{ "cells": [ { "cell_type": "markdown", "id": "a1b2c3d4e5f6a7b8c9d0e1f2a3b4c5d6", "metadata": { "papermill": { "duration": 0.004547, "end_time": "2026-06-30T01:09:03.375930+00:00", "exception": false, "start_time": "2026-06-30T01:09:03.371383+00:00", "status": "completed" }, "tags": [] }, "source": [ "# 1D Action-Angle Coordinates and Inverse Transformations\n", "\n", "galpy supports one-dimensional action-angle coordinates through\n", "`actionAngleVertical` and their inverse transformations through\n", "`actionAngleVerticalInverse`. These are useful for studying vertical\n", "oscillations in disk potentials or any general 1D potential.\n", "\n", "For the special case of the **harmonic oscillator**, `actionAngleHarmonic`\n", "and `actionAngleHarmonicInverse` provide exact analytical action-angle\n", "coordinates and their inverse. These work like the other 1D classes\n", "described below, but only require the oscillator frequency $\\omega$." ] }, { "cell_type": "code", "execution_count": 1, "id": "f3ed0cf0", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:09:03.383884Z", "iopub.status.busy": "2026-06-30T01:09:03.383680Z", "iopub.status.idle": "2026-06-30T01:09:05.586258Z", "shell.execute_reply": "2026-06-30T01:09:05.585345Z" }, "papermill": { "duration": 2.207641, "end_time": "2026-06-30T01:09:05.587018+00:00", "exception": false, "start_time": "2026-06-30T01:09:03.379377+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "J = 0.52\n", "(J, Omega) = (0.52, np.float64(1.0))\n", "(J, Omega, angle) = (0.52, np.float64(1.0), np.float64(1.373400766945016))\n" ] } ], "source": [ "from galpy.actionAngle import actionAngleHarmonic, actionAngleHarmonicInverse\n", "\n", "aAH = actionAngleHarmonic(omega=1.0)\n", "print(\"J =\", aAH(1.0, 0.2))\n", "print(\"(J, Omega) =\", aAH.actionsFreqs(1.0, 0.2))\n", "print(\"(J, Omega, angle) =\", aAH.actionsFreqsAngles(1.0, 0.2))" ] }, { "cell_type": "markdown", "id": "e7ab10bd", "metadata": { "papermill": { "duration": 0.00284, "end_time": "2026-06-30T01:09:05.593128+00:00", "exception": false, "start_time": "2026-06-30T01:09:05.590288+00:00", "status": "completed" }, "tags": [] }, "source": [ "The inverse transformation recovers the original $(x, v_x)$:" ] }, { "cell_type": "code", "execution_count": 2, "id": "a1761169", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:09:05.600166Z", "iopub.status.busy": "2026-06-30T01:09:05.599812Z", "iopub.status.idle": "2026-06-30T01:09:05.603576Z", "shell.execute_reply": "2026-06-30T01:09:05.602703Z" }, "papermill": { "duration": 0.008148, "end_time": "2026-06-30T01:09:05.604239+00:00", "exception": false, "start_time": "2026-06-30T01:09:05.596091+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(x, vx) = (np.float64(1.0), np.float64(0.19999999999999996))\n" ] } ], "source": [ "aAHI = actionAngleHarmonicInverse(omega=1.0)\n", "J, O, a = aAH.actionsFreqsAngles(1.0, 0.2)\n", "print(\"(x, vx) =\", aAHI(J, a))" ] }, { "cell_type": "markdown", "id": "59e8dcb1", "metadata": { "papermill": { "duration": 0.006091, "end_time": "2026-06-30T01:09:05.613535+00:00", "exception": false, "start_time": "2026-06-30T01:09:05.607444+00:00", "status": "completed" }, "tags": [] }, "source": [ "For general (non-harmonic) 1D potentials, read on." ] }, { "cell_type": "code", "execution_count": 3, "id": "b1c2d3e4f5a6b7c8d9e0f1a2b3c4d5e6", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:09:05.620837Z", "iopub.status.busy": "2026-06-30T01:09:05.620648Z", "iopub.status.idle": "2026-06-30T01:09:05.629514Z", "shell.execute_reply": "2026-06-30T01:09:05.628773Z" }, "papermill": { "duration": 0.013417, "end_time": "2026-06-30T01:09:05.630109+00:00", "exception": false, "start_time": "2026-06-30T01:09:05.616692+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy\n", "import matplotlib.pyplot as plt\n", "import warnings\n", "\n", "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n", "warnings.filterwarnings(\"ignore\", category=UserWarning)" ] }, { "cell_type": "markdown", "id": "c1d2e3f4a5b6c7d8e9f0a1b2c3d4e5f6", "metadata": { "papermill": { "duration": 0.002997, "end_time": "2026-06-30T01:09:05.636416+00:00", "exception": false, "start_time": "2026-06-30T01:09:05.633419+00:00", "status": "completed" }, "tags": [] }, "source": [ "## actionAngleVertical\n", "\n", "`actionAngleVertical` computes one-dimensional action-angle coordinates\n", "for vertical oscillations. We first need to extract a vertical potential\n", "from a 3D potential using `toVerticalPotential`." ] }, { "cell_type": "code", "execution_count": 4, "id": "d1e2f3a4b5c6d7e8f9a0b1c2d3e4f5a6", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:09:05.643479Z", "iopub.status.busy": "2026-06-30T01:09:05.643295Z", "iopub.status.idle": "2026-06-30T01:09:05.646371Z", "shell.execute_reply": "2026-06-30T01:09:05.645711Z" }, "papermill": { "duration": 0.007677, "end_time": "2026-06-30T01:09:05.647163+00:00", "exception": false, "start_time": "2026-06-30T01:09:05.639486+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "from galpy.potential import toVerticalPotential, MWPotential2014\n", "\n", "vp = toVerticalPotential(MWPotential2014, 1.0)" ] }, { "cell_type": "markdown", "id": "e1f2a3b4c5d6e7f8a9b0c1d2e3f4a5b6", "metadata": { "papermill": { "duration": 0.002956, "end_time": "2026-06-30T01:09:05.653244+00:00", "exception": false, "start_time": "2026-06-30T01:09:05.650288+00:00", "status": "completed" }, "tags": [] }, "source": [ "This extracts the vertical potential at $R = 1$ (in natural units). Now\n", "we set up the `actionAngleVertical` object:" ] }, { "cell_type": "code", "execution_count": 5, "id": "f1a2b3c4d5e6f7a8b9c0d1e2f3a4b5c6", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:09:05.660313Z", "iopub.status.busy": "2026-06-30T01:09:05.660092Z", "iopub.status.idle": "2026-06-30T01:09:05.663173Z", "shell.execute_reply": "2026-06-30T01:09:05.662443Z" }, "papermill": { "duration": 0.007376, "end_time": "2026-06-30T01:09:05.663719+00:00", "exception": false, "start_time": "2026-06-30T01:09:05.656343+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "from galpy.actionAngle import actionAngleVertical\n", "\n", "aAV = actionAngleVertical(pot=vp)" ] }, { "cell_type": "markdown", "id": "a2b3c4d5e6f7a8b9c0d1e2f3a4b5c6d7", "metadata": { "papermill": { "duration": 0.002822, "end_time": "2026-06-30T01:09:05.669597+00:00", "exception": false, "start_time": "2026-06-30T01:09:05.666775+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Computing actions, frequencies, and angles\n", "\n", "The action-angle object can be called with `(x, vx)` to compute\n", "the action $J$. The input is the vertical position and vertical velocity." ] }, { "cell_type": "code", "execution_count": 6, "id": "b2c3d4e5f6a7b8c9d0e1f2a3b4c5d6e7", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:09:05.676336Z", "iopub.status.busy": "2026-06-30T01:09:05.676130Z", "iopub.status.idle": "2026-06-30T01:09:05.688686Z", "shell.execute_reply": "2026-06-30T01:09:05.687719Z" }, "papermill": { "duration": 0.016689, "end_time": "2026-06-30T01:09:05.689245+00:00", "exception": false, "start_time": "2026-06-30T01:09:05.672556+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "text/plain": [ "array([0.01231433])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "aAV(0.1, 0.1)" ] }, { "cell_type": "markdown", "id": "c2d3e4f5a6b7c8d9e0f1a2b3c4d5e6f7", "metadata": { "papermill": { "duration": 0.003002, "end_time": "2026-06-30T01:09:05.695563+00:00", "exception": false, "start_time": "2026-06-30T01:09:05.692561+00:00", "status": "completed" }, "tags": [] }, "source": [ "To also get the frequency $\\Omega$, use `actionsFreqs`:" ] }, { "cell_type": "code", "execution_count": 7, "id": "d2e3f4a5b6c7d8e9f0a1b2c3d4e5f6a7", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:09:05.702768Z", "iopub.status.busy": "2026-06-30T01:09:05.702576Z", "iopub.status.idle": "2026-06-30T01:09:05.716689Z", "shell.execute_reply": "2026-06-30T01:09:05.715873Z" }, "papermill": { "duration": 0.018642, "end_time": "2026-06-30T01:09:05.717353+00:00", "exception": false, "start_time": "2026-06-30T01:09:05.698711+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "text/plain": [ "(array([0.01231433]), array([1.72942467]))" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "aAV.actionsFreqs(0.1, 0.1)" ] }, { "cell_type": "markdown", "id": "e2f3a4b5c6d7e8f9a0b1c2d3e4f5a6b7", "metadata": { "papermill": { "duration": 0.00307, "end_time": "2026-06-30T01:09:05.723854+00:00", "exception": false, "start_time": "2026-06-30T01:09:05.720784+00:00", "status": "completed" }, "tags": [] }, "source": [ "And to get the angle as well, use `actionsFreqsAngles`:" ] }, { "cell_type": "code", "execution_count": 8, "id": "f2a3b4c5d6e7f8a9b0c1d2e3f4a5b6c7", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:09:05.731741Z", "iopub.status.busy": "2026-06-30T01:09:05.731537Z", "iopub.status.idle": "2026-06-30T01:09:05.746616Z", "shell.execute_reply": "2026-06-30T01:09:05.745791Z" }, "papermill": { "duration": 0.020225, "end_time": "2026-06-30T01:09:05.747418+00:00", "exception": false, "start_time": "2026-06-30T01:09:05.727193+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "text/plain": [ "(array([0.01231433]), array([1.72942467]), array([0.9955371]))" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "aAV.actionsFreqsAngles(0.1, 0.1)" ] }, { "cell_type": "markdown", "id": "a3b4c5d6e7f8a9b0c1d2e3f4a5b6c7d8", "metadata": { "papermill": { "duration": 0.003305, "end_time": "2026-06-30T01:09:05.754313+00:00", "exception": false, "start_time": "2026-06-30T01:09:05.751008+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Action conservation along a 1D orbit\n", "\n", "A key property of action variables is that they are conserved along an\n", "orbit. Let's verify this by integrating a 1D orbit and computing the\n", "action at each time step." ] }, { "cell_type": "code", "execution_count": 9, "id": "b3c4d5e6f7a8b9c0d1e2f3a4b5c6d7e8", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:09:05.762324Z", "iopub.status.busy": "2026-06-30T01:09:05.762091Z", "iopub.status.idle": "2026-06-30T01:09:05.777121Z", "shell.execute_reply": "2026-06-30T01:09:05.776353Z" }, "papermill": { "duration": 0.020046, "end_time": "2026-06-30T01:09:05.777886+00:00", "exception": false, "start_time": "2026-06-30T01:09:05.757840+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "from galpy.orbit import Orbit\n", "\n", "o = Orbit([0.1, 0.1]) # 1D orbit: (x, vx)\n", "ts = numpy.linspace(0.0, 20.0, 1001)\n", "o.integrate(ts, vp)" ] }, { "cell_type": "markdown", "id": "38449838", "metadata": { "papermill": { "duration": 0.003229, "end_time": "2026-06-30T01:09:05.784735+00:00", "exception": false, "start_time": "2026-06-30T01:09:05.781506+00:00", "status": "completed" }, "tags": [] }, "source": [ "Now compute the action at each time step and verify conservation:" ] }, { "cell_type": "code", "execution_count": 10, "id": "c3d4e5f6a7b8c9d0e1f2a3b4c5d6e7f8", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:09:05.792545Z", "iopub.status.busy": "2026-06-30T01:09:05.792331Z", "iopub.status.idle": "2026-06-30T01:09:13.324849Z", "shell.execute_reply": "2026-06-30T01:09:13.323974Z" }, "papermill": { "duration": 7.537512, "end_time": "2026-06-30T01:09:13.325712+00:00", "exception": false, "start_time": "2026-06-30T01:09:05.788200+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Compute the action at each time step\n", "actions = aAV(o.x(ts), o.vx(ts))\n", "plt.plot(ts, actions)\n", "plt.xlabel(r\"$t$\")\n", "plt.ylabel(r\"$J$\")\n", "plt.title(\"Action conservation along a 1D orbit\")\n", "plt.ylim(actions.mean() - 0.01, actions.mean() + 0.01);" ] }, { "cell_type": "markdown", "id": "d3e4f5a6b7c8d9e0f1a2b3c4d5e6f7a8", "metadata": { "papermill": { "duration": 0.003309, "end_time": "2026-06-30T01:09:13.333362+00:00", "exception": false, "start_time": "2026-06-30T01:09:13.330053+00:00", "status": "completed" }, "tags": [] }, "source": [ "The action is conserved to high precision along the orbit, as expected." ] }, { "cell_type": "markdown", "id": "e3f4a5b6c7d8e9f0a1b2c3d4e5f6a7b8", "metadata": { "papermill": { "duration": 0.003293, "end_time": "2026-06-30T01:09:13.340114+00:00", "exception": false, "start_time": "2026-06-30T01:09:13.336821+00:00", "status": "completed" }, "tags": [] }, "source": [ "## actionAngleVerticalInverse\n", "\n", "`actionAngleVerticalInverse` computes the reverse transformation: from\n", "action-angle coordinates $(J, \\theta)$ back to phase-space coordinates\n", "$(x, v_x)$. This is useful for constructing tori in 1D potentials.\n", "\n", "We demonstrate this with the `IsothermalDiskPotential`." ] }, { "cell_type": "code", "execution_count": 11, "id": "f3a4b5c6d7e8f9a0b1c2d3e4f5a6b7c8", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:09:13.348250Z", "iopub.status.busy": "2026-06-30T01:09:13.348023Z", "iopub.status.idle": "2026-06-30T01:09:13.350870Z", "shell.execute_reply": "2026-06-30T01:09:13.350192Z" }, "papermill": { "duration": 0.007953, "end_time": "2026-06-30T01:09:13.351542+00:00", "exception": false, "start_time": "2026-06-30T01:09:13.343589+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "from galpy.potential import IsothermalDiskPotential\n", "\n", "ip = IsothermalDiskPotential(amp=1.0, sigma=0.6)" ] }, { "cell_type": "markdown", "id": "a4b5c6d7e8f9a0b1c2d3e4f5a6b7c8d9", "metadata": { "papermill": { "duration": 0.003295, "end_time": "2026-06-30T01:09:13.358328+00:00", "exception": false, "start_time": "2026-06-30T01:09:13.355033+00:00", "status": "completed" }, "tags": [] }, "source": [ "Set up the inverse action-angle object. The `nta` parameter controls the\n", "number of angle points used internally, and `Es` specifies the energies\n", "for which to set up the transformation. Using `setup_interp=True` enables\n", "interpolation between tori at different energies." ] }, { "cell_type": "code", "execution_count": 12, "id": "b4c5d6e7f8a9b0c1d2e3f4a5b6c7d8e9", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:09:13.366390Z", "iopub.status.busy": "2026-06-30T01:09:13.366157Z", "iopub.status.idle": "2026-06-30T01:09:13.517004Z", "shell.execute_reply": "2026-06-30T01:09:13.516245Z" }, "papermill": { "duration": 0.156052, "end_time": "2026-06-30T01:09:13.517868+00:00", "exception": false, "start_time": "2026-06-30T01:09:13.361816+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "from galpy.actionAngle import actionAngleVerticalInverse\n", "\n", "aAVI = actionAngleVerticalInverse(\n", " pot=ip,\n", " nta=512,\n", " Es=numpy.linspace(0.05, 1.0, 10),\n", " setup_interp=True,\n", ")" ] }, { "cell_type": "markdown", "id": "c4d5e6f7a8b9c0d1e2f3a4b5c6d7e8f9", "metadata": { "papermill": { "duration": 0.00322, "end_time": "2026-06-30T01:09:13.524940+00:00", "exception": false, "start_time": "2026-06-30T01:09:13.521720+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Evaluating the inverse transformation\n", "\n", "We can evaluate the transformation to get $(x, v_x)$ from a given action\n", "$J$ and an array of angles $\\theta$." ] }, { "cell_type": "code", "execution_count": 13, "id": "d4e5f6a7b8c9d0e1f2a3b4c5d6e7f8a9", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:09:13.532692Z", "iopub.status.busy": "2026-06-30T01:09:13.532483Z", "iopub.status.idle": "2026-06-30T01:09:13.539483Z", "shell.execute_reply": "2026-06-30T01:09:13.538720Z" }, "papermill": { "duration": 0.012028, "end_time": "2026-06-30T01:09:13.540319+00:00", "exception": false, "start_time": "2026-06-30T01:09:13.528291+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "angles = numpy.linspace(0, 2 * numpy.pi, 100)\n", "x, vx = aAVI(0.1, angles)" ] }, { "cell_type": "markdown", "id": "e4f5a6b7c8d9e0f1a2b3c4d5e6f7a8b9", "metadata": { "papermill": { "duration": 0.003571, "end_time": "2026-06-30T01:09:13.548272+00:00", "exception": false, "start_time": "2026-06-30T01:09:13.544701+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Plotting the torus\n", "\n", "The resulting $(x, v_x)$ pairs trace out a torus (a closed curve in 1D\n", "phase space)." ] }, { "cell_type": "code", "execution_count": 14, "id": "f4a5b6c7d8e9f0a1b2c3d4e5f6a7b8c9", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:09:13.556207Z", "iopub.status.busy": "2026-06-30T01:09:13.556001Z", "iopub.status.idle": "2026-06-30T01:09:13.682249Z", "shell.execute_reply": "2026-06-30T01:09:13.681336Z" }, "papermill": { "duration": 0.131194, "end_time": "2026-06-30T01:09:13.682894+00:00", "exception": false, "start_time": "2026-06-30T01:09:13.551700+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(x, vx)\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$v_x$\")\n", "plt.title(r\"Torus at $J = 0.1$\");" ] }, { "cell_type": "markdown", "id": "b3188764", "metadata": { "papermill": { "duration": 0.003454, "end_time": "2026-06-30T01:09:13.690130+00:00", "exception": false, "start_time": "2026-06-30T01:09:13.686676+00:00", "status": "completed" }, "tags": [] }, "source": [ "You can also specify a torus using its energy instead by using the ``aA1Dinv.J`` method:" ] }, { "cell_type": "code", "execution_count": 15, "id": "30868012", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:09:13.698590Z", "iopub.status.busy": "2026-06-30T01:09:13.698392Z", "iopub.status.idle": "2026-06-30T01:09:13.813645Z", "shell.execute_reply": "2026-06-30T01:09:13.812694Z" }, "papermill": { "duration": 0.120484, "end_time": "2026-06-30T01:09:13.814313+00:00", "exception": false, "start_time": "2026-06-30T01:09:13.693829+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x, vx = aAVI(aAVI.J(0.1), angles)\n", "plt.plot(x, vx)\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$v_x$\")\n", "plt.title(rf\"Torus at $E = 0.1$ (using energy; J = {aAVI.J(0.1):.3f})\");" ] }, { "cell_type": "markdown", "id": "a5b6c7d8e9f0a1b2c3d4e5f6a7b8c9d0", "metadata": { "papermill": { "duration": 0.003633, "end_time": "2026-06-30T01:09:13.821936+00:00", "exception": false, "start_time": "2026-06-30T01:09:13.818303+00:00", "status": "completed" }, "tags": [] }, "source": [ "We can also plot tori at multiple action values to visualize the\n", "phase-space structure:" ] }, { "cell_type": "code", "execution_count": 16, "id": "b5c6d7e8f9a0b1c2d3e4f5a6b7c8d9e0", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:09:13.830373Z", "iopub.status.busy": "2026-06-30T01:09:13.830139Z", "iopub.status.idle": "2026-06-30T01:09:14.019637Z", "shell.execute_reply": "2026-06-30T01:09:14.018678Z" }, "papermill": { "duration": 0.194995, "end_time": "2026-06-30T01:09:14.020646+00:00", "exception": false, "start_time": "2026-06-30T01:09:13.825651+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "angles = numpy.linspace(0, 2 * numpy.pi, 200)\n", "for J in [0.05, 0.1, 0.2, 0.3]:\n", " x, vx = aAVI(J, angles)\n", " plt.plot(x, vx, label=rf\"$J = {J}$\")\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$v_x$\")\n", "plt.legend()\n", "plt.title(\"Tori at different action values\");" ] }, { "cell_type": "markdown", "id": "c5d6e7f8a9b0c1d2e3f4a5b6c7d8d9e0", "metadata": { "papermill": { "duration": 0.003907, "end_time": "2026-06-30T01:09:14.029081+00:00", "exception": false, "start_time": "2026-06-30T01:09:14.025174+00:00", "status": "completed" }, "tags": [] }, "source": [ "The `setup_interp=True` option allows smooth interpolation between the\n", "tori computed at the specified energies, enabling evaluation at arbitrary\n", "action values within the range covered by those energies." ] } ], "metadata": { "kernelspec": { "display_name": "py313", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.14" }, "papermill": { "default_parameters": {}, "duration": 12.129807, "end_time": "2026-06-30T01:09:14.649454+00:00", "environment_variables": {}, "exception": null, "input_path": "doc/source/tutorials/action_angle/vertical_and_inverse.ipynb", "output_path": "doc/source/tutorials/action_angle/vertical_and_inverse.ipynb", "parameters": {}, "start_time": "2026-06-30T01:09:02.519647+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }