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Vestnik SamGU. Estestvenno-Nauchnaya Ser., 2014, Issue 7(118), Pages 60–69
(Mi vsgu427)
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This article is cited in 24 scientific papers (total in 24 papers)
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
(published under the terms of the Creative Commons Attribution 4.0 International License)
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.
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
Linking options:
https://www.mathnet.ru/eng/vsgu427 https://www.mathnet.ru/eng/vsgu/y2014/i7/p60
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Abstract page: | 222 | Full-text PDF : | 81 | References: | 61 |
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