Orbit Taxonomy in an Electromagnetic Binary System of Two Magnetic Dipoles

Abstract

We elucidate the orbital dynamics of a binary system of two magnetic dipoles, by utilizing the grid classification method. Our target is to unveil how the total energy (expressed through the Jacobi constant), as well as the ratio of the magnetic moments affect the character of the trajectories of the test particle. By integrating numerically large data sets of starting conditions of trajectories in different types of 2D maps, we manage to reveal the basins corresponding to bounded, close encounter and escape motion, along with the respective time scales of the phenomena.