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

2019/03/03 by Francoise, Jean-Pierre, Tarama, Daisuke
#14D06 #37J35 #58K10 #58K50 #70E15 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1903.00917

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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