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

    2013, Volume 18, Number 6, pp.  600-607

    Author(s): Montgomery R.

    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
    Citation: Montgomery R., MICZ-Kepler: Dynamics on the Cone over $SO(n)$, Regular and Chaotic Dynamics, 2013, Volume 18, Number 6, pp. 600-607

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