Santa Cruz, CA, USA
Dept. of Mathematics, University of California
MICZ-Kepler: Dynamics on the Cone over $SO(n)$
2013, vol. 18, no. 6, pp. 600-607
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.