Ukrainian Mathematical Bulletin
Volume 1, Issue 4, 2004 pp. 569-586.
Separation of Variables and Integral Manifolds in One Problem of Motion of Generalized Kowalevski TopAuthors: M.P.Kharlamov and A.Yu.Savushkin
Author institution: Michael P. Kharlamov, Center of Computer Engineering, Volgograd Academy of State Service, 8 Gagarin Str., Volgograd, Russia mharlamov@vags.ru Alexander Yu. Savushkin, Chair of Information Systems, Volgograd Academy of State Service, 8 Gagarin Str., Volgograd, Russia kismm@vags.ru
Summary: In the phase space of the integrable Hamiltonian system with three degrees of freedom used to describe the motion of a Kowalevski-type top in a double constant force field, we point out the four-dimensional invariant manifold. It is shown that this manifold consists of critical motions generating a smooth sheet of the bifurcation diagram, and the induced dynamic system is Hamiltonian with certain subset of points of degeneration of the symplectic structure. We find the transformation separating variables in this system. As a result, the solutions can be represented in terms of elliptic functions of time. The corresponding phase topology is completely described.
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