Geometrical approach to separation of variables in mechanical systems

Abstract

The article presents a compact review of the analytical results (2002-2009) in the study of the system describing the motion of a top in two constant fields. The Liouville integrability of this system under certain condition of the Kowalevski type was established by A.G.Reyman and M.A.Semenov-Tian-Shansky. We present some geometrical foundations of finding separations of variables. Two systems of local planar coordinates are introduced leading to separation of variables for two subsystems with two degrees of freedom in the dynamics of the generalized Kowalevski top.

26 pages, 4 figures

References in corpus (4)

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