New Variables of Separation for the Steklov-Lyapunov System

Abstract

A rigid body in an ideal fluid is an important example of Hamiltonian systems on a dual to the semidirect product Lie algebra e(3)=so(3)⋉R³. We present the bi-Hamiltonian structure and the corresponding variables of separation on this phase space for the Steklov-Lyapunov system and it's gyrostatic deformation.