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Sbornik: Mathematics, 2012, Volume 203, Issue 2, Pages 257–287
DOI: https://doi.org/10.1070/SM2012v203n02ABEH004222 (Mi sm7758) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Classification of singularities in the problem of motion of the Kovalevskaya top in a double force field

P. E. Ryabova, M. P. Kharlamovb

a Financial University under the Government of the Russian Federation, Moscow
b Volgograd Academy of Public Administration
English version PDF (714 kB) Citations (6) Russian version article
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DOI: https://doi.org/10.1070/SM2012v203n02ABEH004222
Abstract: The problem of motion of the Kovalevskaya top in a double force field is investigated (the integrable case of A. G. Reyman and M. A. Semenov-Tian-Shansky without a gyrostatic momentum). It is a completely integrable Hamiltonian system with three degrees of freedom not reducible to a family of systems with two degrees of freedom. The critical set of the integral map is studied. The critical subsystems and bifurcation diagrams are described. The classification of all nondegenerate critical points is given. The set of these points consists of equilibria (nondegenerate singularities of rank 0), of singular periodic motions (nondegenerate singularities of rank 1), and also of critical two-frequency motions (nondegenerate singularities of rank 2).
Bibliography: 32 titles.
Keywords: singularities of integrable Hamiltonian systems, momentum map, bifurcation diagram.
Received: 22.06.2010 and 07.04.2011
Bibliographic databases:
Document Type: Article
UDC: 517.938.5+531.38
MSC: Primary 70E40; Secondary 37J35, 37N05, 70G40
Language: English
Original paper language: Russian
Citation: P. E. Ryabov, M. P. Kharlamov, “Classification of singularities in the problem of motion of the Kovalevskaya top in a double force field”, Sb. Math., 203:2 (2012), 257–287
Citation in format AMSBIB
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\paper Classification of singularities in the problem of motion of the Kovalevskaya top in a~double force field
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\yr 2012
\vol 203
\issue 2
\pages 257--287
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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