Geodesic
Discrete Geodesic Flows on Stiefel Manifolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected issues of mathematics and mechanics, Tome 310 (2020), pp. 176-188.

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We study integrable discretizations of geodesic flows of Euclidean metrics on the cotangent bundles of the Stiefel manifolds $V_{n,r}$. In particular, for $n=3$ and $r=2$, after the identification $V_{3,2}\cong \mathrm {SO}(3)$, we obtain a discrete analog of the Euler case of the rigid body motion corresponding to the inertia operator $I=(1,1,2)$. In addition, billiard-type mappings are considered; one of them turns out to be the “square root” of the discrete Neumann system on $V_{n,r}$.
Keywords: discrete geodesic flows, noncommutative integrability, canonical transformations
Mots-clés : quadratic matrix equations, billiards. 
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Božidar Jovanović; Yuri N. Fedorov. Discrete Geodesic Flows on Stiefel Manifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected issues of mathematics and mechanics, Tome 310 (2020), pp. 176-188. http://geodesic.mathdoc.fr/item/TM_2020_310_a12/

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