Regular and Chaotic Dynamics

, Volume 18, Issue 6, pp 600–607 | Cite as

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

  • Richard MontgomeryEmail author


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/r 2, agrees with the rotational part of the cone’s kinetic energy.


Kepler problem MICZ-K system co-adjoint orbit Sternberg phase space symplectic reduction superintegrable systems 

MSC2010 numbers

70Hxx 37J35 53D20 


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Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Dept. of MathematicsUniversity of CaliforniaSanta CruzUSA

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