We consider integrable generalizations of the spherical pendulum system to the Stiefel variety V(n, r) = SO(n)/SO(n - r) for a certain metric. For the case of V(n, 2) an alternative integrable model of the pendulum is presented. We also describe a system on the Stiefel variety with a fourth-degree potential. The latter has invariant relations on T*V(n, r) which provide the complete integrability of the flow reduced on the oriented Grassmannian variety G+(n, r) = SO(n)/SO(r) × SO(n - r).
Journal of Physics A Mathematical General
- Pub Date:
- April 2012
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Mathematical Physics;
- 14 pages