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).
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