|Authors:||Jovanović, Božidar||Title:||Billiards on constant curvature spaces and generating functions for systems with constraints||Journal:||Theoretical and Applied Mechanics||Volume:||44||Issue:||1||First page:||103||Last page:||114||Issue Date:||1-Jan-2017||Rank:||M24||ISSN:||1450-5584||DOI:||10.2298/TAM170523005J||Abstract:||
In this note we consider a method of generating functions for systems with constraints and, as an example, we prove that the billiard mappings for billiards on the Euclidean space, sphere, and the Lobachevsky space are sympletic. Further, by taking a quadratic generating function we get the skew-hodograph mapping introduced by Moser and Veselov, which relates the ellipsoidal billiards in the Euclidean space with the Heisenberg magnetic spin chain model on a sphere. We define analogous mapping for the ellipsoidal billiard on the Lobachevsky space. It relates the billiard with the Heisenberg spin model on the light-like cone in the Lorentz-Poincare-Minkowski space.
|Keywords:||Dirac brackets | Ellipsoidal billiards | Generating functions | Heisenberg spin model | Skew-hodograph mapping||Publisher:||Serbian Society for Mechanics||Project:||Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems|
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