{ "cells": [ { "cell_type": "markdown", "id": "a1b2c3d4e5f6a7b8c9d0e1f2a3b4c5d6", "metadata": { "papermill": { "duration": 0.004324, "end_time": "2026-05-16T13:42:05.218559+00:00", "exception": false, "start_time": "2026-05-16T13:42:05.214235+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": "2026-05-16T13:42:05.226979Z", "iopub.status.busy": "2026-05-16T13:42:05.226751Z", "iopub.status.idle": "2026-05-16T13:42:07.560881Z", "shell.execute_reply": "2026-05-16T13:42:07.559715Z" }, "papermill": { "duration": 2.339376, "end_time": "2026-05-16T13:42:07.561592+00:00", "exception": false, "start_time": "2026-05-16T13:42:05.222216+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": 0.003255, "end_time": "2026-05-16T13:42:07.568568+00:00", "exception": false, "start_time": "2026-05-16T13:42:07.565313+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": "2026-05-16T13:42:07.576564Z", "iopub.status.busy": "2026-05-16T13:42:07.576243Z", "iopub.status.idle": "2026-05-16T13:42:07.580118Z", "shell.execute_reply": "2026-05-16T13:42:07.579247Z" }, "papermill": { "duration": 0.009029, "end_time": "2026-05-16T13:42:07.581035+00:00", "exception": false, "start_time": "2026-05-16T13:42:07.572006+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": 0.003492, "end_time": "2026-05-16T13:42:07.588117+00:00", "exception": false, "start_time": "2026-05-16T13:42:07.584625+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": "2026-05-16T13:42:07.595925Z", "iopub.status.busy": "2026-05-16T13:42:07.595720Z", "iopub.status.idle": "2026-05-16T13:42:07.604417Z", "shell.execute_reply": "2026-05-16T13:42:07.603659Z" }, "papermill": { "duration": 0.013652, "end_time": "2026-05-16T13:42:07.605234+00:00", "exception": false, "start_time": "2026-05-16T13:42:07.591582+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": 0.003381, "end_time": "2026-05-16T13:42:07.612149+00:00", "exception": false, "start_time": "2026-05-16T13:42:07.608768+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": "2026-05-16T13:42:07.620047Z", "iopub.status.busy": "2026-05-16T13:42:07.619864Z", "iopub.status.idle": "2026-05-16T13:42:07.623310Z", "shell.execute_reply": "2026-05-16T13:42:07.622387Z" }, "papermill": { "duration": 0.008337, "end_time": "2026-05-16T13:42:07.623979+00:00", "exception": false, "start_time": "2026-05-16T13:42:07.615642+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": 0.003375, "end_time": "2026-05-16T13:42:07.630871+00:00", "exception": false, "start_time": "2026-05-16T13:42:07.627496+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": "2026-05-16T13:42:07.641188Z", "iopub.status.busy": "2026-05-16T13:42:07.640976Z", "iopub.status.idle": "2026-05-16T13:42:07.643969Z", "shell.execute_reply": "2026-05-16T13:42:07.643074Z" }, "papermill": { "duration": 0.007689, "end_time": "2026-05-16T13:42:07.644608+00:00", "exception": false, "start_time": "2026-05-16T13:42:07.636919+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": 0.003359, "end_time": "2026-05-16T13:42:07.651542+00:00", "exception": false, "start_time": "2026-05-16T13:42:07.648183+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": "2026-05-16T13:42:07.659470Z", "iopub.status.busy": "2026-05-16T13:42:07.659290Z", "iopub.status.idle": "2026-05-16T13:42:07.673894Z", "shell.execute_reply": "2026-05-16T13:42:07.672993Z" }, "papermill": { "duration": 0.019456, "end_time": "2026-05-16T13:42:07.674536+00:00", "exception": false, "start_time": "2026-05-16T13:42:07.655080+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": 0.003407, "end_time": "2026-05-16T13:42:07.681666+00:00", "exception": false, "start_time": "2026-05-16T13:42:07.678259+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": "2026-05-16T13:42:07.689716Z", "iopub.status.busy": "2026-05-16T13:42:07.689534Z", "iopub.status.idle": "2026-05-16T13:42:07.705281Z", "shell.execute_reply": "2026-05-16T13:42:07.704335Z" }, "papermill": { "duration": 0.020615, "end_time": "2026-05-16T13:42:07.705895+00:00", "exception": false, "start_time": "2026-05-16T13:42:07.685280+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": 0.003543, "end_time": "2026-05-16T13:42:07.713132+00:00", "exception": false, "start_time": "2026-05-16T13:42:07.709589+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": "2026-05-16T13:42:07.721592Z", "iopub.status.busy": "2026-05-16T13:42:07.721407Z", "iopub.status.idle": "2026-05-16T13:42:07.737782Z", "shell.execute_reply": "2026-05-16T13:42:07.737025Z" }, "papermill": { "duration": 0.021617, "end_time": "2026-05-16T13:42:07.738602+00:00", "exception": false, "start_time": "2026-05-16T13:42:07.716985+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": 0.003551, "end_time": "2026-05-16T13:42:07.745986+00:00", "exception": false, "start_time": "2026-05-16T13:42:07.742435+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": "2026-05-16T13:42:07.754791Z", "iopub.status.busy": "2026-05-16T13:42:07.754368Z", "iopub.status.idle": "2026-05-16T13:42:07.769501Z", "shell.execute_reply": "2026-05-16T13:42:07.768582Z" }, "papermill": { "duration": 0.020258, "end_time": "2026-05-16T13:42:07.770177+00:00", "exception": false, "start_time": "2026-05-16T13:42:07.749919+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": 0.00354, "end_time": "2026-05-16T13:42:07.777442+00:00", "exception": false, "start_time": "2026-05-16T13:42:07.773902+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": "2026-05-16T13:42:07.785716Z", "iopub.status.busy": "2026-05-16T13:42:07.785521Z", "iopub.status.idle": "2026-05-16T13:42:16.178028Z", "shell.execute_reply": "2026-05-16T13:42:16.176930Z" }, "papermill": { "duration": 8.39778, "end_time": "2026-05-16T13:42:16.178898+00:00", "exception": false, "start_time": "2026-05-16T13:42:07.781118+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": 0.003722, "end_time": "2026-05-16T13:42:16.186796+00:00", "exception": false, "start_time": "2026-05-16T13:42:16.183074+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": 0.003677, "end_time": "2026-05-16T13:42:16.194393+00:00", "exception": false, "start_time": "2026-05-16T13:42:16.190716+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": "2026-05-16T13:42:16.203152Z", "iopub.status.busy": "2026-05-16T13:42:16.202886Z", "iopub.status.idle": "2026-05-16T13:42:16.206210Z", "shell.execute_reply": "2026-05-16T13:42:16.205374Z" }, "papermill": { "duration": 0.008868, "end_time": "2026-05-16T13:42:16.207144+00:00", "exception": false, "start_time": "2026-05-16T13:42:16.198276+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": 0.003733, "end_time": "2026-05-16T13:42:16.214742+00:00", "exception": false, "start_time": "2026-05-16T13:42:16.211009+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": "2026-05-16T13:42:16.223497Z", "iopub.status.busy": "2026-05-16T13:42:16.223318Z", "iopub.status.idle": "2026-05-16T13:42:16.344766Z", "shell.execute_reply": "2026-05-16T13:42:16.343724Z" }, "papermill": { "duration": 0.126883, "end_time": "2026-05-16T13:42:16.345584+00:00", "exception": false, "start_time": "2026-05-16T13:42:16.218701+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": 0.003804, "end_time": "2026-05-16T13:42:16.353835+00:00", "exception": false, "start_time": "2026-05-16T13:42:16.350031+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": "2026-05-16T13:42:16.362860Z", "iopub.status.busy": "2026-05-16T13:42:16.362612Z", "iopub.status.idle": "2026-05-16T13:42:16.370149Z", "shell.execute_reply": "2026-05-16T13:42:16.369359Z" }, "papermill": { "duration": 0.013381, "end_time": "2026-05-16T13:42:16.371142+00:00", "exception": false, "start_time": "2026-05-16T13:42:16.357761+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": 0.003737, "end_time": "2026-05-16T13:42:16.378888+00:00", "exception": false, "start_time": "2026-05-16T13:42:16.375151+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": "2026-05-16T13:42:16.387544Z", "iopub.status.busy": "2026-05-16T13:42:16.387364Z", "iopub.status.idle": "2026-05-16T13:42:16.517398Z", "shell.execute_reply": "2026-05-16T13:42:16.516377Z" }, "papermill": { "duration": 0.135497, "end_time": "2026-05-16T13:42:16.518276+00:00", "exception": false, "start_time": "2026-05-16T13:42:16.382779+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": 0.003895, "end_time": "2026-05-16T13:42:16.526506+00:00", "exception": false, "start_time": "2026-05-16T13:42:16.522611+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": "2026-05-16T13:42:16.535522Z", "iopub.status.busy": "2026-05-16T13:42:16.535316Z", "iopub.status.idle": "2026-05-16T13:42:16.751841Z", "shell.execute_reply": "2026-05-16T13:42:16.750687Z" }, "papermill": { "duration": 0.222095, "end_time": "2026-05-16T13:42:16.752596+00:00", "exception": false, "start_time": "2026-05-16T13:42:16.530501+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": 0.004099, "end_time": "2026-05-16T13:42:16.761164+00:00", "exception": false, "start_time": "2026-05-16T13:42:16.757065+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": "2026-05-16T13:42:16.770548Z", "iopub.status.busy": "2026-05-16T13:42:16.770367Z", "iopub.status.idle": "2026-05-16T13:42:16.955954Z", "shell.execute_reply": "2026-05-16T13:42:16.954855Z" }, "papermill": { "duration": 0.191311, "end_time": "2026-05-16T13:42:16.956693+00:00", "exception": false, "start_time": "2026-05-16T13:42:16.765382+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": 0.004361, "end_time": "2026-05-16T13:42:16.966037+00:00", "exception": false, "start_time": "2026-05-16T13:42:16.961676+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": "3.13.13" }, "papermill": { "default_parameters": {}, "duration": 13.250977, "end_time": "2026-05-16T13:42:17.586630+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": "2026-05-16T13:42:04.335653+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }