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arXiv · 1903.00917

The Rigid Body Dynamics in an ideal fluid: Clebsch Top and Kummer surfaces

Jean-Pierre Francoise·Daisuke Tarama
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Abstract

This is an expository presentation of a completely integrable Hamiltonian system of Clebsch top under a special condition introduced by Weber. After a brief account on the geometric setting of the system, the structure of the Poisson commuting first integrals is discussed following the methods by Magri and Skrypnyk. Introducing supplementary coordinates, a geometric connection to Kummer surfaces, a typical class of K3 surfaces, is mentioned and also the system is linearized on the Jacobian of a hyperelliptic curve of genus two determined by the system. Further some special solutions contained in some vector subspace are discussed. Finally, an explicit computation of the action-angle coordinates is introduced.

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Jean-Pierre Francoise, Daisuke Tarama. 2019-03-03. The Rigid Body Dynamics in an ideal fluid: Clebsch Top and Kummer surfaces. https://arxiv.org/abs/1903.00917

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