Effect of perturbations in the Coriolis and centrifugal forces in the Robe-finite straight segment model with arbitrary density parameter

The present article is a study of the effect of small perturbations epsilon and epsilon ' in the Coriolis and centrifugal forces, respectively, on the existence and stability of the equilibrium points in the Robe's restricted three-body problem when the smaller primary is a finite straight segment. The effect of small perturbations in the centrifugal force has a substantial effect on the location of the equilibrium points, but a small perturbation in the Coriolis force has no impact on them. The present model has two collinear, two out-of-plane, and an infinite number of noncollinear equilibrium points. Furthermore, we have discussed the stability of the equilibrium points analytically. The collinear equilibrium points L-1 and L-2 are found to be conditionally stable for the parameters mu, k, l, epsilon, and epsilon '. It is perceived that, for any epsilon with divide epsilon divide MUCH LESS-THAN 1 and epsilon ' <= 0.2, L-1 is stable, and for epsilon ' >= 0.23, it becomes unstable. Furthermore, for any epsilon with |epsilon| MUCH LESS-THAN 1 and epsilon ' <= -0.025, L-2 is stable, and for epsilon ' >= -0.024, it becomes unstable. The noncollinear and out-of-plane equilibrium points are always unstable.