Separation of variables in the generalized 4th Appelrot class

Abstract

We consider the analogue of the 4th Appelrot class of motions of the Kowalevski top for the case of two constant force fields. The trajectories of this family fill the four-dimensional surface O^4 in the six-dimensional phase space. The constants of three first integrals in involution restricted to this surface fill one of the sheets of the bifurcation diagram in R^3. We point out the pair of partial integrals to obtain the explicit parametric equations of this sheet. The induced system on O^4 is shown to be Hamiltonian with two degrees of freedom having the thin set of points where the induced symplectic structure degenerates. The region of existence of motions in terms of the integral constants is found. We provide the separation of variables on O^4 and the algebraic formulae for the initial phase variables.

LaTex, 16 pages, 1 figure

References in corpus (3)

• Bifurcation diagrams of the Kowalevski top in two constant fields
• Separation of variables and integral manifolds in one problem of motion of generalized Kowalevski top
• Bifurcation diagram of the generalized 4th Appelrot class

Cited by in corpus (6)

• Extensions of the Appelrot classes for the generalized gyrostat in a double force field
• Classification of singularities in the problem of motion of the Kovalevskaya top in a double force field
• Phase topology of one system with separated variables and singularities of the symplectic structure
• One class of solutions with two invariant relations for the problem of motion of the Kowalevski top in double constant field
• Geometrical approach to separation of variables in mechanical systems
• Phase topology of one nonclassical integrable problem of dynamics