Investigating the properties of equilibrium points of the collinear restricted 4-body problem

The circular version of the planar restricted 4-body problem is considered. We assume that the two peripheral bodies have no spherical shape, but they are either prolate or oblate. The dynamical properties of the points of equilibrium of the system are investigated using several types of numerical methods and techniques. In particular, we calculate not only the coordinates of the positions of the libration points but also their linear stability and dynamical types. Our main objective is to reveal the influence of the mass parameter of the system along with the shape parameter on the equilibrium dynamics. Our analysis indicates that in the case where the peripheral bodies are prolate in shape, the equilibrium dynamics of the system is more interesting and complex with respect to the case where the two peripheral bodies have oblate shapes.