Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 012, 14 pages      arXiv:1101.4345

New Variables of Separation for the Steklov-Lyapunov System

Andrey V. Tsiganov
St. Petersburg State University, St. Petersburg, Russia

Received October 31, 2011, in final form March 12, 2012; Published online March 20, 2012

A rigid body in an ideal fluid is an important example of Hamiltonian systems on a dual to the semidirect product Lie algebra $e(3) = so(3)\ltimes\mathbb R^3$. 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.

Key words: bi-Hamiltonian geometry; variables of separation.

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