Orbit Radial Dynamic Analysis of Two-Craft Coulomb Formation at Libration Points

Abstract

The linearized orbit radial dynamics and stability analysis of a two-craft virtual Coulomb structure at Earth–moon libration points are investigated. The linearized study assumes that the sunlit areas of the two-craft structure are equal such that the differential solar radiation pressure on the formation is zero. The relative distance between the two satellites of the Coulomb tether is controlled using electrostatic Coulomb forces. The separation distance between the satellites is stabilized with a charge feedback law that maintains the relative distance at a constant value. The electrostatic virtual tether between the two craft is capable of both tensile and compressive forces. The gravity gradient torques on the formation due to the two celestial objects is exploited to stabilize the Coulomb tether formation in the orbit radial direction. Controlling the separation distance stabilizes the in-plane rotation angle; however, the out-of-plane rotational motion is not affected by the spacecraft charge control law. The new two-craft dynamics at the libration points is provided as a general framework in which circular Earth orbit dynamics form a special case. Furthermore, an alternate linear control technique for a two-craft Coulomb virtual tether formation’s radial equilibrium at a collinear libration point is developed and analyzed. Numerical simulations using charge feedback law are presented at both a collinear and a triangular libration point.