This article is cited in 3 papers

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

Richard Montgomery

Dept. of Mathematics, University of California, Santa Cruz, CA, USA

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.

MSC: 70Hxx, 37J35, 53D20

Received: 09.08.2013
Accepted: 29.10.2013

Language: English

DOI: 10.1134/S1560354713060038

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