On the Perturbed Restricted 2+2 Body Problem when the Primaries are Non-spherical

The present investigation deals with the outcomes of the small perturbations $$\sigma _1$$ and $$\sigma _2$$ in the Coriolis and centrifugal forces respectively, in the oblate straight segment setup of the restricted $$2+2$$ body problem. We describe the dynamical system that consists of the primaries of masses $$m_1$$ and $$m_2$$ as oblate spheroid and straight segment, respectively. With this setup, we obtain the equations of motion of the infinitesimal bodies having masses $$m_3$$ and $$m_4$$ under the gravitational attraction of the primary bodies, their mutual attraction and the small perturbations in the Coriolis and centrifugal forces. We determine the equilibrium points by using the perturbation technique in the equilibrium points for the case $$m_4=0$$ . We get fourteen equilibrium points, six of which are on the line connecting the centers of the primaries and eight of which lie on the $$xy-$$ plane but not on the $$x-$$ axis. The stability of the equilibrium points for a particular set of the parameters is analyzed and it is concluded that the collinear equilibrium points are unstable. The four non-collinear equilibrium points are stable for some combinations of $$\sigma _1$$ and $$\sigma _2$$ and rest are unstable for all values of $$\sigma _1$$ and $$\sigma _2$$ . The permissible and forbidden regions of motion of the infinitesimal body are also studied for the different values of the Jacobian constant and it is perceived that the permissible regions of motion expands on decreasing the value of the Jacobian constant. These regions are subsequently affected by the involvement of the mass, oblateness, length and perturbations in the Coriolis and centrifugal forces parameters.