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arXiv · 1202.1660

Three natural mechanical systems on Stiefel varieties

Yuri N. Fedorov·Bozidar Jovanović
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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 four-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 $G^+(n,r)=SO(n)/SO(r)\times SO(n-r)$.

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Yuri N. Fedorov, Bozidar Jovanović. 2012-02-08. Three natural mechanical systems on Stiefel varieties. https://doi.org/10.1088/1751-8113/45/16/165204

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