Abstract
The Lax representations of the geodesic flow, the Jacobi-Rosochatius problem and its perturbations by means of separable polynomial potentials, on a ellipsoid are constructed. We prove complete integrability in the case of a generic symmetric ellipsoid and describe analogous systems on complex projective spaces. Also, we consider billiards within an ellipsoid under the influence of the Hook and Rosochatius potentials between the impacts. A geometric interpretation of the integrability analogous to the classical Chasles and Poncelet theorems is given.
Connections
Explore this paper’s authors, topics and related work.
Building this map preview
BZPEER is loading the nearby papers, people, topics and institutions for this page.
Reviews 0
Write a review
No reviews yet.
Discussion 0
Add a comment
No comments yet.