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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2011, Issue 2, Pages 147–162 (Mi vuu223)  

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

COMPUTER SCIENCE

The electronic atlas of bifurcation diagrams of the Kowalevski–Yehia gyrostat

I. I. Kharlamovaa, P. E. Ryabovb

a Volgograd Academy of Public Administration, Volgograd, Russia
b Financial University under the Government of the Russian Federation, Moscow, Russia
Full-text PDF (484 kB) Citations (4)
References:
Abstract: The integrable case of Kowalevski–Yehia in the dynamics of a gyrostat is considered. We present a new approach to classifying the bifurcation diagrams of reduced systems. We find efficiently checked existence conditions for the critical motions on the area integral constant sections of the surfaces bearing the 3-diagram of the complete system. The cases where these conditions qualitatively change give the analytical expressions of the dependencies between the area constant and the gyrostatic momentum forming the classifying set for the two-parametric family of the reduced systems' diagrams. Finally, we present a computer system, which satisfies the given definition of the electronic atlas.
Keywords: integrable Hamiltonian system, bifurcation diagram, electronic atlas.
Received: 17.03.2011
Bibliographic databases:
Document Type: Article
UDC: 517.938.5+531.38
MSC: 70E17, 70G40
Language: Russian
Citation: I. I. Kharlamova, P. E. Ryabov, “The electronic atlas of bifurcation diagrams of the Kowalevski–Yehia gyrostat”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 2, 147–162
Citation in format AMSBIB
\Bibitem{KhaRya11}
\by I.~I.~Kharlamova, P.~E.~Ryabov
\paper The electronic atlas of bifurcation diagrams of the Kowalevski--Yehia gyrostat
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2011
\issue 2
\pages 147--162
\mathnet{http://mi.mathnet.ru/vuu223}
\elib{https://elibrary.ru/item.asp?id=16386094}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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