Closed stable orbits in a strongly coupled resonant Wilberforce pendulum

TL;DR

This paper proves the existence of stable, closed orbits in a strongly coupled Wilberforce pendulum with a 1:2 resonance, using geometric reduction and averaging methods.

Contribution

It introduces a novel combination of geometric singular symplectic reduction and averaging techniques to establish stable orbits in a resonant Wilberforce pendulum.

Findings

Existence of closed stable orbits in the 1:2 resonance case.

Application of combined geometric and averaging methods.

Advancement in understanding resonant coupled oscillators.

Abstract

We prove the existence of closed stable orbits in a strongly coupled Wilberforce pendulum, for the case of a $1:2$ resonance, by using techniques of geometric singular symplectic reduction combined with the more classical averaging method of Moser.