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This article is cited in 1 scientific paper (total in 1 paper)
Discrete Geodesic Flows on Stiefel Manifolds
Božidar Jovanovića, Yuri N. Fedorovb a Mathematical Institute SANU, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Belgrade, Serbia
b Department of Mathematics, Polytechnic University of Catalonia, C. Pau Gargallo 14, 08028 Barcelona, Spain
Abstract:
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, quadratic matrix equations, billiards.
Received: December 1, 2019 Revised: December 1, 2019 Accepted: June 18, 2020
Citation:
Božidar Jovanović, Yuri N. Fedorov, “Discrete Geodesic Flows on Stiefel Manifolds”, Selected issues of mathematics and mechanics, Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov, Trudy Mat. Inst. Steklova, 310, Steklov Math. Inst., Moscow, 2020, 176–188; Proc. Steklov Inst. Math., 310 (2020), 163–174
Linking options:
https://www.mathnet.ru/eng/tm4107https://doi.org/10.4213/tm4107 https://www.mathnet.ru/eng/tm/v310/p176
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