Non-Hamiltonian systems separable by Hamilton-Jacobi method
2008 (English)In: Journal of Geometry and Physics, ISSN 0393-0440, Vol. 58, no 5, 557-575 p.Article in journal (Refereed) Published
We show that with every separable classical Stäckel system of Benenti type on a Riemannian space one can associate, by a proper deformation of the metric tensor, a multi-parameter family of non-Hamiltonian systems on the same space, sharing the same trajectories and related to the seed system by appropriate reciprocal transformations. These systems are known as bi-cofactor systems and are integrable in quadratures as the seed Hamiltonian system is. We show that with each class of bi-cofactor systems a pair of separation curves can be related. We also investigate the conditions under which a given flat bi-cofactor system can be deformed to a family of geodesically equivalent flat bi-cofactor systems. © 2007 Elsevier Ltd. All rights reserved.
Place, publisher, year, edition, pages
2008. Vol. 58, no 5, 557-575 p.
separability, Stäckel systems, bicofactor systems, separation curves
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-40802DOI: 10.1016/j.geomphys.2007.12.008Local ID: 54152OAI: oai:DiVA.org:liu-40802DiVA: diva2:261651