An insight on the restricted problem of 2+2 bodies with straight segment

In the present paper, an effort to generalize the restricted problem of2 + 2bodies has been made by considering the primary bodiesm(1)andm(2)to be a point mass and straight segment of length 2l, respectively. The motion of the two infinitesimal bodiesm(i),i = 3, 4 has been investigated, in which eachm(i),i = 3, 4 is moving in the gravitational field ofm(j),j = 1, 2, 3, 4 withi not equal j. For the present problem, 14 equilibrium points are obtained, of which 6 are collinear and the rest are noncollinear. The length parameterlhas a subsequent effect on the location of all the equilibrium points. Systematic stability analysis has been carried out by using the theory of perturbation. All the equilibrium points are found to be unstable.