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On the Steklov-Lyapunov case of the rigid body motion

A. V. Tsiganov
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Abstract

We construct a Poisson map between manifolds with linear Poisson brackets corresponding to the two samples of Lie algebra $e(3)$. Using this map we establish equivalence of the Steklov-Lyapunov system and the motion of a particle on the surface of the sphere under the influence of the fourth order potential. To study separation of variables for the Steklov case on the Lie algebra $so(4)$ we use the twisted Poisson map between the bi-Hamiltonian manifolds $e(3)$ and $so(4)$.

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A. V. Tsiganov. 2004-06-10. On the Steklov-Lyapunov case of the rigid body motion. https://doi.org/10.1070/rd2004v009n02abeh000267

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