A Note on the Rotationally Symmetric SO(4) Euler Rigid Body

TL;DR

This paper analyzes a special case of the SO(4) Euler rigid body with symmetric inertia, using bihamiltonian geometry to algebraically integrate its equations via separation of variables.

Contribution

It introduces a bihamiltonian geometric approach to integrate the symmetric SO(4) Euler rigid body algebraically, advancing the understanding of its integrability.

Findings

Successful algebraic integration of the symmetric SO(4) Euler rigid body

Application of bihamiltonian geometry to rigid body dynamics

Demonstration of separation of variables method in this context

Abstract

We consider an SO(4) Euler rigid body with two 'inertia momenta' coinciding. We study it from the point of view of bihamiltonian geometry. We show how to algebraically integrate it by means of the method of separation of variables.