Regular and Chaotic Dynamics

, Volume 17, Issue 3–4, pp 337–358 | Cite as

Integrable variational equations of non-integrable systems

  • Andrzej J. MaciejewskiEmail author
  • Maria Przybylska


Paper is devoted to the solvability analysis of variational equations obtained by linearization of the Euler-Poisson equations for the symmetric rigid body with a fixed point on the equatorial plain. In this case Euler-Poisson equations have two pendulum like particular solutions. Symmetric heavy top is integrable only in four famous cases. In this paper is shown that a family of cases can be distinguished such that Euler-Poisson equations are not integrable but variational equations along particular solutions are solvable. The connection of this result with analysis made in XIX century by R. Liouville is also discussed.


rigid body Euler-Poisson equations solvability in special functions differential Galois group 

MSC2010 numbers

70E17 70E40 37J30 70H07 34M15 


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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.J. Kepler Institute of AstronomyUniversity of Zielona GóraZielona GóraPoland
  2. 2.Institute of PhysicsUniversity of Zielona GóraZielona GóraPoland

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