The inverted pendulum

It is a surprising fact that an inverted pendulum can be stabilised in the upright position through vertical oscillation of its pivot at a suitable amplitude and (high) frequency. This also works for an inverted double pendulum and in fact much more generally too (see D. Acheson, "A Pendulum Theorem", 1993).

It would be nice to have an animation which allows one to explore the region of stability for the inverted single or double pendulum by adjusting the amplitude and frequency of the pivot's oscillation (and perhaps also some other parameters, such as gravity) using sliders.

No files, tests, or entry points are named. Start by reviewing the issue and D. Acheson's “A Pendulum Theorem” reference, then define whether the animation covers a single pendulum, double pendulum, or both. Done means users can adjust pivot amplitude and frequency with sliders and explore the resulting stability region.

Scritto dal modello di indicizzazione a partire dal testo della issue.