Geodesic
The Sokolov case, integrable Kirchhoff elasticae, and genus~2 theta functions via discriminantly separable polynomials
Informatics and Automation, Algebraic topology, convex polytopes, and related topics, Tome 286 (2014), pp. 246-261

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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. 
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     author = {Vladimir Dragovi\'c and Katarina Kuki\'c},
     title = {The {Sokolov} case, integrable {Kirchhoff} elasticae, and genus~2 theta functions via discriminantly separable polynomials},
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     year = {2014},
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     url = {http://geodesic.mathdoc.fr/item/TRSPY_2014_286_a12/}
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Vladimir Dragović; Katarina Kukić. The Sokolov case, integrable Kirchhoff elasticae, and genus~2 theta functions via discriminantly separable polynomials. Informatics and Automation, Algebraic topology, convex polytopes, and related topics, Tome 286 (2014), pp. 246-261. http://geodesic.mathdoc.fr/item/TRSPY_2014_286_a12/