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Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2014, Issue 7(118), Pages 60–69 (Mi vsgu427)  

Mathematics

Integrable systems on tangent bundle of multi-dimensional sphere

N. V. Pokhodnyaa, M. V. Shamolinb

a Sholokhov Moscow State University for Humanities, Moscow, 109240, Russian Federation
b Institute of Mechanics, Lomonosov Moscow State University, Moscow, 119192, Russian Federation

Abstract: The systems which have finite-dimensional spheres as the space of positions, are arising in many problems of multi-dimensional dynamics. Accordingly, tangent bundles of those spheres become phase spaces of such systems. In the article activity of inductive transition in the system on tangent bundle of low-dimensional sphere under increase of its dimension and absence of force field is analyzed. At that, nonconservative fields of forces are presented with the presence of which the systems possess the complete choice of first integrals expressing in terms of finite combination of elementary functions and are, in general, the transcendental functions of its variables.

Keywords: dynamical system, integrability in terms of elementary functions, transcendental first integral.

Full text: PDF file (138 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file

Document Type: Article
UDC: 517.925+531.01
Received: 29.03.2014
Accepted:29.03.2014

Citation: N. V. Pokhodnya, M. V. Shamolin, “Integrable systems on tangent bundle of multi-dimensional sphere”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2014, no. 7(118), 60–69

Citation in format AMSBIB
\Bibitem{PokSha14}
\by N.~V.~Pokhodnya, M.~V.~Shamolin
\paper Integrable systems on tangent bundle of multi-dimensional sphere
\jour Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya
\yr 2014
\issue 7(118)
\pages 60--69
\mathnet{http://mi.mathnet.ru/vsgu427}


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  • Вестник Самарского государственного университета. Естественнонаучная серия
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