Extensions of the Appelrot classes for the generalized gyrostat in a double force field

Abstract

For the integrable system on $e(3,2)$ found by Sokolov and Tsiganov we obtain explicit equations of some invariant 4-dimensional manifolds on which the induced systems are almost everywhere Hamiltonian with two degrees of freedom. These subsystems generalize the famous Appelrot classes of critical motions of the Kowalevski top. For each subsystem we point out a commutative pair of independent integrals, describe the sets of degeneration of the induced symplectic structure. With the help of the obtained invariant relations, for each subsystem we calculate the outer type of its points considered as critical points of the initial system with three degrees of freedom.

LaTex, 24 pp. Submitted to Regular and Chaotic Dynamics on 05.09.2013

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Cited by in corpus (4)

• New invariant relations for the generalized two-field gyrostat
• Phase Topology of Two Vortices of the Identical Intensities in Bose-Einstein Condensate
• On one unstable bifurcation in the dynamics of vortex structure
• Phase topology of the Kowalevski-Sokolov top