New Variables of Separation for the Steklov-Lyapunov System
Andrey V. Tsiganov
TL;DR
This paper introduces new variables of separation and a bi-Hamiltonian structure for the Steklov-Lyapunov system and its gyrostatic deformation, advancing the understanding of integrable systems on $e(3)$.
Contribution
It provides novel separation variables and bi-Hamiltonian structures for the Steklov-Lyapunov system, including its gyrostatic deformation, which were not previously known.
Findings
New variables of separation for the system
Bi-Hamiltonian structure established
Extension to gyrostatic deformation
Abstract
A rigid body in an ideal fluid is an important example of Hamiltonian systems on a dual to the semidirect product Lie algebra . 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.
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