New examples of conservative systems on S^2 possessing an integral cubic in momenta

Details New examples of conservative systems on S^2 possessing an integral cubic in momenta New examples of conservative systems on S^2 possessing an integral cubic in momenta

1997-11-10

arxiv.org/abs/dg-ga/9711005v1

Mathematics

Differential Geometry

10 pages, AMS-LaTeX

Scientific paper

It has been proved that on 2-dimensional orientable compact manifolds of genus $g>1$ there is no integrable geodesic flow with an integral polynomial in momenta. There is a conjecture that all integrable geodesic flows on $T^2$ possess an integral quadratic in momenta. All geodesic flows on $S^2$ and $T^2$ possessing integrals linear and quadratic in momenta have been described by Kolokol'tsov, Babenko and Nekhoroshev. So far there has been known only one example of conservative system on $S^2$ possessing an integral cubic in momenta: the case of Goryachev-Chaplygin in the dynamics of a rigid body. The aim of this paper is to propose a new one-parameter family of examples of complete integrable conservative systems on $S^2$ possessing an integral cubic in momenta. We show that our family does not include the case of Goryachev-Chaplygin.

Affiliated with

Also associated with

No associations

Rating

New examples of conservative systems on S^2 possessing an integral cubic in momenta does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with New examples of conservative systems on S^2 possessing an integral cubic in momenta, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and New examples of conservative systems on S^2 possessing an integral cubic in momenta will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-640475