Regular and Chaotic Dynamics

, Volume 17, Issue 5, pp 431–438 | Cite as

On the cases of Kirchhoff and Chaplygin of the Kirchhoff equations



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.


Kirchhoff equations Kirchhoff case Chaplygin case algebraic integrable systems 

MSC2010 numbers

70E40 70E45 70E20 


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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Mathematical InstituteSerbian Academy of Science and ArtBelgradeSerbia
  2. 2.Group of Mathematical PhysicsUniversity of LisbonLisbonPortugal

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