Perturbed Planar Restricted Four-Body Problem with Repulsive Manev Potential

Abstract

In this paper, we carried out a numerical study of the planar restricted four-body problem with repulsive Manev potential and perturbations in the Coriolis and centrifugal forces such that the peripherals possess Eulerian configuration. We have presented the equations of motion in the rotating frame and investigated the existence and location of the equilibrium points. We have found that there exist six equilibrium points all of which lie along the coordinate axes and shift in positions as the perturbation parameter is varied. We have also examined the linear stability of these equilibrium points and they are found unstable. The dynamical behavior of this system is also investigated using the Lyapunov Characteristic Exponents and the system is found to be chaotic.