Authors: Fedorov, Yuri
Jovanović, Božidar 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Three natural mechanical systems on Stiefel varieties
Journal: Journal of Physics A: Mathematical and Theoretical
Volume: 45
Issue: 16
Issue Date: 27-Apr-2012
Rank: M21
ISSN: 1751-8113
DOI: 10.1088/1751-8113/45/16/165204
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 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).
Publisher: IOP Science

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