Abstract:
It is proven that the completely integrable general Kirchhoff case of the Kirchhoff equations for B≠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.
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.
Citation:
Vladimir Dragović, Borislav Gajić, “On the Cases of Kirchhoff and Chaplygin of the Kirchhoff Equations”, Regul. Chaotic Dyn., 17:5 (2012), 431–438
\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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https://www.mathnet.ru/eng/rcd413
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