Magnetic Geodesic Flows on Coadjoint Orbits

TL;DR

This paper studies a class of magnetic geodesic flows on coadjoint orbits of compact Lie groups, demonstrating their complete integrability when influenced by the Kirillov-Konstant 2-form.

Contribution

It introduces a new class of integrable magnetic geodesic flows on coadjoint orbits with a specific magnetic field, expanding understanding of geometric mechanics.

Findings

Identification of integrable magnetic flows on coadjoint orbits

Use of Kirillov-Konstant 2-form as magnetic field

Extension of integrability results to magnetic settings

Abstract

We describe a class of completely integrable $G$-invariant magnetic geodesic flows on (co)adjoint orbits of a compact connected Lie group $G$ with magnetic field given by the Kirillov-Konstant 2-form.