Geodesic
Billiards on constant curvature spaces and generating functions for systems with constraints
Theoretical and applied mechanics, Tome 44 (2017) no. 1, p. 103

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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.
DOI : 10.2298/TAM170523005J
Classification : 37J10, 53D22, 51M05
Keywords: Dirac brackets, generating functions, ellipsoidal billiards, Heisenberg spin model, skew-hodograph mapping 
Božidar Jovanović. Billiards on constant curvature spaces and generating functions for systems with constraints. Theoretical and applied mechanics, Tome 44 (2017) no. 1, p. 103 . doi: 10.2298/TAM170523005J
@article{10_2298_TAM170523005J,
     author = {Bo\v{z}idar Jovanovi\'c},
     title = {Billiards on constant curvature spaces and generating functions for systems with constraints},
     journal = {Theoretical and applied mechanics},
     pages = {103 },
     year = {2017},
     volume = {44},
     number = {1},
     doi = {10.2298/TAM170523005J},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/TAM170523005J/}
}
TY  - JOUR
AU  - Božidar Jovanović
TI  - Billiards on constant curvature spaces and generating functions for systems with constraints
JO  - Theoretical and applied mechanics
PY  - 2017
SP  - 103 
VL  - 44
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.2298/TAM170523005J/
DO  - 10.2298/TAM170523005J
LA  - en
ID  - 10_2298_TAM170523005J
ER  - 
%0 Journal Article
%A Božidar Jovanović
%T Billiards on constant curvature spaces and generating functions for systems with constraints
%J Theoretical and applied mechanics
%D 2017
%P 103 
%V 44
%N 1
%U http://geodesic.mathdoc.fr/articles/10.2298/TAM170523005J/
%R 10.2298/TAM170523005J
%G en
%F 10_2298_TAM170523005J

Cité par Sources :