Non-Linear Stability in the CR3B Problem under the Effects of Beyond-Newtonian Dynamics and Kerr Like Primaries

In the present research work, we have carried out an analysis of the non-linear stability of the circular restricted three-body problem (CR3BP) with Kerr-like primaries. The model discussed here includes three bodies, two of which are Kerr primaries that spin on their axes and at the same time, revolve around the mutual center of mass (origin) and the third is an infinitesimal mass. We take here, the parameter \(\epsilon \) which represents the transition from Newtonian dynamics to beyond-Newtonian dynamics. With this perturbation, we evaluate the equation of motion of infinitesimal mass and then discuss the nonlinear stability of triangular stationary points \({{\mathbb{L}}_{4}}\) and \({{\mathbb{L}}_{5}}\). We use the KAM Theorem for the stability analysis and obtained some meaningful conclusions numerically. Further, these obtained results on stability and other dynamical properties like the location of \({{\mathbb{L}}_{4}}\) and \({{\mathbb{L}}_{5}}\), potential surfaces, and regions of motions have been discussed graphically.