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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. 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

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.

Full text: PDF file (484 kB)
References: PDF file   HTML file
UDC: 517.938.5+531.38
MSC: 70E17, 70G40
Received: 17.03.2011

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{http://elibrary.ru/item.asp?id=16386094}


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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. 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
    2. N. S. Slavina, “Topological classification of systems of Kovalevskaya-Yehia type”, Sb. Math., 205:1 (2014), 101–155  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. P. E. Ryabov, A. Yu. Savushkin, “Fazovaya topologiya volchka Kovalevskoi – Sokolova”, Nelineinaya dinam., 11:2 (2015), 287–317  mathnet
    4. 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
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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