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Integrable variational equations of non-integrable systems

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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.

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Authors and Affiliations

  1. J. Kepler Institute of Astronomy, University of Zielona Góra, Licealna 9, PL-65-417, Zielona Góra, Poland

    Andrzej J. Maciejewski

  2. Institute of Physics, University of Zielona Góra, Licealna 9, PL-65-417, Zielona Góra, Poland

    Maria Przybylska

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  1. Andrzej J. Maciejewski
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  2. Maria Przybylska
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Correspondence to Andrzej J. Maciejewski.

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Maciejewski, A.J., Przybylska, M. Integrable variational equations of non-integrable systems. Regul. Chaot. Dyn. 17, 337–358 (2012). https://doi.org/10.1134/S1560354712030094

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  • DOI: https://doi.org/10.1134/S1560354712030094

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