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Regular and Chaotic Dynamics, 2012, Volume 17, Issue 5, Pages 431–438
DOI: https://doi.org/10.1134/S156035471205005X (Mi rcd413) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On the Cases of Kirchhoff and Chaplygin of the Kirchhoff Equations

Vladimir Dragovićab, Borislav Gajićb

a Group of Mathematical Physics, University of Lisbon, av. Prof. Gama Pinto 2, PT-1649-003 Lisbon, Portugal
b Mathematical Institute, Serbian Academy of Science and Art, Kneza Mihaila 36, 11000 Belgrade, Serbia
Citations (5)
DOI: https://doi.org/10.1134/S156035471205005X
Abstract: It is proven that the completely integrable general Kirchhoff case of the Kirchhoff equations for $B\ne 0$ is not an algebraic complete integrable system. Similar analytic behavior of the general solution of the Chaplygin case is detected. Four-dimensional analogues of the Kirchhoff and the Chaplygin cases are defined on $e(4)$ with the standard Lie–Poisson bracket.
Keywords: Kirchhoff equations, Kirchhoff case, Chaplygin case, algebraic integrable systems.
Funding agency Grant number
Serbian Ministry of Science and Technological Development 174020
Fundação para a Ciência e a Tecnologia PTDC/MAT/104173/2008
The research was partially supported by the Serbian Ministry of Education and Science, Project 174020 Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems and by the Mathematical Physics Group of the University of Lisbon, Project Probabilistic approach to finite and infinite dimensional dynamical systems, PTDC/MAT/104173/2008.
Received: 13.10.2011
Accepted: 11.04.2012
Bibliographic databases:
Document Type: Article
MSC: 70E40, 70E45, 70E20
Language: English
Citation: Vladimir Dragović, Borislav Gajić, “On the Cases of Kirchhoff and Chaplygin of the Kirchhoff Equations”, Regul. Chaotic Dyn., 17:5 (2012), 431–438
Citation in format AMSBIB
\Bibitem{DraGaj12}
\by Vladimir Dragovi\'c, Borislav Gaji\'c
\paper On the Cases of Kirchhoff and Chaplygin of the Kirchhoff Equations
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 5
\pages 431--438
\mathnet{http://mi.mathnet.ru/rcd413}
\crossref{https://doi.org/10.1134/S156035471205005X}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2989515}
\zmath{https://zbmath.org/?q=an:1252.70022}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2012RCD....17..431D}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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