Authors: Dragović, Vladimir 
Kukić, Katarina
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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