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Regular and Chaotic Dynamics, 2013, Volume 18, Issue 6, Pages 600–607
DOI: https://doi.org/10.1134/S1560354713060038 (Mi rcd151) 		 
This article is cited in 2 scientific papers (total in 2 papers)

MICZ-Kepler: Dynamics on the Cone over $SO(n)$

Richard Montgomery

Dept. of Mathematics, University of California, Santa Cruz, CA, USA
Citations (2)
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DOI: https://doi.org/10.1134/S1560354713060038
Abstract: We show that the $n$-dimensional MICZ-Kepler system arises from symplectic reduction of the "Kepler problem" on the cone over the rotation group $SO(n)$. As a corollary we derive an elementary formula for the general solution of the MICZ-Kepler problem. The heart of the computation is the observation that the additional MICZ-Kepler potential, $|\phi|^2/r^2$, agrees with the rotational part of the cone’s kinetic energy.
Keywords: Kepler problem, MICZ-K system, co-adjoint orbit, Sternberg phase space, symplectic reduction, superintegrable systems.
Funding agency Grant number
National Science Foundation DMS-1305844
I gratefully acknowledge support by the US NSF grant number DMS-1305844.
Received: 09.08.2013
Accepted: 29.10.2013
Bibliographic databases:
Document Type: Article
MSC: 70Hxx, 37J35, 53D20
Language: English
Citation: Richard Montgomery, “MICZ-Kepler: Dynamics on the Cone over $SO(n)$”, Regul. Chaotic Dyn., 18:6 (2013), 600–607
Citation in format AMSBIB
\Bibitem{Mon13}
\by Richard Montgomery
\paper MICZ-Kepler: Dynamics on the Cone over $SO(n)$
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 6
\pages 600--607
\mathnet{http://mi.mathnet.ru/rcd151}
\crossref{https://doi.org/10.1134/S1560354713060038}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3146581}
\zmath{https://zbmath.org/?q=an:1286.70012}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000329108900003}
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  • https://www.mathnet.ru/eng/rcd/v18/i6/p600
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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