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Nelin. Dinam., 2007, Volume 3, Number 3, Pages 331–348 (Mi nd142)  

This article is cited in 6 scientific papers (total in 6 papers)

Critical subsystems of the Kowalevski gyrostat in two constant fields

M. P. Kharlamov

Volgograd Academy of Public Administration

Abstract: The Kowalevski gyrostat in two constant fields is known as the unique profound example of an integrable Hamiltonian system with three degrees of freedom not reducible to a family of systems in fewer dimensions. As the first approach to topological analysis of this system we find the critical set of the integral map; this set consists of the trajectories with number of frequencies less than three. We obtain the equations of the bifurcation diagram in three-dimensional space of the first integrals constants.

Keywords: Kowalevski gyrostat, two constant fields, critical set, bifurcation diagram.

Full text: PDF file (228 kB)

Document Type: Article
MSC: 70E17, 70G40

Citation: M. P. Kharlamov, “Critical subsystems of the Kowalevski gyrostat in two constant fields”, Nelin. Dinam., 3:3 (2007), 331–348

Citation in format AMSBIB
\Bibitem{Kha07}
\by M.~P.~Kharlamov
\paper Critical subsystems of the Kowalevski gyrostat in two constant fields
\jour Nelin. Dinam.
\yr 2007
\vol 3
\issue 3
\pages 331--348
\mathnet{http://mi.mathnet.ru/nd142}


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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, “Analiticheskaya klassifikatsiya osobennostei integriruemogo sluchaya Kovalevskoi–Yakhya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2010, no. 4, 25–30  mathnet
    2. Kharlamov M.P., Savushkin A.Yu., “Geometricheskii podkhod k razdeleniyu peremennykh v mekhanicheskikh sistemakh”, Vestn. Volgogradskogo gos. un-ta. Ser. 1: Matem. Fiz., 2010, no. 13, 47–74  elib
    3. I. I. Kharlamova, P. E. Ryabov, “Elektronnyi atlas bifurkatsionnykh diagramm girostata Kovalevskoi–Yakhya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 2, 147–162  mathnet  elib
    4. M. P. Kharlamov, P. E. Ryabov, “Diagrammy Smeila–Fomenko i grubye invarianty sluchaya Kovalevskoi–Yakhya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 4, 40–59  mathnet
    5. P. E. Ryabov, “Phase topology of one irreducible integrable problem in the dynamics of a rigid body”, Theoret. and Math. Phys., 176:2 (2013), 1000–1015  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. P. E. Ryabov, A. Yu. Savushkin, “Fazovaya topologiya volchka Kovalevskoi – Sokolova”, Nelineinaya dinam., 11:2 (2015), 287–317  mathnet
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