Symmetry in systems with gyroscopic forces
Differential Geometry
2014-02-05 v1 Mathematical Physics
Dynamical Systems
math.MP
Abstract
We consider a generalization of the notion of a natural mechanical system to the case of additional forces of gyroscopic type. Such forces appear, for example, as a result of global reduction of a natural system with symmetry. We study symmetries in the systems with gyroscopic forces to find out when these systems admit a global analogue of a cyclic integral. The results are applied to the problem of the motion of a rigid body about a fixed point in potential and gyroscopic forces to find the most general form of such forces admitting the global area type integral.
Cite
@article{arxiv.1402.0663,
title = {Symmetry in systems with gyroscopic forces},
author = {M. P. Kharlamov},
journal= {arXiv preprint arXiv:1402.0663},
year = {2014}
}
Comments
LaTex, 9 pages, English translation of the paper previuosly published only in Russian