Formation-Flying Planar Periodic Orbits in the Presence of Intersatellite Lorentz Force

Abstract

This study presents formation-flying periodic orbits in a new satellite-relative motion scenario, which considers the presence of intersatellite Lorentz force. A nonlinear dynamical model for the proposed relative motion is established based on the Hill–Clohessy–Wiltshire equation, under the assumption that a chief satellite generates a rotating magnetic dipole while a constantly charging deputy satellite moves close to the artificial magnetic field of the chief satellite. Moreover, we assume that the barycenter of the proposed system is constrained in a circular reference orbit, and the rotating magnetic axis of the dipole is perpendicular to the reference orbital plane. We first derived equilibrium points (and analyzed their stabilities), an integral constant, and zero-velocity surfaces for the proposed relative motion based on system parameters, such as the charge-to-mass ratio of the deputy satellite, the moment and rotating rate of the magnetic dipole, and the angular velocity of the reference orbit. With regard to the zero-velocity surfaces, bounded periodic orbits in the reference orbital plane are searched out using Poincare maps. Planar periodic orbits near the equilibrium points are numerically computed via differential correction based on the stability characteristic of equilibrium points, and a special case is analytically solved using the Lindstedt $-$ Poincare method. The periodic orbits of relative motion presented in this study differ from those in traditional satellite formation flying. The difference suggests potential applications of the presented periodic orbits, such as propellantless satellite formation maintenance and noncontact capture of electrostatically charged space debris.