|Title:||The Sokolov case, integrable Kirchhoff elasticae, and genus 2 theta functions via discriminantly separable polynomials||Journal:||Proceedings of the Steklov Institute of Mathematics||Volume:||286||Issue:||1||First page:||224||Last page:||239||Issue Date:||1-Jan-2014||Rank:||M23||ISSN:||0081-5438||DOI:||10.1134/S0081543814060133||Abstract:||
We use the discriminantly separable polynomials of degree 2 in each of three variables to integrate explicitly the Sokolov case of a rigid body in an ideal fluid and integrable Kirchhoff elasticae in terms of genus 2 theta functions. The integration procedure is a natural generalization of the one used by Kowalevski in her celebrated 1889 paper. The algebraic background for the most important changes of variables in this integration procedure is associated to the structure of the two-valued groups on an elliptic curve. Such two-valued groups have been introduced by V.M. Buchstaber.
|Publisher:||Springer Link||Project:||Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems|
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