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Nelin. Dinam., 2008, Volume 4, Number 4, Pages 407–416 (Mi nd245)  

This article is cited in 1 scientific paper (total in 1 paper)

Algebraic reduction of systems on two- and three-dimensional spheres

A. V. Borisov, I. S. Mamaev, S. M. Ramodanov


Abstract: The paper develops further the algebraic-reduction method for $SO(4)$-symmetrie systems on the three-dimensional sphere. Canonical variables for the reduced system are constructed both on two-dimensional and three-dimensional spheres. The method is illustrated by applying it to the two-body problem on a sphere (the bodies are assumed to interact with a potential that depends only on the geodesic distance between them) and the three-vortex problem on a two-dimensional sphere.

Keywords: Poisson structure. Lie algebra, subalgebra, Andoyer variables.

Full text: PDF file (180 kB)

Document Type: Article
UDC: 512.77, 517.912
MSC: 70Hxx, 70G65
Received: 03.12.2008

Citation: A. V. Borisov, I. S. Mamaev, S. M. Ramodanov, “Algebraic reduction of systems on two- and three-dimensional spheres”, Nelin. Dinam., 4:4 (2008), 407–416

Citation in format AMSBIB
\Bibitem{BorMamRam08}
\by A.~V.~Borisov, I.~S.~Mamaev, S.~M.~Ramodanov
\paper Algebraic reduction of systems on two- and three-dimensional spheres
\jour Nelin. Dinam.
\yr 2008
\vol 4
\issue 4
\pages 407--416
\mathnet{http://mi.mathnet.ru/nd245}


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  • http://mi.mathnet.ru/eng/nd/v4/i4/p407

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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
  • Нелинейная динамика
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