Stability and Reconfiguration Analysis of a Circularly Spinning Two-Craft Coulomb Tether

Abstract

The concept of a spinning two-craft Coulomb tether is introduced. Here a physical tether is replaced with an electrostatic force field resulting in an attractive Coulomb force between the two craft. This results in conic section motions similar to the two-body gravitational problem, with spinning in-plane and out-of-plane motions. The spacecraft charge is assumed to be regulated with an active charge servo system. The stability of a Coulomb tether with constant spacecraft charges is investigated. The reduced equations of motion for a deep-space mission are obtained and linearized to determine eigenvalues of the perturbed motion. This analysis shows that if the plasma Debye length is smaller than the spacecraft separation distance, the radial motion is guaranteed to be unstable. For larger Debye lengths the nonlinear radial motion is locally stable. The perturbed out-of-plane motion is shown to always be stable regardless of Debye length. Further, open-loop charge solutions are obtained to perform reconfiguration where the circular orbit radius is changed to a new value. This maneuver is related to the classical Hohmann transfer orbit between circular orbits. However, in the Coulomb tether concept, the reconfiguration is achieved by varying the effective gravitational parameter through spacecraft charge changes.