An elliptic billiard in a potential force field: classification of motions, topological analysis

Abstract

Abstract Given an ellipse , b>0$?> , we consider an absolutely elastic billiard in it with potential , , . This dynamical system is integrable and has two degrees of freedom. We obtain the iso-energy invariants of rough and fine Liouville equivalence, and conduct a comparative analysis of other systems known in rigid body mechanics. To obtain the results we apply the method of separation of variables and construct a new method, which is equivalent to the bifurcation diagram but does not require it to be constructed. Bibliography: 17 titles.