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, |ϕ|2/r2, agrees with the rotational part of the cone’s kinetic energy.
\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/rcd151
https://www.mathnet.ru/eng/rcd/v18/i6/p600
This publication is cited in the following 2 articles:
Stefano Baranzini, Alessandro Portaluri, Ran Yang, “Morse index of circular solutions for attractive central force problems on surfaces”, Journal of Mathematical Analysis and Applications, 537:1 (2024), 128250
Maxence Mayrand, “Particle Motion in Monopoles and Geodesics on Cones”, SIGMA, 10 (2014), 102, 17 pp.
Citation in format AMSBIB
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