On the Steklov–Lyapunov case of the rigid body motion

    2004, Volume 9, Number 2, pp.  77-89

    Author(s): Tsiganov A. V.

    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 $so(4)$.
    Citation: Tsiganov A. V., On the Steklov–Lyapunov case of the rigid body motion, Regular and Chaotic Dynamics, 2004, Volume 9, Number 2, pp. 77-89


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