  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 $so(4)$.
