Abstract

In this paper we study part of the dynamics of a circular restricted (N + 2)-body problem on the sphere S2 and considering the logarithmic potential, where N primaries remain in a ring type configuration (identical masses placed at the vertices of a regular polygon in a fixed parallel and rotating uniformly with respect to the Z-axis) and a (N + 1)-th primary of mass M ? ? fixed at the south pole of S2. Such a particular configuration will be called ring-pole configuration (RP). An infinitesimal mass particle has an equilibrium position at the north pole for any value of M, any parallel where the ring has been fixed (we use as parameter z = cos ?, where ? is the polar angle of the ring) and any number N ? 2 of masses forming the ring. We study the non-linear stability of the north pole in terms of the parameters (z, M, N) and some bifurcations near the north pole. © 2023 American Institute of Mathematical Sciences. All rights reserved.