{ "cells": [ { "cell_type": "markdown", "id": "a1f2b3c4d5e6", "metadata": { "papermill": { "duration": 0.003311, "end_time": "2026-05-16T13:40:14.881180+00:00", "exception": false, "start_time": "2026-05-16T13:40:14.877869+00:00", "status": "completed" }, "tags": [] }, "source": [ "# Action-Angle Coordinates: Adiabatic Approximation\n", "\n", "The adiabatic approximation (`actionAngleAdiabatic`) separates the radial\n", "and vertical motions, computing $J_z$ at each radius while assuming that\n", "the radial motion is slow compared to the vertical oscillation\n", "(e.g., [Binney & McMillan 2010](http://adsabs.harvard.edu/abs/2010MNRAS.401.2318B)).\n", "This is fast but less accurate than the [Staeckel method](staeckel.ipynb) for orbits with\n", "large vertical excursions.\n", "\n", "