Classification of singularities in the problem of motion of the Kovalevskaya top in a double force field

Abstract

The problem of motion of the Kovalevskaya top in a double force field is investigated (the integrable case of A.G. Reyman and M.A. Semenov-Tian-Shansky without a gyrostatic momentum). It is a completely integrable Hamiltonian system with three degrees of freedom not reducible to a family of systems with two degrees of freedom. The critical set of the integral map is studied. The critical subsystems and bifurcation diagrams are described. The classification of all nondegenerate critical points is given. The set of these points consists of equilibria (nondegenerate singularities of rank 0), of singular periodic motions (nondegenerate singularities of rank 1), and also of critical two-frequency motions (nondegenerate singularities of rank 2).

arXiv commentLaTex, 30 pages, in Russian, 6 figures, 32 references. Submitted version

References in corpus (6)

• Torus Actions and Integrable Systems
• Bifurcation diagrams of the Kowalevski top in two constant fields
• Bifurcation of common levels of first integrals of the Kovalevskaya problem
• Topological analysis of classical integrable systems in the dynamics of the rigid body
• Separation of variables in the generalized 4th Appelrot class
• Separation of variables and integral manifolds in one problem of motion of generalized Kowalevski top

Cited by in corpus (2)

• Extensions of the Appelrot classes for the generalized gyrostat in a double force field
• Phase topology of one system with separated variables and singularities of the symplectic structure