Spacecraft Formation Flying Dynamics and Control Using the Geomagnetic Lorentz Force

TLDR

The motion of a charged satellite in Earth’s magnetic field is governed by the Lorentz force, offering a propellantless propulsion concept. The study aims to derive a dynamic model of a charged satellite for formation flying and to develop a charge‑reduction strategy using sequential quadratic programming. The authors use Hill–Clohessy–Wiltshire and Tschauner–Hempel equations to obtain analytical approximations, then apply sequential quadratic programming to solve the nonlinear orbital transfer problem and minimize charge. Linearized analysis demonstrates that stepwise charge control renders the system controllable.

Abstract

The motion of a charged satellite subjected to the Earth's magnetic field is considered. The Lorentz force, which acts on a charged particle when it is moving through a magnetic field, provides a new concept of propellantless electromagnetic propulsion. A dynamic model of a charged satellite, including the effect of the Lorentz force in the vicinity of a circular or an elliptic orbit, is derived and its application to formation flying is considered. Based on Hill–Clohessy–Wiltshire equations and Tschauner–Hempel equations, analytical approximations for the relative motion in Earth orbit are obtained. The analysis based on the linearized equations shows the controllability of the system by stepwise charge control. The sequential quadratic programming method is applied to solve the orbital transfer problem of the original nonlinear equations in which the analytical solutions cannot be obtained. A strategy to reduce the charge amount using sequential quadratic programming is also developed.