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 μ c ≤ μ < 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.

This paper studies the existence of periodic orbits around the triangular points of the restricted three-body problem (R3BP) in the range of linear stability. The problem is generalized in the sense that the bigger and smaller primaries are considered as triaxial and oblate spheroidal bodies, respectively and is perturbed due to the introduction of small perturbations in the Coriolis and the centrifugal forces. It is observed that long and short periodic orbits exist around these points and that their period, orientation and eccentricities are affected by the above parameters.