Geometrical approach to separation of variables in mechanical systems
Dynamical Systems
2012-11-26 v1 Exactly Solvable and Integrable 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.
Keywords
Cite
@article{arxiv.1211.5478,
title = {Geometrical approach to separation of variables in mechanical systems},
author = {Mikhail P. Kharlamov and Alexander Y. Savushkin},
journal= {arXiv preprint arXiv:1211.5478},
year = {2012}
}
Comments
26 pages, 4 figures