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arXiv · 0812.0217

On bi-hamiltonian geometry of some integrable systems on the sphere with cubic integral of motion

A V Vershilov·A V Tsiganov
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Abstract

We obtain bi-Hamiltonian structure for a family of integrable systems on the sphere S with an additional integral of third order in momenta. These results are applied to the Goryachev system and Goryachev-Chaplygin top for which we give an explicit procedure to find the separated coordinates and the separated relations.

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A V Vershilov, A V Tsiganov. 2008-12-12. On bi-hamiltonian geometry of some integrable systems on the sphere with cubic integral of motion. https://doi.org/10.1088/1751-8113%2F42%2F10%2F105203

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