New Variables of Separation for the Steklov-Lyapunov System

preprint2012arXivOpen access

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.

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New Variables of Separation for the Steklov-Lyapunov System

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