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Nelin. Dinam., 2007, Volume 3, Number 1, Pages 49–56 (Mi nd123)  

This article is cited in 2 scientific papers (total in 2 papers)

On isomorphisms of some integrable systems on a plane and a sphere

A. V. Borisovab, I. S. Mamaevab

a Udmurt State University
b Institute of Computer Science

Abstract: We consider trajectory isomorphisms between various integrable systems on an $n$-dimensional sphere $S^n$ and a Euclidean space $\mathbb R^n$. Some of the systems are classical integrable problems of Celestial Mechanics in plane and curved spaces. All the systems under consideration have an additional first integral quadratic in momentum and can be integrated analytically by using the separation of variables. We show that some integrable problems in constant curvature spaces are not essentially new from the viewpoint of the theory of integration, and they can be analyzed using known results of classical Celestial Mechanics.

Keywords: integrable systems, two-center problem, isomorphisms

Full text: PDF file (166 kB)

Document Type: Article
UDC: 532.5
MSC: 37N05, 70F10
Received: 07.09.2006

Citation: A. V. Borisov, I. S. Mamaev, “On isomorphisms of some integrable systems on a plane and a sphere”, Nelin. Dinam., 3:1 (2007), 49–56

Citation in format AMSBIB
\Bibitem{BorMam07}
\by A.~V.~Borisov, I.~S.~Mamaev
\paper On isomorphisms of some integrable systems on a plane and a sphere
\jour Nelin. Dinam.
\yr 2007
\vol 3
\issue 1
\pages 49--56
\mathnet{http://mi.mathnet.ru/nd123}


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    This publication is cited in the following articles:
    1. A. A. Burov, “On the motion of a solid body on spherical surfaces”, Journal of Mathematical Sciences, 199:5 (2014), 501–509  mathnet  crossref  mathscinet
    2. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Figury ravnovesiya neodnorodnoi samogravitiruyuschei zhidkosti”, Nelineinaya dinam., 10:1 (2014), 73–100  mathnet
  • Нелинейная динамика
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