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This article is cited in 15 scientific papers (total in 15 papers)
Superintegrable Generalizations of the Kepler and Hook Problems
Ivan A. Bizyaeva, Alexey V. Borisovabc, Ivan S. Mamaevad a Udmurt State University,
Universitetskaya 1, Izhevsk, 426034 Russia
b A. A. Blagonravov Mechanical Engineering Research Institute of RAS,
Bardina str. 4, Moscow, 117334, Russia
c National Research Nuclear University “MEPhI”,
Kashirskoye shosse 31, Moscow, 115409, Russia
d Institute of Mathematics and Mechanics of the Ural Branch of RAS,
S. Kovalevskaja str. 16, Ekaterinburg, 620990, Russia
Abstract:
In this paper we consider superintegrable systems which are an immediate
generalization of the Kepler and Hook problems, both in two-dimensional
spaces — the plane $\mathbb{R}^2$ and the sphere $S^2$ — and in
three-dimensional spaces $\mathbb{R}^3$ and $S^3$. Using the central
projection and the reduction procedure proposed in [21], we show an
interrelation between the superintegrable systems found previously and
show new ones. In all cases the superintegrals are presented in explicit
form.
Keywords:
superintegrable systems, Kepler and Hook problems, isomorphism, central projection, reduction, highest degree polynomial superintegrals.
Received: 27.03.2014 Accepted: 13.05.2014
Citation:
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Superintegrable Generalizations of the Kepler and Hook Problems”, Regul. Chaotic Dyn., 19:3 (2014), 415–434
Linking options:
https://www.mathnet.ru/eng/rcd163 https://www.mathnet.ru/eng/rcd/v19/i3/p415
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Abstract page: | 206 | References: | 64 |
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