Abstract
On the basis of previous analysis and control for two- to four-craft static Coulomb formations, this paper continues to further study the analytic solutions for an equal mass five-craft Coulomb formation under the Hill-frame formation. The paper analyzes the co-linear formation of one-dimension, planar formation of two-dimension and hexahedral formation of three-dimension for equal mass five-craft Coulomb formation flying. The authors discuss the conditions of an analytical solution to determine the net charges of craft in each case of static formation. Due to perturbations and disturbances in the GEO altitude, the static configuration can merely maintain its transient state. For the purpose of keeping it stable over the longtime, the Coulomb formation must be subjected to external control. This paper uses LQR control as an example. Finally, through the control applied, craft can stably maintain a static configuration around the static equilibrium point. Moreover, numerical simulation results are illustrated, and the paper discusses situations of Coulomb static configurations when the number of satellites is more than five.
