Geodesic
Discrete Geodesic Flows on Stiefel Manifolds
Informatics and Automation, 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. 
@article{TRSPY_2020_310_a12,
     author = {Bo\v{z}idar Jovanovi\'c and Yuri N. Fedorov},
     title = {Discrete {Geodesic} {Flows} on {Stiefel} {Manifolds}},
     journal = {Informatics and Automation},
     pages = {176--188},
     publisher = {mathdoc},
     volume = {310},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2020_310_a12/}
}
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Božidar Jovanović; Yuri N. Fedorov. Discrete Geodesic Flows on Stiefel Manifolds. Informatics and Automation, Selected issues of mathematics and mechanics, Tome 310 (2020), pp. 176-188. http://geodesic.mathdoc.fr/item/TRSPY_2020_310_a12/