This article is cited in 5 papers

On the Cases of Kirchhoff and Chaplygin of the Kirchhoff Equations

Vladimir Dragović^ab, Borislav Gajić<sup>b

a</sup> 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

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.

MSC: 70E40, 70E45, 70E20

Received: 13.10.2011
Accepted: 11.04.2012

Language: English

DOI: 10.1134/S156035471205005X

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