The study of equilibrium dynamics of the collinear restricted four-body problem with non-spherical test particle

In the present manuscript, the dynamics of the non-spherical test particle in the planar version of spatial collinear restricted four-body problem is presented. Using the numerical methods, the parametric variation of the position of libration points (LPs) is illustrated when the oblateness/prolateness parameters vary in the pre-assumed intervals. Moreover, it is also unveiled how these parameters affect the stability of the LPs and the regions of motion. For all the LPs, we have shown their nature by classifying them not only in two category i.e., as linearly stable and unstable but also as minima, index-1, and index-2 saddles. The performed numerical investigations strongly suggest that the oblateness/prolateness parameters are indeed very influential factors in this dynamical model.