Stability and control of relative equilibria for the three-spacecraft Coulomb tether problem

This paper studies the stability and control of relative equilibria for the spinning three-craft Coulomb tether problem. General conditions are derived whose solutions are all relative equilibria for the spinning charged three-craft cluster. In particular, the collinear three-craft spinning family of solutions are derived. Routhian reduction is used to employ the conservation of angular momentum to simplify the equations of motion of the system and, hence, restricting the analysis to its internal shape dynamics. This paper mainly focuses on symmetric Coulomb-tether systems, where all three craft have the same mass and nominal charge values. Based on a linearized analysis, the uncontrolled symmetric three-craft Coulomb tether system is shown to be unstable. Linear feedback control based on the linearized equations is derived to control the nonlinear dynamics of the system. The closed-loop system converges to a neighborhood of the desired equilibrium in general. If the initial condition is chosen such that the system angular momentum is equivalent to that of the desired equilibrium, asymptotic convergence is achieved.