Three natural mechanical systems on Stiefel varieties
Abstract
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 fourthdegree 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).
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 April 2012
 DOI:
 10.1088/17518113/45/16/165204
 arXiv:
 arXiv:1202.1660
 Bibcode:
 2012JPhA...45p5204F
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Mathematical Physics;
 17B80;
 53D25;
 70H06;
 70H33;
 70H45
 EPrint:
 14 pages