Abstract
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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