On the dynamics of a beyond-Newtonian photogravitational collinear R4BP with spinning primaries

The equilibrium dynamics of the beyond-Newtonian photogravitational collinear restricted four-body problem (R4BP) with spinning primaries are investigated. An effective potential is constructed, yielding modified equations of motion together with a generalized Jacobi integral. Numerical methods are deployed to determine the co-ordinates of equilibrium points of the system, as well as their linear stability. A systematic and rigorous analysis is carried out to elucidate the influence of the transition parameters ϵ0,1,2 and the radiation pressure factors q0,1,2 on the system’s dynamics. Extending earlier work, we consider the general case in which the main primaries are characterized by distinct transition parameter values. Consequently, the relative contribution of classical Newtonian and post-Newtonian gravitational effects is allowed to vary independently for each primary. On the other hand, the location and number of total equilibria strongly depend on the numerical value of the transition parameters. The equations of motion are numerically integrated, and the phase-space structure is analysed through the Poincaré surface of section (PSS). The results unveil the co-existence of regular and chaotic regions in phase space. Further, to quantify the stability of trajectories, we use the Lyapunov exponent.