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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Volume 286, Pages 246–261
DOI: https://doi.org/10.1134/S0371968514030133 (Mi tm3565) 		 
This article is cited in 9 scientific papers (total in 9 papers)

The Sokolov case, integrable Kirchhoff elasticae, and genus 2 theta functions via discriminantly separable polynomials

Vladimir Dragovićab, Katarina Kukićc

a Department of Mathematical Sciences, University of Texas at Dallas, Richardson, TX, USA
b Mathematical Institute SANU, Belgrade, Serbia
c Faculty for Traffic and Transport Engineering, University of Belgrade, Belgrade, Serbia
Full-text PDF (242 kB) Citations (9)
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DOI: https://doi.org/10.1134/S0371968514030133
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.
Received in April 2013
English version:
Proceedings of the Steklov Institute of Mathematics, 2014, Volume 286, Pages 224–239
DOI: https://doi.org/10.1134/S0081543814060133
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: English
Citation: Vladimir Dragović, Katarina Kukić, “The Sokolov case, integrable Kirchhoff elasticae, and genus 2 theta functions via discriminantly separable polynomials”, Algebraic topology, convex polytopes, and related topics, Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 286, MAIK Nauka/Interperiodica, Moscow, 2014, 246–261; Proc. Steklov Inst. Math., 286 (2014), 224–239
Citation in format AMSBIB
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\by Vladimir~Dragovi{\'c}, Katarina~Kuki{\'c}
\paper The Sokolov case, integrable Kirchhoff elasticae, and genus~2 theta functions via discriminantly separable polynomials
\inbook Algebraic topology, convex polytopes, and related topics
\bookinfo Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 70th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2014
\vol 286
\pages 246--261
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 9 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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