The Kowalevski top as a reduction of a Hamiltonian system on 𝔰𝔭(4,ℝ)*

Ivanescu, C.; Savu, A.

doi:10.1090/S0002-9939-02-06541-3

The Kowalevski top as a reduction of a Hamiltonian system on $\mathfrak {sp}(4, \mathbb {R})^*$
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by C. Ivanescu and A. Savu

Proc. Amer. Math. Soc. 131 (2003), 607-618

DOI: https://doi.org/10.1090/S0002-9939-02-06541-3

Published electronically: May 22, 2002

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Abstract:

We show that the Kowalevski top and Kowalevski gyrostat are obtained as a reduction of a Hamiltonian system on $\mathfrak {sp}(4,\mathbb {R})^*$. 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 $\mathfrak {sp}(4, \mathbb {R})^*$. Also we show that the nontrivial integral of motion of the Kowalevski top comes from a Casimir function of the Lie-Poisson algebra $\mathfrak {sp}(4, \mathbb {R})^*$.

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