Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2006, Volume 2, Number 4, Pages 453–472 (Mi nd184)  

This article is cited in 7 scientific papers (total in 7 papers)

Generalized 4th Appelrot class: region of existence of motions and separation of variables

M. P. Kharlamov

Volgograd Academy of Public Administration
Full-text PDF (242 kB) Citations (7)
Abstract: We consider the analogue of the 4th Appelrot class of the Kowalevskaya top for the case of double force field. The trajectories of this family fill the 4-dimensional surface in the 6-dimensional phase space. We point out two almost everywhere independent partial integrals that give the regular parametrization of the corresponding sheet of the bifurcation diagram in the complete problem. Projections of the Liouville tori onto the plane of auxiliary variables are investigated. The bifurcation diagram of the partial integrals is found. The region of existence of motions in terms of the integral constants is established. We introduce the change of variables that separate the system of differential equations for this case.
Keywords: Kowalevskaya top, double field, Appelrot classes, separation of variables.
Document Type: Article
UDC: 531.38
MSC: 70E17, 70G40
Language: Russian
Citation: M. P. Kharlamov, “Generalized 4th Appelrot class: region of existence of motions and separation of variables”, Nelin. Dinam., 2:4 (2006), 453–472
Citation in format AMSBIB
\Bibitem{Kha06}
\by M.~P.~Kharlamov
\paper Generalized 4th Appelrot class: region of existence of motions and separation of variables
\jour Nelin. Dinam.
\yr 2006
\vol 2
\issue 4
\pages 453--472
\mathnet{http://mi.mathnet.ru/nd184}
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  • https://www.mathnet.ru/eng/nd/v2/i4/p453
  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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