     "end_time": "2026-05-16T13:49:15.981160+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:15.915043+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R at 5 Gyr = 7.704903471220543\n"
     ]
    }
   ],
   "source": [
    "o_phys = Orbit([1.0, 0.1, 1.0, 0.0, 0.1, 0.0], ro=8.0, vo=220.0)\n",
    "ts_phys = numpy.linspace(0.0, 5.0, 1000) * units.Gyr\n",
    "o_phys.integrate(ts_phys, MWPotential2014)\n",
    "print(\"R at 5 Gyr =\", o_phys.R(ts_phys[-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30e0fbf8",
   "metadata": {
    "papermill": {
     "duration": 0.012849,
     "end_time": "2026-05-16T13:49:16.007035+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:15.994186+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "<div class=\"alert alert-warning\">\n",
    "\n",
    "**Warning**\n",
    "\n",
    "When the integration times are not specified using a Quantity, they are assumed to be in natural units.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7623eae2785240b9bd12b16a66d81610",
   "metadata": {
    "papermill": {
     "duration": 0.013051,
     "end_time": "2026-05-16T13:49:16.033029+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:16.019978+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Parallel integration of multiple orbits\n",
    "\n",
    "Multi-orbit objects are integrated in parallel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7cdc8c89c7104fffa095e18ddfef8986",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:16.060537Z",
     "iopub.status.busy": "2026-05-16T13:49:16.060311Z",
     "iopub.status.idle": "2026-05-16T13:49:16.177758Z",
     "shell.execute_reply": "2026-05-16T13:49:16.176141Z"
    },
    "papermill": {
     "duration": 0.132615,
     "end_time": "2026-05-16T13:49:16.178802+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:16.046187+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "All 100 orbits integrated.\n",
      "R shape at all times: (100, 1001)\n"
     ]
    }
   ],
   "source": [
    "numpy.random.seed(42)\n",
    "vxvvs = numpy.column_stack(\n",
    "    [\n",
    "        numpy.random.uniform(0.8, 1.2, 100),\n",
    "        numpy.random.normal(0.0, 0.05, 100),\n",
    "        numpy.random.uniform(0.9, 1.1, 100),\n",
    "        numpy.random.normal(0.0, 0.05, 100),\n",
    "        numpy.random.normal(0.0, 0.05, 100),\n",
    "        numpy.random.uniform(0.0, 2 * numpy.pi, 100),\n",
    "    ]\n",
    ")\n",
    "os = Orbit(vxvvs)\n",
    "ts = numpy.linspace(0.0, 10.0, 1001)\n",
    "os.integrate(ts, MWPotential2014)\n",
    "print(\"All\", os.size, \"orbits integrated.\")\n",
    "print(\"R shape at all times:\", os.R(ts).shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b118ea5561624da68c537baed56e602f",
   "metadata": {
    "papermill": {
     "duration": 0.012222,
     "end_time": "2026-05-16T13:49:16.204296+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:16.192074+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Continuing integrations\n",
    "\n",
    "galpy supports *continuing* orbit integrations in both forward and backward time\n",
    "directions. For forward continuation, if the first time of the new integration\n",
    "matches the last time of the previous integration, the two are merged into a single\n",
    "continuous orbit. Backward continuation works similarly: if the first time of the new\n",
    "integration matches the first time of the previous one and goes in the opposite\n",
    "direction, the orbit is integrated backward and prepended.\n",
    "\n",
    "The two time arrays do not need the same number of points or spacing. The only\n",
    "requirement is that the starting time of the new array matches the appropriate\n",
    "endpoint of the existing one.\n",
    "\n",
    "Continuation is not supported when ``t`` is per-orbit (shape ``orbit.shape + (nt,)``); each per-orbit integrate restarts from the original initial conditions. It is also disabled after a ``bruteSOS`` or ``SOS`` call, which rewrite ``self.t`` into a non-standard (NaN-padded crossings) form."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "938c804e27f84196a10c8828c723f798",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:16.230561Z",
     "iopub.status.busy": "2026-05-16T13:49:16.230330Z",
     "iopub.status.idle": "2026-05-16T13:49:16.547448Z",
     "shell.execute_reply": "2026-05-16T13:49:16.546411Z"
    },
    "papermill": {
     "duration": 0.331379,
     "end_time": "2026-05-16T13:49:16.548189+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:16.216810+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time range now covers t = -5 to 10\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "o_cont = Orbit([1.0, 0.1, 1.0, 0.0, 0.1, 0.0])\n",
    "\n",
    "# Forward integration\n",
    "ts_fwd = numpy.linspace(0.0, 5.0, 5000)\n",
    "o_cont.integrate(ts_fwd, MWPotential2014)\n",
    "\n",
    "# Continue forward\n",
    "ts_ext = numpy.linspace(5.0, 10.0, 5000)\n",
    "o_cont.integrate(ts_ext, MWPotential2014)\n",
    "\n",
    "# Backward integration from t=0\n",
    "ts_bwd = numpy.linspace(0.0, -5.0, 5000)\n",
    "o_cont.integrate(ts_bwd, MWPotential2014)\n",
    "\n",
    "print(\"Time range now covers t = -5 to 10\")\n",
    "o_cont.plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "504fb2a444614c0babb325280ed9130a",
   "metadata": {
    "papermill": {
     "duration": 0.013368,
     "end_time": "2026-05-16T13:49:16.575166+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:16.561798+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Displaying orbits: various projections\n",
    "\n",
    "Use `o.plot()` with `d1` and `d2` to select projections."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "59bbdb311c014d738909a11f9e486628",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:16.603252Z",
     "iopub.status.busy": "2026-05-16T13:49:16.602941Z",
     "iopub.status.idle": "2026-05-16T13:49:16.622777Z",
     "shell.execute_reply": "2026-05-16T13:49:16.621835Z"
    },
    "papermill": {
     "duration": 0.034868,
     "end_time": "2026-05-16T13:49:16.623482+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:16.588614+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "o = Orbit([1.0, 0.1, 1.0, 0.0, 0.1, 0.0])\n",
    "ts = numpy.linspace(0.0, 10.0, 10000)\n",
    "o.integrate(ts, MWPotential2014)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc5362ed",
   "metadata": {
    "papermill": {
     "duration": 0.013618,
     "end_time": "2026-05-16T13:49:16.650945+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:16.637327+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "The default projection is $R$ vs. $z$ (meridional plane):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b43b363d81ae4b689946ece5c682cd59",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:16.679012Z",
     "iopub.status.busy": "2026-05-16T13:49:16.678764Z",
     "iopub.status.idle": "2026-05-16T13:49:16.859267Z",
     "shell.execute_reply": "2026-05-16T13:49:16.858426Z"
    },
    "papermill": {
     "duration": 0.195866,
     "end_time": "2026-05-16T13:49:16.860348+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:16.664482+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Default: R vs. z (meridional plane)\n",
    "o.plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b0341ed",
   "metadata": {
    "papermill": {
     "duration": 0.013948,
     "end_time": "2026-05-16T13:49:16.888422+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:16.874474+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Face-on view in the disk plane (`x` vs. `y`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8a65eabff63a45729fe45fb5ade58bdc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:16.917947Z",
     "iopub.status.busy": "2026-05-16T13:49:16.917714Z",
     "iopub.status.idle": "2026-05-16T13:49:17.066578Z",
     "shell.execute_reply": "2026-05-16T13:49:17.065371Z"
    },
    "papermill": {
     "duration": 0.164883,
     "end_time": "2026-05-16T13:49:17.067339+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:16.902456+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Face-on view: x vs. y\n",
    "o.plot(d1=\"x\", d2=\"y\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "161fe1c0",
   "metadata": {
    "papermill": {
     "duration": 0.013674,
     "end_time": "2026-05-16T13:49:17.095138+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:17.081464+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Phase-space projections (`R` vs. `vR`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c3933fab20d04ec698c2621248eb3be0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:17.124052Z",
     "iopub.status.busy": "2026-05-16T13:49:17.123807Z",
     "iopub.status.idle": "2026-05-16T13:49:17.340181Z",
     "shell.execute_reply": "2026-05-16T13:49:17.339449Z"
    },
    "papermill": {
     "duration": 0.232395,
     "end_time": "2026-05-16T13:49:17.341394+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:17.108999+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Phase space: R vs. vR\n",
    "o.plot(d1=\"R\", d2=\"vR\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07fefe67",
   "metadata": {
    "papermill": {
     "duration": 0.017865,
     "end_time": "2026-05-16T13:49:17.374139+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:17.356274+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Sky coordinates can also be plotted when `ro` and `vo` are set. Here we plot Galactic `(l, b)`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4dd4641cc4064e0191573fe9c69df29b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:17.411705Z",
     "iopub.status.busy": "2026-05-16T13:49:17.411480Z",
     "iopub.status.idle": "2026-05-16T13:49:17.650052Z",
     "shell.execute_reply": "2026-05-16T13:49:17.648891Z"
    },
    "papermill": {
     "duration": 0.258144,
     "end_time": "2026-05-16T13:49:17.650780+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:17.392636+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sky coordinates (requires ro/vo)\n",
    "o_sky = Orbit([1.0, 0.1, 1.0, 0.0, 0.1, 0.0], ro=8.0, vo=220.0)\n",
    "o_sky.integrate(ts, MWPotential2014)\n",
    "o_sky.plot(d1=\"ll\", d2=\"bb\", marker=\"o\", ms=5, ls=\"None\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "991595f7",
   "metadata": {
    "papermill": {
     "duration": 0.016933,
     "end_time": "2026-05-16T13:49:17.685085+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:17.668152+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "And equatorial `(RA, Dec)`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8309879909854d7188b41380fd92a7c3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:17.719431Z",
     "iopub.status.busy": "2026-05-16T13:49:17.719206Z",
     "iopub.status.idle": "2026-05-16T13:49:17.959906Z",
     "shell.execute_reply": "2026-05-16T13:49:17.958650Z"
    },
    "papermill": {
     "duration": 0.258873,
     "end_time": "2026-05-16T13:49:17.960601+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:17.701728+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "o_sky.plot(d1=\"ra\", d2=\"dec\", marker=\"o\", ms=5, ls=\"None\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ed186c9a28b402fb0bc4494df01f08d",
   "metadata": {
    "papermill": {
     "duration": 0.017324,
     "end_time": "2026-05-16T13:49:17.995848+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:17.978524+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Custom expression plotting\n",
    "\n",
    "You can use arbitrary expressions in `o.plot()` calls using `numexpr` syntax (requires the `numexpr` package). For example, `o.plot(d1=\"t\", d2=\"R*cos(phi)\")` will evaluate the expression and plot it directly. If `numexpr` is not installed, you can install it with `pip install numexpr`.\n",
    "\n",
    "Let's demonstrate both approaches:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "cb1e1581032b452c9409d6c6813c49d1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:18.032533Z",
     "iopub.status.busy": "2026-05-16T13:49:18.032309Z",
     "iopub.status.idle": "2026-05-16T13:49:18.242668Z",
     "shell.execute_reply": "2026-05-16T13:49:18.241651Z"
    },
    "papermill": {
     "duration": 0.229986,
     "end_time": "2026-05-16T13:49:18.243347+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:18.013361+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numexpr\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "# Using numexpr expressions directly in o.plot()\n",
    "o.plot(d1=\"t\", d2=\"R*cos(phi)*sin(phi)\")\n",
    "plt.title(r\"Using numexpr: $R\\,\\cos\\phi*\\sin\\phi$ vs. $t$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cddf14fe",
   "metadata": {
    "papermill": {
     "duration": 0.015838,
     "end_time": "2026-05-16T13:49:18.276661+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:18.260823+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Without `numexpr`, you can specify the computation manually using a lambda function of time given as ``d1`` or ``d2``, which is useful for functions that cannot be parsed by ``numexpr``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f73e762f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:18.310542Z",
     "iopub.status.busy": "2026-05-16T13:49:18.310311Z",
     "iopub.status.idle": "2026-05-16T13:49:18.473794Z",
     "shell.execute_reply": "2026-05-16T13:49:18.472793Z"
    },
    "papermill": {
     "duration": 0.181868,
     "end_time": "2026-05-16T13:49:18.474433+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:18.292565+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "o.plot(\n",
    "    d1=\"t\",\n",
    "    d2=lambda t: o.R(t) * numpy.cos(o.phi(t)) * numpy.sin(o.phi(t)),\n",
    "    ylabel=r\"$R\\,\\cos\\phi\\,\\sin\\phi$\",\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43a35ea4",
   "metadata": {
    "papermill": {
     "duration": 0.015105,
     "end_time": "2026-05-16T13:49:18.505366+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:18.490261+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Animating the orbit\n",
    "\n",
    "In a [jupyter notebook](http://jupyter.org) or in [jupyterlab](http://jupyterlab.readthedocs.io/en/stable/) (jupyterlab versions >= 0.33) you can also create an animation of an orbit *after* you have integrated it. For example, consider the following orbit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "837cf516",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:18.536402Z",
     "iopub.status.busy": "2026-05-16T13:49:18.536193Z",
     "iopub.status.idle": "2026-05-16T13:49:18.542839Z",
     "shell.execute_reply": "2026-05-16T13:49:18.541761Z"
    },
    "papermill": {
     "duration": 0.023361,
     "end_time": "2026-05-16T13:49:18.543707+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:18.520346+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "lp = LogarithmicHaloPotential(normalize=1.0)\n",
    "op = Orbit([1.0, 0.1, 1.1, 0.0, 0.1, 0.0], ro=8.0, vo=220.0)\n",
    "op.integrate(ts, lp)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60bfdd2a",
   "metadata": {
    "papermill": {
     "duration": 0.015893,
     "end_time": "2026-05-16T13:49:18.575640+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:18.559747+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "If we then do ``op.animate()`` we get the following"
   ]
  },
  {
   "cell_type": "raw",
   "id": "4f7a7408",
   "metadata": {
    "papermill": {
     "duration": 0.014955,
     "end_time": "2026-05-16T13:49:18.606404+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:18.591449+00:00",
     "status": "completed"
    },
    "tags": [],
    "vscode": {
     "languageId": "raw"
    }
   },
   "source": [
    "<style>\n",
    "  .galpybutton {\n",
    "      background-color:#ffffff;\n",
    "      -moz-border-radius:16px;\n",
    "      -webkit-border-radius:16px;\n",
    "      border-radius:16px;\n",
    "      border:1px solid #1f77b4;\n",
    "      display:inline-block;\n",
    "      cursor:pointer;\n",
    "      color:#1f77b4;\n",
    "      font-family:Courier;\n",
    "      font-size:17px;\n",
    "      padding:8px 10px;\n",
    "      text-decoration:none;\n",
    "      text-shadow:0px 1px 0px #2f6627;\n",
    "  }\n",
    "  .galpybutton:hover {\n",
    "      background-color:#ffffff;\n",
    "  }\n",
    "  .galpybutton:active {\n",
    "      position:relative;\n",
    "      top:1px;\n",
    "  }\n",
    "  .galpybutton:focus{\n",
    "      outline:0;\n",
    "  }\n",
    "  </style>\n",
    "\n",
    "  <div id='galpy-knpeaurozjomyixuoikkmtea' style='width:600px;height:400px;'></div>\n",
    "  <div class=\"controlbutton\" id=\"galpy-knpeaurozjomyixuoikkmtea-play\" style=\"margin-left:70px;display: inline-block;\">\n",
    "  <button class=\"galpybutton\" id=\"galpy-knpeaurozjomyixuoikkmtea-playpause\" style='width: 108px !important'>Play</button></div>\n",
    "  <div class=\"controlbutton\" id=\"galpy-knpeaurozjomyixuoikkmtea-timestwo\" style=\"margin-left:10px;display: inline-block;\">\n",
    "  <button class=\"galpybutton\">Speed<font face=\"Arial\">&thinsp;</font>x<font face=\"Arial\">&thinsp;</font>2</button></div>\n",
    "  <div class=\"controlbutton\" id=\"galpy-knpeaurozjomyixuoikkmtea-timeshalf\" style=\"margin-left:10px;display: inline-block;\">\n",
    "  <button class=\"galpybutton\">Speed<font face=\"Arial\">&thinsp;</font>/<font face=\"Arial\">&thinsp;</font>2</button></div>\n",
    "  <div class=\"controlbutton\" id=\"galpy-knpeaurozjomyixuoikkmtea-replay\" style=\"margin-left:10px;display: inline-block;\">\n",
    "  <button class=\"galpybutton\">Replay</button></div>\n",
    "\n",
    "  <script src=\"https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js\"></script>\n",
    "  <script src=\"https://ajax.googleapis.com/ajax/libs/jquery/3.6.1/jquery.min.js\"></script>\n",
    "\n",
    "  <script>\n",
    "  require.config({\n",
    "    paths: {\n",
    "      Plotly: 'https://cdnjs.cloudflare.com/ajax/libs/plotly.js/2.16.4/plotly.min',\n",
    "    }\n",
    "  });\n",
    "  </script>\n",
    "\n",
    "  <script>\n",
    "  require(['Plotly'], function (Plotly) {\n",
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    "    let layout = {\n",
    "    xaxis: {\n",
    "      title: 'R (kpc)',\n",
    "      domain: [0,1],\n",
    "  },\n",
    "    yaxis: {title: 'z (kpc)'},\n",
    "    margin: {t: 20},\n",
    "    hovermode: 'closest',\n",
    "    showlegend: false,\n",
    "  };\n",
    "    let numPerFrame= 5;\n",
    "    let cnt= 1;\n",
    "    let interval;\n",
    "    let trace_slice_len;\n",
    "    let trace_slice_begin;\n",
    "    let trace_slice_end;\n",
    "\n",
    "    setup_trace();\n",
    "\n",
    "    $('.controlbutton button').click(function() {\n",
    "      let button_type= this.parentNode.id;\n",
    "      if ( button_type === 'galpy-knpeaurozjomyixuoikkmtea-play' ) {\n",
    "        clearInterval(interval);\n",
    "        interval= animate_trace();\n",
    "        document.querySelector('#galpy-knpeaurozjomyixuoikkmtea-playpause').textContent = 'Pause';\n",
    "        document.getElementById('galpy-knpeaurozjomyixuoikkmtea-play').id = 'galpy-knpeaurozjomyixuoikkmtea-pause';\n",
    "      }\n",
    "      else if ( button_type === 'galpy-knpeaurozjomyixuoikkmtea-pause' ) {\n",
    "          clearInterval(interval);\n",
    "          document.querySelector('#galpy-knpeaurozjomyixuoikkmtea-playpause').textContent = 'Resume';\n",
    "          document.getElementById('galpy-knpeaurozjomyixuoikkmtea-pause').id = 'galpy-knpeaurozjomyixuoikkmtea-play';\n",
    "          }\n",
    "      else if ( button_type === 'galpy-knpeaurozjomyixuoikkmtea-timestwo' ) {\n",
    "        cnt/= 2;\n",
    "        numPerFrame*= 2;\n",
    "      }\n",
    "      else if ( button_type === 'galpy-knpeaurozjomyixuoikkmtea-timeshalf' ) {\n",
    "        cnt*= 2;\n",
    "        numPerFrame/= 2;\n",
    "      }\n",
    "      else if ( button_type === 'galpy-knpeaurozjomyixuoikkmtea-replay' ) {\n",
    "        $(\"#galpy-knpeaurozjomyixuoikkmtea-playpause\").removeAttr('disabled');\n",
    "        document.querySelector('#galpy-knpeaurozjomyixuoikkmtea-playpause').textContent = 'Pause';\n",
    "        try { // doesn't exist if replay with pressing pause\n",
    "        document.getElementById('galpy-knpeaurozjomyixuoikkmtea-play').id = 'galpy-knpeaurozjomyixuoikkmtea-pause';\n",
    "        }\n",
    "        catch (err) {\n",
    "        }\n",
    "        cnt= 1;\n",
    "        try { // doesn't exist if animation has already ended\n",
    "          Plotly.deleteTraces('galpy-knpeaurozjomyixuoikkmtea',[1, ]);\n",
    "        }\n",
    "        catch (err) {\n",
    "        }\n",
    "          Plotly.deleteTraces('galpy-knpeaurozjomyixuoikkmtea', [0]);\n",
    "        clearInterval(interval);\n",
    "        setup_trace();\n",
    "        interval= animate_trace();\n",
    "      }\n",
    "    });\n",
    "\n",
    "    function setup_trace() {\n",
    "\n",
    "      let trace1= {\n",
    "        x: data.x1_0.slice(0,numPerFrame),\n",
    "        y: data.y1_0.slice(0,numPerFrame),\n",
    "        customdata: data.time,\n",
    "        hovertemplate: '<b>Object 0</b>' + '<br><b>R (kpc)</b>: %{x:.2f}' + '<br><b>z (kpc)</b>: %{y:.2f}' + '<br><b>t (Gyr)</b>: %{customdata:.2f}',\n",
    "        name: '',\n",
    "        mode: 'lines',\n",
    "        line: {\n",
    "          shape: 'spline',\n",
    "          width: 0.8,\n",
    "          color: '#1f77b4',\n",
    "         },\n",
    "        type: \"scattergl\",\n",
    "      };\n",
    "\n",
    "      let trace2= {\n",
    "        x: data.x1_0.slice(0,numPerFrame),\n",
    "        y: data.y1_0.slice(0,numPerFrame),\n",
    "        customdata: data.time,\n",
    "        hovertemplate: '<b>Object 0 (Current location)</b>' + '<br><b>R (kpc)</b>: %{x:.2f}' + '<br><b>z (kpc)</b>: %{y:.2f}' + '<br><b>t (Gyr)</b>: %{customdata:.2f}',\n",
    "        name: '',\n",
    "        mode: 'lines',\n",
    "        line: {\n",
    "          shape: 'spline',\n",
    "          width: 3.,\n",
    "          color: '#1f77b4',\n",
    "          },\n",
    "        type: \"scattergl\",\n",
    "      };\n",
    "\n",
    "\n",
    "\n",
    "      let traces= [trace1,trace2];\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "      Plotly.newPlot('galpy-knpeaurozjomyixuoikkmtea',traces,layout,{staticPlot: false});\n",
    "    }\n",
    "\n",
    "    function animate_trace() {\n",
    "      return setInterval(function() {\n",
    "        // Make sure narrow and thick trace end in the same\n",
    "        // and the highlighted length has constant length\n",
    "        trace_slice_len= Math.floor(numPerFrame);\n",
    "        if ( trace_slice_len < 1) trace_slice_len= 1;\n",
    "        trace_slice_begin= Math.floor(cnt*numPerFrame);\n",
    "        trace_slice_end= Math.floor(Math.min(cnt*numPerFrame+trace_slice_len,data.x1_0.length-1));\n",
    "        traces = {x: [data.x1_0.slice(trace_slice_begin,trace_slice_end), ], y: [data.y1_0.slice(trace_slice_begin,trace_slice_end), ], customdata:[data.time.slice(trace_slice_begin,trace_slice_end), ]};\n",
    "        Plotly.extendTraces('galpy-knpeaurozjomyixuoikkmtea', traces, [0, ]);\n",
    "        trace_slice_begin-= trace_slice_len;\n",
    "        traces = {x: [data.x1_0.slice(trace_slice_begin,trace_slice_end), ], y: [data.y1_0.slice(trace_slice_begin,trace_slice_end), ], customdata:[data.time.slice(trace_slice_begin,trace_slice_end), ]};\n",
    "        Plotly.restyle('galpy-knpeaurozjomyixuoikkmtea', traces, [1, ]);\n",
    "        cnt+= 1;\n",
    "        // need to clearInterval here otherwise the pan/zoom/rotate is bugged somehow at the end of play\n",
    "        if (cnt*numPerFrame+trace_slice_len>data.x1_0.length) {\n",
    "            document.getElementById(\"galpy-knpeaurozjomyixuoikkmtea-playpause\").disabled = \"disabled\";\n",
    "            document.querySelector('#galpy-knpeaurozjomyixuoikkmtea-playpause').textContent = 'Finished!';\n",
    "            // making sure the whole orbits is plotted when finished\n",
    "            trace_slice_begin = trace_slice_end;\n",
    "            trace_slice_end = -1;\n",
    "            traces = {x: [data.x1_0.slice(trace_slice_begin,trace_slice_end), ], y: [data.y1_0.slice(trace_slice_begin,trace_slice_end), ], customdata:[data.time.slice(trace_slice_begin,trace_slice_end), ]};\n",
    "            Plotly.extendTraces('galpy-knpeaurozjomyixuoikkmtea', traces, [0, ]);\n",
    "            // make sure trace heads are gone when finished playing, sometimes they will stay around\n",
    "            Plotly.deleteTraces('galpy-knpeaurozjomyixuoikkmtea', [1, ]);\n",
    "            clearInterval(interval);\n",
    "        };\n",
    "          }, 30);\n",
    "      }\n",
    "  });\n",
    "  </script>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b881565b",
   "metadata": {
    "papermill": {
     "duration": 0.014983,
     "end_time": "2026-05-16T13:49:18.636515+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:18.621532+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "<div class=\"alert alert-info\">\n",
    "\n",
    "**Tip**\n",
    "\n",
    "There is currently no option to save the animation within ``galpy``, but you could use screen capture software (for example, QuickTime's [Screen Recording](https://support.apple.com/kb/ph5882?locale=en_CA) feature) to record your screen while the animation is running and save it as a video.\n",
    "\n",
    "</div>\n",
    "\n",
    "``animate`` has options to specify the width and height of the resulting animation, and it can also animate up to three projections of an orbit at the same time. For example, we can look at the orbit in both (x,y) and (R,z) at the same time with ``op.animate(d1=['x','R'],d2=['y','z'],width=800)``, which gives"
   ]
  },
  {
   "cell_type": "raw",
   "id": "6ff006f3",
   "metadata": {
    "papermill": {
     "duration": 0.015957,
     "end_time": "2026-05-16T13:49:18.668262+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:18.652305+00:00",
     "status": "completed"
    },
    "tags": [],
    "vscode": {
     "languageId": "raw"
    }
   },
   "source": [
    "<style>\n",
    "  .galpybutton {\n",
    "      background-color:#ffffff;\n",
    "      -moz-border-radius:16px;\n",
    "      -webkit-border-radius:16px;\n",
    "      border-radius:16px;\n",
    "      border:1px solid #1f77b4;\n",
    "      display:inline-block;\n",
    "      cursor:pointer;\n",
    "      color:#1f77b4;\n",
    "      font-family:Courier;\n",
    "      font-size:17px;\n",
    "      padding:8px 10px;\n",
    "      text-decoration:none;\n",
    "      text-shadow:0px 1px 0px #2f6627;\n",
    "  }\n",
    "  .galpybutton:hover {\n",
    "      background-color:#ffffff;\n",
    "  }\n",
    "  .galpybutton:active {\n",
    "      position:relative;\n",
    "      top:1px;\n",
    "  }\n",
    "  .galpybutton:focus{\n",
    "      outline:0;\n",
    "  }\n",
    "  </style>\n",
    "\n",
    "  <div id='galpy-inbxvjdspcnngdiraredcdou' style='width:800px;height:400px;'></div>\n",
    "  <div class=\"controlbutton\" id=\"galpy-inbxvjdspcnngdiraredcdou-play\" style=\"margin-left:170px;display: inline-block;\">\n",
    "  <button class=\"galpybutton\" id=\"galpy-inbxvjdspcnngdiraredcdou-playpause\"  style='width: 108px !important'>Play</button></div>\n",
    "  <div class=\"controlbutton\" id=\"galpy-inbxvjdspcnngdiraredcdou-timestwo\" style=\"margin-left:10px;display: inline-block;\">\n",
    "  <button class=\"galpybutton\">Speed<font face=\"Arial\">&thinsp;</font>x<font face=\"Arial\">&thinsp;</font>2</button></div>\n",
    "  <div class=\"controlbutton\" id=\"galpy-inbxvjdspcnngdiraredcdou-timeshalf\" style=\"margin-left:10px;display: inline-block;\">\n",
    "  <button class=\"galpybutton\">Speed<font face=\"Arial\">&thinsp;</font>/<font face=\"Arial\">&thinsp;</font>2</button></div>\n",
    "  <div class=\"controlbutton\" id=\"galpy-inbxvjdspcnngdiraredcdou-replay\" style=\"margin-left:10px;display: inline-block;\">\n",
    "  <button class=\"galpybutton\">Replay</button></div>\n",
    "\n",
    "  <script src=\"https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js\"></script>\n",
    "  <script src=\"https://ajax.googleapis.com/ajax/libs/jquery/3.6.1/jquery.min.js\"></script>\n",
    "\n",
    "\n",
    "  <script>\n",
    "  require.config({\n",
    "    paths: {\n",
    "      Plotly: 'https://cdnjs.cloudflare.com/ajax/libs/plotly.js/2.16.4/plotly.min',\n",
    "    }\n",
    "  });\n",
    "  </script>\n",
    "\n",
    "  <script>\n",
    "  require(['Plotly'], function (Plotly) {\n",
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    "    let layout = {\n",
    "    xaxis: {\n",
    "      title: 'x (kpc)',\n",
    "      domain: [0,0.45],\n",
    "  },\n",
    "    yaxis: {title: 'y (kpc)'},\n",
    "    margin: {t: 20},\n",
    "    hovermode: 'closest',\n",
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    "      domain: [0.55,1],\n",
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    "    yaxis2: {\n",
    "      title: 'z (kpc)',\n",
    "      anchor: 'x2',\n",
    "  },\n",
    "  };\n",
    "    let numPerFrame= 5;\n",
    "    let cnt= 1;\n",
    "    let interval;\n",
    "    let trace_slice_len;\n",
    "    let trace_slice_begin;\n",
    "    let trace_slice_end;\n",
    "\n",
    "    setup_trace();\n",
    "\n",
    "    $('.controlbutton button').click(function() {\n",
    "      let button_type= this.parentNode.id;\n",
    "      if ( button_type === 'galpy-inbxvjdspcnngdiraredcdou-play' ) {\n",
    "        clearInterval(interval);\n",
    "        interval= animate_trace();\n",
    "        document.querySelector('#galpy-inbxvjdspcnngdiraredcdou-playpause').textContent = 'Pause';\n",
    "        document.getElementById('galpy-inbxvjdspcnngdiraredcdou-play').id = 'galpy-inbxvjdspcnngdiraredcdou-pause';\n",
    "      }\n",
    "      else if ( button_type === 'galpy-inbxvjdspcnngdiraredcdou-pause' ) {\n",
    "          clearInterval(interval);\n",
    "          document.querySelector('#galpy-inbxvjdspcnngdiraredcdou-playpause').textContent = 'Resume';\n",
    "          document.getElementById('galpy-inbxvjdspcnngdiraredcdou-pause').id = 'galpy-inbxvjdspcnngdiraredcdou-play';\n",
    "          }\n",
    "      else if ( button_type === 'galpy-inbxvjdspcnngdiraredcdou-timestwo' ) {\n",
    "        cnt/= 2;\n",
    "        numPerFrame*= 2;\n",
    "      }\n",
    "      else if ( button_type === 'galpy-inbxvjdspcnngdiraredcdou-timeshalf' ) {\n",
    "        cnt*= 2;\n",
    "        numPerFrame/= 2;\n",
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    "      else if ( button_type === 'galpy-inbxvjdspcnngdiraredcdou-replay' ) {\n",
    "        $(\"#galpy-inbxvjdspcnngdiraredcdou-playpause\").removeAttr('disabled');\n",
    "        document.querySelector('#galpy-inbxvjdspcnngdiraredcdou-playpause').textContent = 'Pause';\n",
    "        try { // doesn't exist if replay with pressing pause\n",
    "        document.getElementById('galpy-inbxvjdspcnngdiraredcdou-play').id = 'galpy-inbxvjdspcnngdiraredcdou-pause';\n",
    "        }\n",
    "        catch (err) {\n",
    "        }\n",
    "        cnt= 1;\n",
    "        try { // doesn't exist if animation has already ended\n",
    "          Plotly.deleteTraces('galpy-inbxvjdspcnngdiraredcdou',[1, 3, ]);\n",
    "        }\n",
    "        catch (err) {\n",
    "        }\n",
    "          Plotly.deleteTraces('galpy-inbxvjdspcnngdiraredcdou', [0, 1]);\n",
    "        clearInterval(interval);\n",
    "        setup_trace();\n",
    "        interval= animate_trace();\n",
    "      }\n",
    "    });\n",
    "\n",
    "    function setup_trace() {\n",
    "\n",
    "      let trace1= {\n",
    "        x: data.x1_0.slice(0,numPerFrame),\n",
    "        y: data.y1_0.slice(0,numPerFrame),\n",
    "        customdata: data.time,\n",
    "        hovertemplate: '<b>Object 0</b>' + '<br><b>x (kpc)</b>: %{x:.2f}' + '<br><b>y (kpc)</b>: %{y:.2f}' + '<br><b>t (Gyr)</b>: %{customdata:.2f}',\n",
    "        name: '',\n",
    "        mode: 'lines',\n",
    "        line: {\n",
    "          shape: 'spline',\n",
    "          width: 0.8,\n",
    "          color: '#1f77b4',\n",
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    "        y: data.y1_0.slice(0,numPerFrame),\n",
    "        customdata: data.time,\n",
    "        hovertemplate: '<b>Object 0 (Current location)</b>' + '<br><b>x (kpc)</b>: %{x:.2f}' + '<br><b>y (kpc)</b>: %{y:.2f}' + '<br><b>t (Gyr)</b>: %{customdata:.2f}',\n",
    "        name: '',\n",
    "        mode: 'lines',\n",
    "        line: {\n",
    "          shape: 'spline',\n",
    "          width: 3.,\n",
    "          color: '#1f77b4',\n",
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    "        type: \"scattergl\",\n",
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    "\n",
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    "      let trace3= {\n",
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    "        y: data.y2_0.slice(0,numPerFrame),\n",
    "        customdata: data.time,\n",
    "        hovertemplate: '<b>Object 0</b>' + '<br><b>R (kpc)</b>: %{x:.2f}' + '<br><b>z (kpc)</b>: %{y:.2f}' + '<br><b>t (Gyr)</b>: %{customdata:.2f}',\n",
    "        name: '',\n",
    "        xaxis: 'x2',\n",
    "        yaxis: 'y2',\n",
    "        mode: 'lines',\n",
    "        line: {\n",
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    "          width: 0.8,\n",
    "          color: '#1f77b4',\n",
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    "        type: \"scattergl\",\n",
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    "        x: data.x2_0.slice(0,numPerFrame),\n",
    "        y: data.y2_0.slice(0,numPerFrame),\n",
    "        customdata: data.time,\n",
    "        hovertemplate: '<b>Object 0 (Current location)</b>' + '<br><b>R (kpc)</b>: %{x:.2f}' + '<br><b>z (kpc)</b>: %{y:.2f}' + '<br><b>t (Gyr)</b>: %{customdata:.2f}',\n",
    "        name: '',\n",
    "        xaxis: 'x2',\n",
    "        yaxis: 'y2',\n",
    "        mode: 'lines',\n",
    "        line: {\n",
    "          shape: 'spline',\n",
    "          width: 3.,\n",
    "          color: '#1f77b4',\n",
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    "        type: \"scattergl\",\n",
    "      };\n",
    "\n",
    "\n",
    "\n",
    "      let traces= [trace1,trace2,trace3,trace4];\n",
    "\n",
    "\n",
    "      Plotly.newPlot('galpy-inbxvjdspcnngdiraredcdou',traces,layout,{staticPlot: false});\n",
    "    }\n",
    "\n",
    "    function animate_trace() {\n",
    "      return setInterval(function() {\n",
    "        // Make sure narrow and thick trace end in the same\n",
    "        // and the highlighted length has constant length\n",
    "        trace_slice_len= Math.floor(numPerFrame);\n",
    "        if ( trace_slice_len < 1) trace_slice_len= 1;\n",
    "        trace_slice_begin= Math.floor(cnt*numPerFrame);\n",
    "        trace_slice_end= Math.floor(Math.min(cnt*numPerFrame+trace_slice_len,data.x1_0.length-1));\n",
    "        traces = {x: [data.x1_0.slice(trace_slice_begin,trace_slice_end), data.x2_0.slice(trace_slice_begin,trace_slice_end), ], y: [data.y1_0.slice(trace_slice_begin,trace_slice_end), data.y2_0.slice(trace_slice_begin,trace_slice_end), ], customdata:[data.time.slice(trace_slice_begin,trace_slice_end), data.time.slice(trace_slice_begin,trace_slice_end), ]};\n",
    "        Plotly.extendTraces('galpy-inbxvjdspcnngdiraredcdou', traces, [0, 2, ]);\n",
    "        trace_slice_begin-= trace_slice_len;\n",
    "        traces = {x: [data.x1_0.slice(trace_slice_begin,trace_slice_end), data.x2_0.slice(trace_slice_begin,trace_slice_end), ], y: [data.y1_0.slice(trace_slice_begin,trace_slice_end), data.y2_0.slice(trace_slice_begin,trace_slice_end), ], customdata:[data.time.slice(trace_slice_begin,trace_slice_end), data.time.slice(trace_slice_begin,trace_slice_end), ]};\n",
    "        Plotly.restyle('galpy-inbxvjdspcnngdiraredcdou', traces, [1, 3, ]);\n",
    "        cnt+= 1;\n",
    "        // need to clearInterval here otherwise the pan/zoom/rotate is bugged somehow at the end of play\n",
    "        if (cnt*numPerFrame+trace_slice_len>data.x1_0.length) {\n",
    "            document.getElementById(\"galpy-inbxvjdspcnngdiraredcdou-playpause\").disabled = \"disabled\";\n",
    "            document.querySelector('#galpy-inbxvjdspcnngdiraredcdou-playpause').textContent = 'Finished!';\n",
    "            // making sure the whole orbits is plotted when finished\n",
    "            trace_slice_begin = trace_slice_end;\n",
    "            trace_slice_end = -1;\n",
    "            traces = {x: [data.x1_0.slice(trace_slice_begin,trace_slice_end), data.x2_0.slice(trace_slice_begin,trace_slice_end), ], y: [data.y1_0.slice(trace_slice_begin,trace_slice_end), data.y2_0.slice(trace_slice_begin,trace_slice_end), ], customdata:[data.time.slice(trace_slice_begin,trace_slice_end), data.time.slice(trace_slice_begin,trace_slice_end), ]};\n",
    "            Plotly.extendTraces('galpy-inbxvjdspcnngdiraredcdou', traces, [0, 2, ]);\n",
    "            // make sure trace heads are gone when finished playing, sometimes they will stay around\n",
    "            Plotly.deleteTraces('galpy-inbxvjdspcnngdiraredcdou', [1, 3, ]);\n",
    "            clearInterval(interval);\n",
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     "end_time": "2026-05-16T13:49:18.698908+00:00",
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     "start_time": "2026-05-16T13:49:18.683762+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "\n",
    "You can also animate orbit in 3D with an optional Milky Way galaxy centered at the origin with ``op.animate3d(mw_plane_bg=True)``, which gives\n"
   ]
  },
  {
   "cell_type": "raw",
   "id": "69c79251",
   "metadata": {
    "papermill": {
     "duration": 0.015892,
     "end_time": "2026-05-16T13:49:18.731019+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:18.715127+00:00",
     "status": "completed"
    },
    "tags": [],
    "vscode": {
     "languageId": "raw"
    }
   },
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    "      let layout = {\n",
    "              scene:{\n",
    "                  // force the scene always look like a cube\n",
    "                  aspectmode: 'cube',\n",
    "                  xaxis: {\n",
    "                      title: 'x (kpc)',\n",
    "                      domain: [0,1],\n",
    "                          },\n",
    "                  yaxis: {title: 'y (kpc)'},\n",
    "                  zaxis: {title: 'z (kpc)'},},\n",
    "                  margin: {t: 20},\n",
    "                  hovermode: 'closest',\n",
    "                  showlegend: false,\n",
    "                  };\n",
    "      let numPerFrame= 5;\n",
    "      let cnt= 1;\n",
    "      let interval;\n",
    "      let trace_slice_len;\n",
    "      let trace_slice_begin;\n",
    "      let trace_slice_end;\n",
    "\n",
    "      // guess on plotly current axis limit\n",
    "      let xaxis_min_guess;\n",
    "      let xaxis_max_guess;\n",
    "      let yaxis_min_guess;\n",
    "      let yaxis_max_guess;\n",
    "      let zaxis_min_guess;\n",
    "      let zaxis_max_guess;\n",
    "\n",
    "      setup_trace();\n",
    "\n",
    "      $('.controlbutton button').click(function() {\n",
    "      let button_type= this.parentNode.id;\n",
    "      if ( button_type === 'galpy-srgqzhsgyxwdxovzaqreowll-play' ) {\n",
    "          clearInterval(interval);\n",
    "          interval= animate_trace();\n",
    "          document.querySelector('#galpy-srgqzhsgyxwdxovzaqreowll-playpause').textContent = 'Pause';\n",
    "          document.getElementById('galpy-srgqzhsgyxwdxovzaqreowll-play').id = 'galpy-srgqzhsgyxwdxovzaqreowll-pause';\n",
    "      }\n",
    "      else if ( button_type === 'galpy-srgqzhsgyxwdxovzaqreowll-pause' ) {\n",
    "          clearInterval(interval);\n",
    "          document.querySelector('#galpy-srgqzhsgyxwdxovzaqreowll-playpause').textContent = 'Resume';\n",
    "          document.getElementById('galpy-srgqzhsgyxwdxovzaqreowll-pause').id = 'galpy-srgqzhsgyxwdxovzaqreowll-play';\n",
    "          }\n",
    "      else if ( button_type === 'galpy-srgqzhsgyxwdxovzaqreowll-timestwo' ) {\n",
    "          cnt/= 2;\n",
    "          numPerFrame*= 2;\n",
    "      }\n",
    "      else if ( button_type === 'galpy-srgqzhsgyxwdxovzaqreowll-timeshalf' ) {\n",
    "          cnt*= 2;\n",
    "          numPerFrame/= 2;\n",
    "      }\n",
    "      else if ( button_type === 'galpy-srgqzhsgyxwdxovzaqreowll-replay' ) {\n",
    "          $(\"#galpy-srgqzhsgyxwdxovzaqreowll-playpause\").removeAttr('disabled');\n",
    "          document.querySelector('#galpy-srgqzhsgyxwdxovzaqreowll-playpause').textContent = 'Pause';\n",
    "          try { // doesn't exist if replay with pressing pause\n",
    "          document.getElementById('galpy-srgqzhsgyxwdxovzaqreowll-play').id = 'galpy-srgqzhsgyxwdxovzaqreowll-pause';\n",
    "          }\n",
    "          catch (err) {\n",
    "          }\n",
    "          cnt= 1;\n",
    "          try { // doesn't exist if animation has already ended\n",
    "          Plotly.deleteTraces('galpy-srgqzhsgyxwdxovzaqreowll',[1, ]);\n",
    "          }\n",
    "          catch (err) {\n",
    "          }\n",
    "          Plotly.deleteTraces('galpy-srgqzhsgyxwdxovzaqreowll', [0]);\n",
    "          clearInterval(interval);\n",
    "          setup_trace();\n",
    "          interval= animate_trace();\n",
    "      }\n",
    "      });\n",
    "\n",
    "      function setup_trace() {\n",
    "\n",
    "      let trace1= {\n",
    "          x: data.x1_0.slice(0,numPerFrame),\n",
    "          y: data.y1_0.slice(0,numPerFrame),\n",
    "          z: data.z1_0.slice(0,numPerFrame),\n",
    "          customdata: data.time,\n",
    "          hovertemplate: '<b>Object 0</b>' + '<br><b>x (kpc)</b>: %{x:.2f}' + '<br><b>y (kpc)</b>: %{y:.2f}' + '<br><b>z (kpc)</b>: %{z:.2f}' + '<br><b>t (Gyr)</b>: %{customdata:.2f}',\n",
    "          mode: 'lines',\n",
    "          name: '',\n",
    "          line: {\n",
    "          shape: 'spline',\n",
    "          width: 3.,\n",
    "          color: '#1f77b4',\n",
    "          },\n",
    "          type: \"scatter3d\",\n",
    "      };\n",
    "\n",
    "      let trace2= {\n",
    "          x: data.x1_0.slice(0,numPerFrame),\n",
    "          y: data.y1_0.slice(0,numPerFrame),\n",
    "          z: data.z1_0.slice(0,numPerFrame),\n",
    "          customdata: data.time,\n",
    "          hovertemplate: '<b>Object 0 (Current location)</b>' + '<br><b>x (kpc)</b>: %{x:.2f}' + '<br><b>y (kpc)</b>: %{y:.2f}' + '<br><b>z (kpc)</b>: %{z:.2f}' + '<br><b>t (Gyr)</b>: %{customdata:.2f}',\n",
    "          mode: 'lines',\n",
    "          name: '',\n",
    "          line: {\n",
    "          shape: 'spline',\n",
    "          width: 8.,\n",
    "          color: '#1f77b4',\n",
    "          },\n",
    "          type: \"scatter3d\",\n",
    "      };\n",
    "      let mw_bg = {\n",
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    "              [255, 255, 255, 255, 253, 247, 243, 235, 227, 216, 197, 184, 192, 197, 189, 161, 134, 121, 117, 119, 129, 135, 132, 126, 119, 105, 92, 95, 124, 162, 176, 136, 151, 189, 174, 155, 149, 140, 170, 209, 213, 211, 229, 237, 243, 248, 253, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 251, 245, 239, 231, 221, 205, 193, 198, 200, 191, 158, 104, 100, 124, 134, 145, 160, 160, 162, 166, 165, 154, 134, 102, 90, 105, 151, 156, 155, 180, 177, 165, 148, 124, 153, 199, 208, 205, 226, 235, 241, 248, 252, 255, 255, 255],\n",
    "              [255, 255, 255, 254, 248, 243, 235, 227, 214, 201, 202, 205, 197, 165, 112, 103, 127, 151, 159, 169, 161, 153, 161, 147, 161, 171, 172, 151, 120, 73, 110, 158, 160, 170, 177, 169, 153, 115, 137, 190, 199, 204, 223, 232, 239, 245, 251, 254, 255, 255],\n",
    "              [255, 255, 255, 253, 247, 241, 233, 222, 207, 203, 206, 201, 177, 135, 116, 145, 161, 162, 156, 143, 139, 132, 152, 174, 173, 161, 162, 179, 156, 108, 90, 139, 158, 158, 175, 169, 151, 134, 143, 176, 199, 204, 219, 230, 237, 243, 250, 254, 255, 255],\n",
    "              [255, 255, 255, 251, 246, 238, 231, 216, 206, 208, 206, 186, 125, 120, 154, 163, 167, 163, 139, 129, 124, 78, 92, 167, 177, 179, 151, 171, 176, 139, 92, 116, 147, 145, 175, 166, 144, 138, 140, 171, 196, 200, 216, 228, 234, 242, 249, 254, 255, 255],\n",
    "              [255, 255, 255, 250, 244, 235, 228, 214, 209, 209, 200, 150, 112, 133, 161, 170, 170, 148, 144, 142, 60, 25, 68, 124, 147, 172, 182, 162, 171, 165, 116, 109, 135, 138, 172, 166, 143, 117, 130, 173, 195, 204, 216, 228, 234, 241, 247, 252, 255, 255],\n",
    "              [255, 255, 255, 249, 242, 233, 224, 213, 208, 208, 179, 126, 131, 156, 162, 175, 154, 125, 148, 94, 67, 59, 38, 76, 119, 128, 154, 173, 161, 172, 117, 91, 133, 130, 164, 158, 141, 118, 126, 168, 196, 210, 216, 227, 234, 240, 246, 252, 255, 255],\n",
    "              [255, 255, 255, 249, 242, 233, 220, 211, 211, 205, 158, 131, 151, 164, 173, 173, 133, 132, 133, 81, 129, 115, 39, 15, 31, 64, 106, 165, 170, 163, 115, 79, 132, 142, 163, 148, 146, 120, 127, 174, 191, 210, 220, 226, 232, 241, 246, 252, 255, 255],\n",
    "              [255, 254, 253, 248, 242, 232, 215, 208, 215, 191, 140, 134, 154, 168, 177, 165, 130, 144, 91, 93, 162, 153, 89, 17, 0, 8, 54, 127, 170, 156, 122, 99, 131, 158, 147, 144, 142, 123, 145, 174, 194, 208, 219, 226, 232, 240, 246, 252, 255, 255],\n",
    "              [255, 255, 253, 247, 242, 231, 214, 211, 215, 182, 131, 139, 157, 170, 175, 156, 129, 144, 99, 115, 170, 175, 127, 59, 4, 0, 21, 83, 145, 156, 121, 117, 125, 149, 140, 137, 142, 131, 150, 178, 198, 209, 217, 227, 233, 240, 246, 252, 255, 255],\n",
    "              [255, 255, 253, 248, 242, 231, 216, 214, 213, 184, 136, 137, 161, 171, 177, 158, 142, 139, 97, 136, 165, 175, 155, 120, 70, 27, 12, 40, 113, 145, 100, 111, 126, 138, 146, 153, 119, 118, 156, 187, 196, 208, 219, 226, 232, 241, 248, 252, 255, 255],\n",
    "              [255, 255, 253, 249, 241, 231, 219, 216, 211, 183, 140, 137, 168, 171, 176, 160, 145, 145, 88, 119, 162, 173, 183, 149, 136, 113, 67, 40, 81, 95, 79, 113, 131, 140, 154, 141, 102, 123, 167, 192, 192, 201, 220, 227, 235, 241, 247, 253, 255, 255],\n",
    "              [255, 254, 253, 249, 242, 231, 221, 220, 215, 181, 133, 140, 164, 173, 176, 155, 149, 156, 92, 97, 160, 166, 184, 184, 164, 148, 126, 67, 33, 49, 106, 137, 146, 162, 156, 125, 120, 154, 184, 190, 180, 199, 222, 229, 235, 242, 249, 252, 255, 255],\n",
    "              [255, 255, 254, 250, 243, 232, 222, 223, 216, 190, 125, 128, 166, 176, 173, 165, 161, 160, 108, 83, 139, 164, 155, 180, 195, 183, 169, 120, 50, 86, 127, 140, 160, 155, 126, 107, 124, 167, 184, 163, 178, 215, 226, 229, 236, 243, 248, 255, 255, 255],\n",
    "              [254, 255, 254, 250, 244, 234, 223, 222, 219, 193, 140, 141, 157, 175, 174, 173, 171, 165, 142, 97, 102, 148, 156, 146, 166, 179, 191, 172, 128, 107, 127, 148, 144, 131, 114, 117, 141, 168, 175, 176, 205, 221, 225, 232, 238, 245, 250, 253, 255, 255],\n",
    "              [255, 255, 254, 251, 245, 237, 224, 219, 222, 199, 161, 134, 148, 169, 175, 179, 176, 168, 157, 132, 95, 104, 150, 156, 140, 145, 147, 153, 154, 144, 147, 143, 121, 91, 108, 158, 171, 174, 181, 205, 215, 221, 228, 233, 240, 245, 250, 255, 255, 255],\n",
    "              [255, 255, 255, 252, 246, 239, 229, 223, 222, 210, 165, 128, 150, 165, 178, 185, 181, 170, 150, 154, 133, 87, 91, 123, 141, 151, 147, 144, 145, 139, 129, 106, 91, 113, 149, 180, 191, 186, 192, 211, 218, 224, 229, 236, 242, 248, 253, 255, 255, 255],\n",
    "              [255, 255, 254, 252, 247, 241, 233, 227, 225, 217, 184, 145, 140, 159, 176, 187, 184, 180, 143, 150, 164, 134, 96, 86, 91, 97, 112, 116, 104, 90, 84, 108, 138, 170, 189, 190, 179, 169, 199, 215, 221, 226, 232, 239, 244, 250, 254, 255, 255, 255],\n",
    "              [255, 255, 254, 252, 248, 243, 236, 231, 227, 221, 201, 161, 142, 159, 170, 184, 188, 186, 168, 149, 158, 164, 154, 129, 113, 94, 96, 108, 111, 105, 123, 168, 185, 187, 180, 170, 170, 188, 211, 220, 225, 229, 235, 242, 247, 252, 255, 255, 255, 255],\n",
    "              [255, 254, 254, 253, 249, 245, 239, 234, 231, 226, 213, 180, 152, 158, 168, 179, 188, 188, 190, 165, 143, 145, 161, 168, 169, 170, 159, 161, 175, 179, 190, 187, 170, 163, 163, 181, 201, 214, 218, 221, 227, 232, 239, 245, 250, 254, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 254, 252, 249, 243, 237, 234, 230, 222, 204, 164, 135, 163, 175, 183, 189, 193, 187, 169, 169, 170, 148, 159, 177, 174, 178, 180, 185, 185, 181, 177, 179, 194, 210, 212, 216, 219, 225, 230, 236, 243, 248, 253, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 254, 252, 248, 241, 236, 234, 229, 219, 191, 151, 152, 163, 175, 182, 188, 194, 188, 183, 190, 177, 158, 165, 173, 161, 161, 173, 184, 188, 199, 207, 209, 211, 214, 220, 224, 228, 234, 241, 246, 251, 254, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 254, 252, 246, 240, 236, 234, 229, 214, 187, 144, 147, 173, 176, 180, 186, 186, 182, 187, 195, 194, 188, 188, 184, 181, 191, 198, 202, 205, 208, 212, 215, 222, 223, 229, 233, 239, 245, 249, 253, 254, 255, 255, 255, 255, 255],\n",
    "              [255, 254, 255, 255, 255, 255, 254, 251, 245, 241, 237, 235, 227, 207, 173, 151, 151, 162, 177, 178, 180, 185, 187, 192, 197, 199, 198, 201, 203, 202, 205, 207, 210, 214, 216, 221, 223, 228, 233, 239, 243, 248, 252, 254, 255, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 251, 245, 241, 239, 236, 226, 206, 184, 149, 141, 168, 176, 180, 185, 189, 190, 193, 197, 200, 205, 207, 209, 210, 211, 214, 215, 217, 221, 227, 233, 237, 242, 246, 251, 254, 255, 255, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 253, 250, 247, 244, 241, 236, 226, 214, 198, 177, 169, 166, 175, 186, 194, 191, 194, 196, 198, 205, 212, 215, 215, 213, 213, 214, 218, 225, 232, 238, 241, 245, 249, 253, 254, 255, 255, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 255, 254, 252, 249, 246, 242, 238, 231, 223, 215, 201, 190, 188, 184, 186, 196, 199, 201, 202, 207, 212, 214, 215, 215, 217, 218, 225, 234, 239, 242, 245, 248, 252, 255, 255, 255, 255, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 254, 253, 251, 248, 245, 240, 234, 228, 222, 218, 217, 211, 203, 205, 207, 206, 204, 206, 211, 216, 220, 223, 226, 228, 234, 240, 244, 246, 249, 251, 253, 255, 255, 255, 255, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 254, 255, 254, 252, 250, 247, 244, 238, 234, 231, 227, 225, 224, 219, 217, 216, 214, 216, 221, 226, 230, 232, 235, 238, 242, 245, 248, 250, 252, 253, 254, 255, 255, 255, 255, 255, 255, 254, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 254, 253, 252, 250, 247, 244, 241, 240, 236, 235, 232, 230, 230, 231, 232, 234, 236, 238, 239, 242, 246, 249, 250, 252, 253, 254, 254, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 254, 254, 252, 253, 250, 247, 246, 245, 244, 244, 243, 243, 243, 244, 245, 247, 247, 250, 252, 253, 253, 254, 254, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 254, 255, 254, 253, 252, 251, 252, 250, 251, 250, 251, 252, 253, 253, 254, 254, 254, 255, 255, 255, 255, 255, 255, 254, 255, 255, 255, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255],\n",
    "              [255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255]\n",
    "          ],\n",
    "              hoverinfo:\"skip\",\n",
    "              showscale:false,\n",
    "              cmax:255,\n",
    "              cmin:0,\n",
    "              type: 'surface',\n",
    "              };\n",
    "\n",
    "      let traces= [trace1,trace2,mw_bg];\n",
    "\n",
    "      Plotly.newPlot('galpy-srgqzhsgyxwdxovzaqreowll',traces,layout);\n",
    "      }\n",
    "\n",
    "      function animate_trace() {\n",
    "      return setInterval(function() {\n",
    "          // Make sure narrow and thick trace end in the same\n",
    "          // and the highlighted length has constant length\n",
    "          trace_slice_len= Math.floor(numPerFrame);\n",
    "          if ( trace_slice_len < 1) trace_slice_len= 1;\n",
    "          trace_slice_begin= Math.floor(cnt*numPerFrame);\n",
    "          trace_slice_end= Math.floor(Math.min(cnt*numPerFrame+trace_slice_len,data.x1_0.length-1));\n",
    "          traces = {x: [data.x1_0.slice(trace_slice_begin,trace_slice_end), ], y: [data.y1_0.slice(trace_slice_begin,trace_slice_end), ], z: [data.z1_0.slice(trace_slice_begin,trace_slice_end), ], customdata:[data.time.slice(trace_slice_begin,trace_slice_end), ]};\n",
    "          Plotly.extendTraces('galpy-srgqzhsgyxwdxovzaqreowll', traces, [0, ]);\n",
    "          trace_slice_begin-= trace_slice_len;\n",
    "          traces = {x: [data.x1_0.slice(trace_slice_begin,trace_slice_end), ], y: [data.y1_0.slice(trace_slice_begin,trace_slice_end), ], z: [data.z1_0.slice(trace_slice_begin,trace_slice_end), ], customdata:[data.time.slice(trace_slice_begin,trace_slice_end), ]};\n",
    "          Plotly.restyle('galpy-srgqzhsgyxwdxovzaqreowll', traces, [1, ]);\n",
    "          cnt+= 1;\n",
    "          // need to clearInterval here otherwise the pan/zoom/rotate is bugged somehow at the end of play\n",
    "          if (cnt*numPerFrame+trace_slice_len>data.x1_0.length) {\n",
    "              document.getElementById(\"galpy-srgqzhsgyxwdxovzaqreowll-playpause\").disabled = \"disabled\";\n",
    "              document.querySelector('#galpy-srgqzhsgyxwdxovzaqreowll-playpause').textContent = 'Finished!';\n",
    "              // making sure the whole orbits is plotted when finished\n",
    "              trace_slice_begin = trace_slice_end;\n",
    "              trace_slice_end = -1;\n",
    "              traces = {x: [data.x1_0.slice(trace_slice_begin,trace_slice_end), ], y: [data.y1_0.slice(trace_slice_begin,trace_slice_end), ], z: [data.z1_0.slice(trace_slice_begin,trace_slice_end), ], customdata:[data.time.slice(trace_slice_begin,trace_slice_end), ]};\n",
    "              Plotly.extendTraces('galpy-srgqzhsgyxwdxovzaqreowll', traces, [0, ]);\n",
    "              // make sure trace heads are gone when finished playing, sometimes they will stay around\n",
    "              Plotly.deleteTraces('galpy-srgqzhsgyxwdxovzaqreowll', [1, ]);\n",
    "              clearInterval(interval);\n",
    "          };\n",
    "      }, 50);\n",
    "      }\n",
    "      });\n",
    "      </script>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d38d457",
   "metadata": {
    "papermill": {
     "duration": 0.015149,
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     "exception": false,
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     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "\n",
    "If you want to embed the animation in a webpage, you can obtain the necessary HTML using the ``_repr_html_()`` function of the IPython.core.display.HTML object returned by ``animate``. By default, the HTML includes the entire orbit's data, but ``animate`` also has an option to store the orbit in a separate ``JSON`` file that will then be loaded by the output HTML code.\n",
    "\n",
    "``animate`` and ``animate3d`` also work for ``Orbit`` instances containing multiple objects."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "379cbbc1e968416e875cc15c1202d7eb",
   "metadata": {
    "papermill": {
     "duration": 0.015594,
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     "start_time": "2026-05-16T13:49:18.777058+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Orbit characterization\n",
    "\n",
    "After integration, compute orbital parameters numerically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "277c27b1587741f2af2001be3712ef0d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:18.825613Z",
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     "shell.execute_reply": "2026-05-16T13:49:18.829579Z"
    },
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     "exception": false,
     "start_time": "2026-05-16T13:49:18.808236+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eccentricity: 0.07484773934372554\n",
      "Apocenter: 1.0847070212241001\n",
      "Pericenter: 0.9336384271952163\n",
      "Max |z|: 0.04328778107544663\n"
     ]
    }
   ],
   "source": [
    "print(\"Eccentricity:\", o.e())\n",
    "print(\"Apocenter:\", o.rap())\n",
    "print(\"Pericenter:\", o.rperi())\n",
    "print(\"Max |z|:\", o.zmax())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fa5554e",
   "metadata": {
    "papermill": {
     "duration": 0.015362,
     "end_time": "2026-05-16T13:49:18.862877+00:00",
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     "start_time": "2026-05-16T13:49:18.847515+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "These parameters can also be computed analytically using the Staeckel approximation, without any orbit integration (see [Fast Orbit Characterization](fast_characterization.ipynb)):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "db7b79bc585a40fcaf58bf750017e135",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:18.895808Z",
     "iopub.status.busy": "2026-05-16T13:49:18.895587Z",
     "iopub.status.idle": "2026-05-16T13:49:18.909431Z",
     "shell.execute_reply": "2026-05-16T13:49:18.908252Z"
    },
    "papermill": {
     "duration": 0.031999,
     "end_time": "2026-05-16T13:49:18.910589+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:18.878590+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Analytic e: 0.07494364311796002\n",
      "Analytic rap: 1.0844978863649968\n",
      "Analytic rperi: 0.9332783818295365\n",
      "Analytic zmax: 0.043063219299077755\n"
     ]
    }
   ],
   "source": [
    "# Analytic computation using the Staeckel approximation (no integration needed)\n",
    "o_new = Orbit([1.0, 0.1, 1.0, 0.0, 0.1, 0.0])\n",
    "print(\"Analytic e:\", o_new.e(analytic=True, pot=MWPotential2014, type=\"staeckel\"))\n",
    "print(\"Analytic rap:\", o_new.rap(analytic=True, pot=MWPotential2014, type=\"staeckel\"))\n",
    "print(\n",
    "    \"Analytic rperi:\", o_new.rperi(analytic=True, pot=MWPotential2014, type=\"staeckel\")\n",
    ")\n",
    "print(\"Analytic zmax:\", o_new.zmax(analytic=True, pot=MWPotential2014, type=\"staeckel\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "916684f9a58a4a2aa5f864670399430d",
   "metadata": {
    "papermill": {
     "duration": 0.015992,
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     "start_time": "2026-05-16T13:49:18.928450+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Energy and energy conservation\n",
    "\n",
    "Energy can be computed at any time using `o.E(pot)`, where ``pot`` is the potential object that does not need to be specified if the orbit has been integrated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1671c31a24314836a5b85d7ef7fbf015",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:18.977396Z",
     "iopub.status.busy": "2026-05-16T13:49:18.977169Z",
     "iopub.status.idle": "2026-05-16T13:49:18.986125Z",
     "shell.execute_reply": "2026-05-16T13:49:18.985260Z"
    },
    "papermill": {
     "duration": 0.026155,
     "end_time": "2026-05-16T13:49:18.986833+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:18.960678+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Energy at t=0: -0.8633506513947898\n",
      "Energy at t=10: -0.8633506513947993\n",
      "Relative energy error: -1.093054796920349e-14\n"
     ]
    }
   ],
   "source": [
    "print(\"Energy at t=0:\", o.E(0.0))\n",
    "print(\"Energy at t=10:\", o.E(ts[-1]))\n",
    "print(\"Relative energy error:\", (o.E(ts[-1]) - o.E(0.0)) / abs(o.E(0.0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f85563e6",
   "metadata": {
    "papermill": {
     "duration": 0.0158,
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     "start_time": "2026-05-16T13:49:19.002759+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "You can also conveniently check energy conservation by plotting the energy over time using ``o.plotE`` or the normalized energy error using ``o.plotEnorm``:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "c26241d3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:19.051630Z",
     "iopub.status.busy": "2026-05-16T13:49:19.051407Z",
     "iopub.status.idle": "2026-05-16T13:49:19.262852Z",
     "shell.execute_reply": "2026-05-16T13:49:19.261671Z"
    },
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     "duration": 0.228855,
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     "status": "completed"
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    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "o.plotEnorm();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33b0902fd34d4ace834912fa1002cf8e",
   "metadata": {
    "papermill": {
     "duration": 0.016101,
     "end_time": "2026-05-16T13:49:19.296391+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:19.280290+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Accessing raw orbital data\n",
    "\n",
    "Evaluate orbital quantities at any time, or get the full array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f6fa52606d8c4a75a9b52967216f8f3f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:19.330443Z",
     "iopub.status.busy": "2026-05-16T13:49:19.330183Z",
     "iopub.status.idle": "2026-05-16T13:49:19.345924Z",
     "shell.execute_reply": "2026-05-16T13:49:19.345059Z"
    },
    "papermill": {
     "duration": 0.033775,
     "end_time": "2026-05-16T13:49:19.346639+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:19.312864+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R(t=5): 1.0248822021703112\n",
      "phi(t=5): -1.355027550131503\n",
      "Full orbit shape: (10000, 6)\n"
     ]
    }
   ],
   "source": [
    "# At specific time\n",
    "print(\"R(t=5):\", o.R(5.0))\n",
    "print(\"phi(t=5):\", o.phi(5.0))\n",
    "\n",
    "# Full orbit array: shape (ntimes, ndim)\n",
    "orbit_array = o.getOrbit()\n",
    "print(\"Full orbit shape:\", orbit_array.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4d66d9d",
   "metadata": {
    "papermill": {
     "duration": 0.015926,
     "end_time": "2026-05-16T13:49:19.378809+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:19.362883+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Sky coordinates and many other quantities are also available as attributes (see the [API documentation](../../reference/orbit.rst) for a complete list)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "f5a1fa73e5044315a093ec459c9be902",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:19.413235Z",
     "iopub.status.busy": "2026-05-16T13:49:19.412966Z",
     "iopub.status.idle": "2026-05-16T13:49:19.432729Z",
     "shell.execute_reply": "2026-05-16T13:49:19.431751Z"
    },
    "papermill": {
     "duration": 0.03809,
     "end_time": "2026-05-16T13:49:19.433498+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:19.395408+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RA(t=5): 204.3700933860206\n",
      "Dec(t=5): -64.02927160795767\n"
     ]
    }
   ],
   "source": [
    "# Sky coordinates at specific time (requires ro/vo)\n",
    "print(\"RA(t=5):\", o_sky.ra(5.0))\n",
    "print(\"Dec(t=5):\", o_sky.dec(5.0))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdf66aed5cc84ca1b48e60bad68798a8",
   "metadata": {
    "papermill": {
     "duration": 0.016023,
     "end_time": "2026-05-16T13:49:19.465921+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:19.449898+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Creating a new orbit from evaluated position\n",
    "\n",
    "Calling an orbit as a function returns a new Orbit at that time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "28d3efd5258a48a79c179ea5c6759f01",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:19.498492Z",
     "iopub.status.busy": "2026-05-16T13:49:19.498269Z",
     "iopub.status.idle": "2026-05-16T13:49:19.503323Z",
     "shell.execute_reply": "2026-05-16T13:49:19.502228Z"
    },
    "papermill": {
     "duration": 0.022293,
     "end_time": "2026-05-16T13:49:19.503960+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:19.481667+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New orbit at t=5: <galpy.orbit.Orbits.Orbit object at 0x7fa61295e950>\n",
      "R: 1.0248822021703112\n"
     ]
    }
   ],
   "source": [
    "o_at_5 = o(5.0)\n",
    "print(\"New orbit at t=5:\", o_at_5)\n",
    "print(\"R:\", o_at_5.R())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f9bc0b9dd2c44919cc8dcca39b469f8",
   "metadata": {
    "papermill": {
     "duration": 0.01621,
     "end_time": "2026-05-16T13:49:19.536639+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:19.520429+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Non-inertial frames\n",
    "\n",
    "The default assumption in galpy is that the frame that an orbit is integrated in is an inertial one. However, galpy also supports orbit integration in non-inertial frames that are rotating or whose center is accelerating (or a combination of the two). When a frame is not an inertial frame, fictitious forces such as the centrifugal and Coriolis forces need to be taken into account. galpy implements all of the necessary forces as part of the [NonInertialFrameForce](../../reference/potentialnoninertialframe.rst#noninertialframe-potential) class. objects of this class are instantiated with arbitrary three-dimensional rotation frequencies (and their time derivative) and/or arbitrary three-dimensional acceleration of the origin. The class documentation linked to above provides full mathematical details on the rotation and acceleration of the non-inertial frame.\n",
    "\n",
    "We can then, for example, integrate the orbit of the Sun in the LSR frame, that is, the frame that is corotating with that of the circular orbit at the location of the Sun. To do this for ``MWPotential2014``, do"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "0e382214b5f147d187d36a2058b9c724",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:19.570401Z",
     "iopub.status.busy": "2026-05-16T13:49:19.570173Z",
     "iopub.status.idle": "2026-05-16T13:49:19.743346Z",
     "shell.execute_reply": "2026-05-16T13:49:19.742407Z"
    },
    "papermill": {
     "duration": 0.191328,
     "end_time": "2026-05-16T13:49:19.744210+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:19.552882+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "galpyWarning: Cannot use symplectic integration because some of the included forces are dissipative (using non-symplectic integrator dopr54_c instead)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from galpy.potential import MWPotential2014, NonInertialFrameForce\n",
    "\n",
    "nip = NonInertialFrameForce(Omega=1.0)  # LSR has Omega=1 in natural units\n",
    "o = Orbit()  # Orbit() is the orbit of the Sun in the inertial frame\n",
    "o.turn_physical_off()  # To use internal units\n",
    "o = Orbit(\n",
    "    [o.R(), o.vR(), o.vT() - 1.0, o.z(), o.vz(), o.phi()]\n",
    ")  # Convert to the LSR frame\n",
    "ts = numpy.linspace(0.0, 20.0, 1001)\n",
    "o.integrate(ts, MWPotential2014 + nip)\n",
    "o.plot(d1=\"x\", d2=\"y\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4923f1a6",
   "metadata": {
    "papermill": {
     "duration": 0.016368,
     "end_time": "2026-05-16T13:49:19.777158+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:19.760790+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "we can compare this to integrating the orbit in the inertial frame and displaying it in the non-inertial LSR frame as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "70a08bdf",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:19.810618Z",
     "iopub.status.busy": "2026-05-16T13:49:19.810382Z",
     "iopub.status.idle": "2026-05-16T13:49:19.990863Z",
     "shell.execute_reply": "2026-05-16T13:49:19.989771Z"
    },
    "papermill": {
     "duration": 0.19805,
     "end_time": "2026-05-16T13:49:19.991564+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:19.793514+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "o.plot(d1=\"x\", d2=\"y\")  # Repeat plot from above\n",
    "o = Orbit()  # Orbit() is the orbit of the Sun in the inertial frame\n",
    "o.turn_physical_off()  # To use internal units\n",
    "o.integrate(ts, MWPotential2014)\n",
    "o.plot(\n",
    "    d1=\"R*cos(phi-t)\", d2=\"R*sin(phi-t)\", overplot=True\n",
    ");  # Omega = 1, so Omega t = t"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2faecf4f",
   "metadata": {
    "papermill": {
     "duration": 0.016368,
     "end_time": "2026-05-16T13:49:20.025022+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:20.008654+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "We can also do all of the above in physical units, in which case the first example above becomes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "3ff85f4f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:20.060635Z",
     "iopub.status.busy": "2026-05-16T13:49:20.060406Z",
     "iopub.status.idle": "2026-05-16T13:49:20.264134Z",
     "shell.execute_reply": "2026-05-16T13:49:20.263281Z"
    },
    "papermill": {
     "duration": 0.222772,
     "end_time": "2026-05-16T13:49:20.265054+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:20.042282+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from galpy.potential import MWPotential2014, NonInertialFrameForce\n",
    "from astropy import units\n",
    "\n",
    "nip = NonInertialFrameForce(Omega=220.0 / 8.0 * units.km / units.s / units.kpc)\n",
    "o = Orbit()  # Orbit() is the orbit of the Sun in the inertial frame\n",
    "o = Orbit(\n",
    "    [\n",
    "        o.R(quantity=True),\n",
    "        o.vR(quantity=True),\n",
    "        o.vT(quantity=True) - 220.0 * units.km / units.s,\n",
    "        o.z(quantity=True),\n",
    "        o.vz(quantity=True),\n",
    "        o.phi(quantity=True),\n",
    "    ]\n",
    ")  # Convert to the LSR frame\n",
    "ts = numpy.linspace(0.0, 20.0, 1001)\n",
    "o.integrate(ts, MWPotential2014 + nip)\n",
    "o.plot(d1=\"x\", d2=\"y\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "773db6d9",
   "metadata": {
    "papermill": {
     "duration": 0.016657,
     "end_time": "2026-05-16T13:49:20.298892+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:20.282235+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "We can also provide the ``Omega=`` frequency as an arbitrary function of time. In this case, the frequency must be returned in internal units and the input time of this function must be in internal units as well (use the routines in [galpy.util.conversion](../../reference/conversion.rst#bovyconversion) for converting from physical to internal units; you need to divide by these to go from physical to internal). For the example above, this would amount to setting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "7f1413dc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:20.333789Z",
     "iopub.status.busy": "2026-05-16T13:49:20.333567Z",
     "iopub.status.idle": "2026-05-16T13:49:20.337161Z",
     "shell.execute_reply": "2026-05-16T13:49:20.336306Z"
    },
    "papermill": {
     "duration": 0.022265,
     "end_time": "2026-05-16T13:49:20.337955+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:20.315690+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "nip = NonInertialFrameForce(Omega=lambda t: 1.0, Omegadot=lambda t: 0.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adefd943",
   "metadata": {
    "papermill": {
     "duration": 0.016822,
     "end_time": "2026-05-16T13:49:20.371660+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:20.354838+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Note that when we supply Omega as a function, it is necessary to specify its time derivative as well as Omegadot (all again in internal units).\n",
    "\n",
    "We give an example of having the origin of the non-inertial frame accelerate in the [orbit examples](examples.ipynb) tutorial."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d9db57e",
   "metadata": {
    "papermill": {
     "duration": 0.017205,
     "end_time": "2026-05-16T13:49:20.405836+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:20.388631+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Surfaces of section\n",
    "\n",
    "galpy can compute surfaces of section (SOS) for 2D and 3D orbits using a special\n",
    "integration method that exactly determines intersections between orbits and a surface.\n",
    "The implemented method follows [Hunter et al. (1998)](https://ui.adsabs.harvard.edu/abs/1998NYASA.867...61H/abstract) in re-writing the integration in terms of an independent angular variable \ud835\udf13 that is equal to a multiple of 2\u2062\ud835\udf0b at intersections of the orbit with a surface of section (see Section 13.1 of [galaxiesbook.org](https://galaxiesbook.org/chapters/III-02.-Orbits-in-Triaxial-Mass-Distributions-and-Surfaces-of-Section_1-Surfaces-of-section.html#while-the-method-we-have-used-so)).\n",
    "\n",
    "Supported surfaces:\n",
    "- **3D orbits:** $z=0, v_z>0$ surface\n",
    "- **2D orbits:** $x=0, v_x>0$ or $y=0, v_y>0$ surfaces\n",
    "\n",
    "Surfaces of section are most useful for static, axisymmetric potentials (3D) or\n",
    "static, non-axisymmetric potentials (2D)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "2d72d937",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:20.441608Z",
     "iopub.status.busy": "2026-05-16T13:49:20.441363Z",
     "iopub.status.idle": "2026-05-16T13:49:20.970101Z",
     "shell.execute_reply": "2026-05-16T13:49:20.969145Z"
    },
    "papermill": {
     "duration": 0.54766,
     "end_time": "2026-05-16T13:49:20.970840+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:20.423180+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Surface of section for the Sun's orbit in MWPotential2014\n",
    "o_sun = Orbit()\n",
    "o_sun.turn_physical_off()\n",
    "o_sun.plotSOS(MWPotential2014);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff5dd71b",
   "metadata": {
    "papermill": {
     "duration": 0.016935,
     "end_time": "2026-05-16T13:49:21.005178+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:20.988243+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "You can also retrieve the SOS crossing values directly using `o.SOS()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "2df4ef51",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:21.039530Z",
     "iopub.status.busy": "2026-05-16T13:49:21.039305Z",
     "iopub.status.idle": "2026-05-16T13:49:21.355306Z",
     "shell.execute_reply": "2026-05-16T13:49:21.354484Z"
    },
    "papermill": {
     "duration": 0.334797,
     "end_time": "2026-05-16T13:49:21.356395+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:21.021598+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of SOS crossings: 500\n"
     ]
    }
   ],
   "source": [
    "# Get the SOS values directly\n",
    "Rs, vRs = o_sun.SOS(MWPotential2014)\n",
    "print(\"Number of SOS crossings:\", len(Rs))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e3527f0",
   "metadata": {
    "papermill": {
     "duration": 0.017453,
     "end_time": "2026-05-16T13:49:21.391304+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:21.373851+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "For 2D orbits, we can compute surfaces of section in the `x` or `y` planes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "bca5328a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:21.427359Z",
     "iopub.status.busy": "2026-05-16T13:49:21.427084Z",
     "iopub.status.idle": "2026-05-16T13:49:21.752458Z",
     "shell.execute_reply": "2026-05-16T13:49:21.751408Z"
    },
    "papermill": {
     "duration": 0.344611,
     "end_time": "2026-05-16T13:49:21.753146+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:21.408535+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 2D example: box orbit in a non-axisymmetric cored logarithmic potential\n",
    "lp_2d = LogarithmicHaloPotential(normalize=True, b=0.9, core=0.2)\n",
    "orb_2d = Orbit([0.1, 0.0, lp_2d.vcirc(0.1, phi=0.0), numpy.pi / 2.0])\n",
    "orb_2d.plotSOS(lp_2d, surface=\"y\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0253e81",
   "metadata": {
    "papermill": {
     "duration": 0.017059,
     "end_time": "2026-05-16T13:49:21.787767+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:21.770708+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Surfaces of section can also be computed for Orbit instances that contain multiple orbits, e.g., for the following two orbits defined to have the same energy and angular momentum:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "a5e5e607",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:21.822868Z",
     "iopub.status.busy": "2026-05-16T13:49:21.822646Z",
     "iopub.status.idle": "2026-05-16T13:49:22.468958Z",
     "shell.execute_reply": "2026-05-16T13:49:22.467872Z"
    },
    "papermill": {
     "duration": 0.664801,
     "end_time": "2026-05-16T13:49:22.469697+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:21.804896+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from galpy.potential import evaluatePotentials\n",
    "\n",
    "\n",
    "def orbit_RvRELz(R, vR, E, Lz, z_init=0.0, pot=None):\n",
    "    \"\"\"Returns Orbit at (R,vR,phi=0,z=z_init) with given (E,Lz)\"\"\"\n",
    "    return Orbit(\n",
    "        [\n",
    "            R,\n",
    "            vR,\n",
    "            Lz / R,\n",
    "            z_init,\n",
    "            numpy.sqrt(\n",
    "                2.0\n",
    "                * (\n",
    "                    E\n",
    "                    - evaluatePotentials(pot, R, z_init)\n",
    "                    - (Lz / R) ** 2.0 / 2.0\n",
    "                    - vR**2.0 / 2\n",
    "                )\n",
    "            ),\n",
    "            0.0,\n",
    "        ],\n",
    "        ro=8.0,\n",
    "        vo=220.0,\n",
    "    )\n",
    "\n",
    "\n",
    "R, E, Lz = 0.8, -1.25, 0.6\n",
    "twoorb = Orbit(\n",
    "    [\n",
    "        orbit_RvRELz(R, 0.0, E, Lz, pot=MWPotential2014),\n",
    "        orbit_RvRELz(R, 0.1, E, Lz, pot=MWPotential2014, z_init=0.1),\n",
    "    ]\n",
    ")\n",
    "twoorb.plotSOS(MWPotential2014);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e7f81ca",
   "metadata": {
    "papermill": {
     "duration": 0.01772,
     "end_time": "2026-05-16T13:49:22.505179+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:22.487459+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "For some force fields, the reparameterization of the orbit in terms of $\\psi$ does not work, because the angle $\\psi$ does not increase monotonically with time. This is notably the case for many orbits integrated in a non-inertial frame (e.g., bar orbits in the bar\u2019s rotating frame). In these cases, you can use a brute-force approach to determining the surface of section implemented in ``Orbit.bruteSOS`` and ``Orbit.plotBruteSOS``, which work similarly to the ``Orbit.SOS`` and ``Orbit.plotSOS`` methods discussed above, but simply look for surface crossings using a regular orbit integration. In this case, you have to specify how long to integrate the orbit for and you can, therefore, not directly control the number of crossings that you will get."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "345088ed",
   "metadata": {
    "papermill": {
     "duration": 0.017004,
     "end_time": "2026-05-16T13:49:22.539679+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:22.522675+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "<div class=\"alert alert-warning\">\n",
    "\n",
    "**Warning**\n",
    "\n",
    "Computing the surface of section leaves the Orbit instance in a state where its internally-stored integrated orbit is that computed during the surface-of-section integration (any previously integrated orbit is overwritten). However, the orbit is only output at intersections with the surface of section. Furthermore, with an Orbit like that of the Sun above whose initial condition is not in the surface of section, the first point along this orbit is not the initial condition, but the first surface-of-section crossing instead. This is because for orbits like this, internally galpy first integrates to the first crossing and then re-starts the integration to obtain many subsequent crossings to create the surface of section.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60066829",
   "metadata": {
    "papermill": {
     "duration": 0.017114,
     "end_time": "2026-05-16T13:49:22.573867+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:22.556753+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": "## Integration of the phase-space volume\n\ngalpy supports the integration of the phase-space volume through the method\n`integrate_dxdv`, for both two-dimensional (planar) and fully three-dimensional\norbits. This can be used to, for example, explicitly verify Liouville's theorem\n(that phase-space volume is conserved along the orbit), quantify an orbit's\nsensitivity to its initial conditions, and compute Lyapunov exponents with the\n`lyapunov` method. See the\n[Phase-Space Volumes and Chaos](phase_space_volumes_and_chaos.ipynb) tutorial\nand the `integrate_dxdv` API documentation for details."
  },
  {
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     "status": "completed"
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   },
   "source": [
    "## Fast orbit integration and available integrators\n",
    "\n",
    "For fast integration of many orbits, galpy provides fast C integrators accessed via the `method=` keyword.\n",
    "\n",
    "**C integrators (recommended for speed):**\n",
    "- `rk4_c`, `rk6_c`: Runge-Kutta methods\n",
    "- `dopr54_c`, `dop853_c`: Dormand-Prince methods\n",
    "- `ias15_c`: IAS15 integrator (Rein & Spiegel 2014), adaptive timestepping for high precision\n",
    "\n",
    "**Symplectic C integrators:**\n",
    "- `leapfrog_c`, `symplec4_c`, `symplec6_c`\n",
    "\n",
    "**Pure Python integrators:**\n",
    "- `leapfrog`, `odeint`, `dop853`\n",
    "\n",
    "For most applications, `symplec4_c` or `dop853_c` are recommended. The `ias15_c` integrator from [Rein & Spiegel 2014](https://ui.adsabs.harvard.edu/abs/2015MNRAS.446.1424R/abstract) is a good choice when extreme high-precision is required, but it is slow compared to other C integrators. The higher order symplectic integrators are described in [Yoshida (1993)](http://adsabs.harvard.edu/abs/1993CeMDA..56...27Y)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "adfc44a8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-16T13:49:22.646510Z",
     "iopub.status.busy": "2026-05-16T13:49:22.646278Z",
     "iopub.status.idle": "2026-05-16T13:49:22.662831Z",
     "shell.execute_reply": "2026-05-16T13:49:22.661979Z"
    },
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     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MiyamotoNagaiPotential has C: True\n",
      "Integration with dop853_c complete.\n"
     ]
    }
   ],
   "source": [
    "# Check if a potential has a C implementation\n",
    "from galpy.potential import MiyamotoNagaiPotential as MNP\n",
    "\n",
    "mp_test = MNP(a=0.5, b=0.0375, amp=1.0, normalize=1.0)\n",
    "print(\"MiyamotoNagaiPotential has C:\", mp_test.hasC)\n",
    "\n",
    "# Integrate using the fast dop853_c method\n",
    "o_fast = Orbit([1.0, 0.1, 1.1, 0.0, 0.1, 0.0])\n",
    "ts = numpy.linspace(0.0, 100.0, 10001)\n",
    "o_fast.integrate(ts, MWPotential2014, method=\"dop853_c\")\n",
    "print(\"Integration with dop853_c complete.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68567952",
   "metadata": {
    "papermill": {
     "duration": 0.017869,
     "end_time": "2026-05-16T13:49:22.698880+00:00",
     "exception": false,
     "start_time": "2026-05-16T13:49:22.681011+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "If no C implementation of the potential (or one of its components) is available, galpy will automatically fall back to using a pure Python integrator. "
   ]
  }
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