Analysis of the relative dynamics of a charged spacecraft moving under the influence of a magnetic field

Abstract

We analyse a dynamical scenario where a constantly charged spacecraft (follower) moves in the vicinity of another one (leader) that follows a circular Keplerian orbit around the Earth and generates a rotating magnetic dipole. The mass of the follower is assumed to be negligible when compared with the one of the leader and they are supposed to be in a high-Earth orbit, so the Lorentz force on the follower due to the geomagnetic field is ignored. With these as

Relative dynamics of charged spacecraft in a magnetic field applied to formation flight

“…In [3,4] Cheng et al extended the above study to three orientations of the dipole: normal, radial and tangential, and performed an extensive dynamical analysis, including the symmetries of the system, the equilibrium points and their stability, and the periodic and the quasi-periodic orbits emanating from these elliptic equilibria.…”

“…Concerning the technical issues for the accomplishment of Lorentz force actuated missions, the two main challenges are the spacecraft surface charging [15], and the thermal control system of the HTSC (see [4,13,2]). According to [27],…”

“…In a paper already mentioned [4], Cheng et al analysed, using Dynamical Systems methods, the relative dynamics of a constantly charged follower spacecraft moving in the artificial magnetic dipole produced by the leader. Using these tools, all the equilibrium points, and several families of periodic orbits and quasi-periodic invariant tori were accurately determined, together with their stability properties.…”

“…The paper is organized as follows: the dynamical model is briefly introduced in Section 2, including the differential equations of motion for the three orientations of the dipole considered. Several configurations about the equilibrium points computed in [4] (consisting of a single or multiple spacecrafts, with either the same or different charges), are analysed in Section 3, including the effects of initial errors in their location. In Section 4, we consider the controllability of the linearised system around the equilibrium points, and we propose a linear quadratic regulator (LQR) feedback control law for the formation keeping, where the charge of the spacecraft is the only control variable.…”

“…The conclusions are given in the last section of the paper. More possible formation flying configurations using as reference trajectories some periodic orbits computed in [4], will be discussed in a forthcoming paper.…”