Updated rotating mass dipole with oblateness of one primary (II): out-of-plane equilibria and their stability

Out-of-plane equilibrium points of the updated rotating mass dipole are investigated in this paper. The updated dipole system is consistent with a point mass connecting a spheroid with a massless rod in a constant distance. The oblateness of the spheroid allows the existence of out-of-plane equilibrium points. These equilibria are determined numerically based on the three dimensional dynamic equations. The influence of the system parameters on the position of these equilibria associated with the topological structure is analyzed in a parametric way. The stability of these equilibria is explored with linearized dynamic equations. Two particular cases with a prolate or an oblate spheroid of the first primary are presented to examine its influence on the distribution of the out-of-plane equilibrium points around the second primary.