Billiards on constant curvature spaces and generating functions for systems with constraints | Zendy

Božidar Jovanović | Zendy

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Billiards on constant curvature spaces and generating functions for systems with constraints

Author(s) -

Božidar Jovanović

Publication year - 2017

Publication title -

theoretical and applied mechanics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.279

H-Index - 6

eISSN - 2406-0925

pISSN - 1450-5584

DOI - 10.2298/tam170523005j

Subject(s) - dynamical billiards , minkowski space , constant curvature , constant (computer programming) , space (punctuation) , euclidean space , mathematics , spin (aerodynamics) , ellipsoid , euclidean geometry , lorentz transformation , mathematical analysis , physics , curvature , pure mathematics , classical mechanics , mathematical physics , geometry , computer science , astronomy , thermodynamics , programming language , operating system

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. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. 174020

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