Motion and stability of a rotating space station-cable-counterweightconfiguration

An analysis of the dynamics of a rotating, connected two-body satellite system is presented. The motion is restricted to the orbital plane in which the system mass center follows a circular orbit. The cable is assumed to be extensible, but of negligible mass. The Lagrangian equations of motion are developed and linearized about the equilibrium motion, where the cable tensile force is balanced by the centrifugal force. Necessary and sufficient Routh-Hurwitz stability criteria are obtained for various special cases. Damping system parameters are optimized by repeated examination of the roots of the system characteristic equation. Minimum time constants are found to be insensitive to small changes in the amount of cable damping, but are dependent on the amount of rotational damping of the end body motions. Spin axis drift attributed to gravity-gradient torques is examined quantitatively and found to be small.