Authors: Jovanović, Božidar 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: The Jacobi-Rosochatius Problem on an Ellipsoid: The Lax Representations and Billiards
Journal: Archive for Rational Mechanics and Analysis
Volume: 210
Issue: 1
First page: 101
Last page: 131
Issue Date: 1-Oct-2013
Rank: M21a
ISSN: 0003-9527
DOI: 10.1007/s00205-013-0638-4
In this article, we construct the Lax representations of the geodesic flow, the Jacobi-Rosochatius problem and its perturbations by means of separable polynomial potentials on an ellipsoid. 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.
Publisher: Springer Link

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