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 Nelin. Dinam.: Year: Volume: Issue: Page: Find

 Nelin. Dinam., 2009, Volume 5, Number 4, Pages 455–462 (Mi nd105)

New superintegrable system on a sphere

A. V. Borisov, A. A. Kilin, I. S. Mamaev

Institute of Computer Science

Abstract: We consider the motion of a material point on the surface of a sphere in the field of $2n+1$ identical Hooke centers (singularities with elastic potential) lying on a great circle. Our main result is that this system is superintegrable. The property of superintegrability for this system has been conjectured by us in [3], where the structure of a superintegral of arbitrarily high odd degree in momemnta was outlined. We also indicate an isomorphism between this system and the one-dimensional $N$-particle system discussed in the recent paper [13] and show that for the latter system an analogous superintegral can be constructed.

Keywords: superintegrable systems, systems with a potential, Hooke center.

Full text: PDF file (214 kB)

Document Type: Article
UDC: 531.38
MSC: 70Hxx, 70H06, 70G65, 37J35, 70F10

Citation: A. V. Borisov, A. A. Kilin, I. S. Mamaev, “New superintegrable system on a sphere”, Nelin. Dinam., 5:4 (2009), 455–462

Citation in format AMSBIB
\Bibitem{BorKilMam09} \by A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev \paper New superintegrable system on a sphere \jour Nelin. Dinam. \yr 2009 \vol 5 \issue 4 \pages 455--462 \mathnet{http://mi.mathnet.ru/nd105}