The Kowalevski top as a reduction of a Hamiltonian system on $\mathfrak {sp}(4, \mathbb {R})^*$

Abstract

We show that the Kowalevski top and Kowalevski gyrostat are obtained as a reduction of a Hamiltonian system on sp(4,R)*. Therefore the Lax-pair representations for the Kowalevski top and Kowalevski gyrostat are obtained via a direct method by transforming the canonical Lax-pair representation of a system on sp(4,R)*. Also we show that the nontrivial integral of motion of the Kowalevski top comes from a Casimir function of the Lie-Poisson algebra sp(4,R)*.