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Tr. Mat. Inst. Steklova, 2014, Volume 286, Pages 246–261 (Mi tm3565)  

This article is cited in 5 scientific papers (total in 5 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

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.

DOI: https://doi.org/10.1134/S0371968514030133

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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 286, 224–239

Bibliographic databases:

UDC: 517.958
Received in April 2013
Language:

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, Tr. 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 Tr. Mat. Inst. Steklova
\yr 2014
\vol 286
\pages 246--261
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. Dragovic, K. Kukic, “Role of discriminantly separable polynomials in integrable dynamical systems”, Tim 2013 Physics Conference, AIP Conf. Proc., 1634, eds. O. Bunoiu, N. Avram, A. Popescu, Amer. Inst. Phys., 2014, 3–8  crossref  mathscinet  isi
    2. P. E. Ryabov, A. Yu. Savushkin, “Fazovaya topologiya volchka Kovalevskoi – Sokolova”, Nelineinaya dinam., 11:2 (2015), 287–317  mathnet
    3. Mikhail P. Kharlamov, Pavel E. Ryabov, Alexander Yu. Savushkin, “Topological Atlas of the Kowalevski–Sokolov Top”, Regul. Chaotic Dyn., 21:1 (2016), 24–65  mathnet  crossref  mathscinet  zmath
    4. V. Dragovic, K. Kukic, “Discriminantly separable polynomials and the generalized Kowalevski top”, Theor. Appl. Mech., 44:2 (2017), 229–236  crossref  isi  scopus
    5. Vladimir Dragović, Milena Radnović, “Caustics of Poncelet Polygons and Classical Extremal Polynomials”, Regul. Chaotic Dyn., 24:1 (2019), 1–35  mathnet  crossref
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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