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Regul. Chaotic Dyn., 2014, Volume 19, Issue 2, Pages 226–244 (Mi rcd128)  

This article is cited in 4 scientific papers (total in 4 papers)

Extensions of the Appelrot Classes for the Generalized Gyrostat in a Double Force Field

Mikhail P. Kharlamov

Russian Academy of National Economy and Public Administration, Volgograd branch, ul. Gagarina 8, Volgograd, 400131 Russia

Abstract: For the integrable system on $e(3,2)$ found by Sokolov and Tsiganov we obtain explicit equations of some invariant 4-dimensional manifolds on which the induced systems are almost everywhere Hamiltonian with two degrees of freedom. These subsystems generalize the famous Appelrot classes of critical motions of the Kowalevski top. For each subsystem we point out a commutative pair of independent integrals, describe the sets of degeneration of the induced symplectic structure. With the help of the obtained invariant relations, for each subsystem we calculate the outer type of its points considered as critical points of the initial system with three degrees of freedom.

Keywords: generalized two-field gyrostat, critical subsystems, Appelrot classes, invariant relations, types of critical points

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-97025
14-01-00119
This work was partially supported by RFBR and the authorities of the Volgograd Region, research projects No. 13-01-97025, 14-01-00119.


DOI: https://doi.org/10.1134/S1560354714020063

References: PDF file   HTML file

Bibliographic databases:

MSC: 70E05, 70E17, 37J15, 37J20
Received: 05.09.2013
Accepted:30.10.2013
Language:

Citation: Mikhail P. Kharlamov, “Extensions of the Appelrot Classes for the Generalized Gyrostat in a Double Force Field”, Regul. Chaotic Dyn., 19:2 (2014), 226–244

Citation in format AMSBIB
\Bibitem{Kha14}
\by Mikhail~P.~Kharlamov
\paper Extensions of the Appelrot Classes for the Generalized
Gyrostat in a Double Force Field
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 2
\pages 226--244
\mathnet{http://mi.mathnet.ru/rcd128}
\crossref{https://doi.org/10.1134/S1560354714020063}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3189259}
\zmath{https://zbmath.org/?q=an:1309.70007}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000334198000006}


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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. P. E. Ryabov, A. Yu. Savushkin, “Fazovaya topologiya volchka Kovalevskoi – Sokolova”, Nelineinaya dinam., 11:2 (2015), 287–317  mathnet
    2. P. E. Ryabov, “New invariant relations for the generalized two-field gyrostat”, J. Geom. Phys., 87 (2015), 415–421  crossref  mathscinet  zmath  isi  scopus
    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. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Generalizations of the Kovalevskaya case and quaternions”, Proc. Steklov Inst. Math., 295 (2016), 33–44  mathnet  crossref  crossref  mathscinet  isi  elib
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