Dynamics of infinitesimal mass near equilibrium points in planar equilateral restricted four-body problem under magnetic force

Abstract

This study examines the impact of magnetic force on a particle of negligible mass within the planar equilateral restricted four-body problem (PERFBP), considering one of the three primary bodies as a dipole. We derived equations that describe the motion of the particle. The parametric evolution of position, existence, and nature of equilibrium points, as well as their linear stability, is performed numerically. Our numerical findings indicate that the magnetic moment, \(\lambda _1\), has a significant impact on both the existence and location of the equilibrium points. We found that for a given value of mass parameter \(\mu \), the number of equilibrium points varies as \(\lambda _1\) increases, reaching a maximum of five after a specific increment. Beyond this point, the number of equilibrium points stabilizes and remains constant. We also observed that as the value of \(\mu \) increases, the variation in the number of equilibrium points stops at lower \(\lambda _1\) values before converging to the constant value of five. It is observed that the motion of the particle is periodic around the primary body \(P_1\) and is bounded as well as chaotic around the primary bodies \(P_2\) and \(P_3\). In some cases, the motion is quasi-periodic, while in other instances, it is chaotic and escapes to infinity when the particle starts near \(L_6\) and \(L_7\). All equilibrium points were found to be unstable in the Lyapunov sense. We conducted numerical simulations to analyse the configuration of zero-velocity curves for the particle. The model provides a relevant framework for understanding the dynamics of a charged particle or spacecraft in the vicinity of the Sun–Jupiter–Trojan asteroid system.