Reduction of the classical MICZ-Kepler problem to a two-dimensional linear isotropic harmonic oscillator

Abstract

The classical MICZ-Kepler problem is shown to be reducible to an isotropic two-dimensional system of linear harmonic oscillators and a conservation law in terms of new variables related to the Ermanno–Bernoulli constants and the components of the Poincaré vector. An algorithmic route to linearization is shown based on Lie symmetry analysis and the reduction method [ Nucci, J. Math. Phys. 37, 1772 (1996) ]. First integrals are also obtained by symmetry analysis and the reduction method [ Marcelli and Nucci,J. Math. Phys. 44, 2111 (2002) ].