Resumen de Bifurcations and equilibrium points in the planar case of the (n+2) body ring problem

Mercedes Arribas Jiménez , Antonio Elipe Sánchez

• We consider the motion ofan infinitesimal particle under the gravitational field of( n + 1) bodies in ring configuration, that consist of n primaries ofequal mass m placed at the vertices ofa regular polygon, plus another primary ofmass m0 = âm located at the geometric center ofthe polygon.By analyzing the phase flow, we determine the equilibria ofthe system, their linear stability and the bifurcations depending on the mass ofthe central primary (parameter Beta).