On the Steklov-Lyapunov case of the rigid body motion

Details On the Steklov-Lyapunov case of the rigid body motion On the Steklov-Lyapunov case of the rigid body motion

2004-06-10

arxiv.org/abs/nlin/0406017v1

Regular and Chaotic Dynamics, v.9(2), p.77-91, 2004

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages, LaTeX with hyperref,amsfonts,amssymb, amsmath,theorem,mathrsfs and xy

Scientific paper

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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