Stability of equilibrium points in the generalized perturbed restricted three-body problem

Abstract

This paper studies the existence and stability of equilibrium points under the influence of small perturbations in the Coriolis and the centrifugal forces, together with the non-sphericity of the primaries. The problem is generalized in the sense that the bigger and smaller primaries are respectively triaxial and oblate spheroidal bodies. It is found that the locations of equilibrium points are affected by the non-sphericity of the bodies and the change in the centrifugal force. It is also seen that the triangular points are stable for 0<μ<μ c and unstable for \(\mu_{c}\le\mu <\frac{1}{2}\), where μ c is the critical mass parameter depending on the above perturbations, triaxiality and oblateness. It is further observed that collinear points remain unstable.