Gravity-Gradient Excitation of a Rotating Cable-Counterweight Space Station in Orbit

Abstract

The gravity-gradient excitation of a whirling cable-counterweight space station in orbit is investigated. The Lagrange’s equations of motion for transverse oscillations of the system are derived and shown to be of the Mathieu type. A few representative cases are investigated analytically and on an IBM 7090 computer. The stability criteria for the axial vibrations are also considered and shown to be of the same kind as those for the transver se vibrations of the cable. Viscous damping is included in the analyses and found to be effective and essential for prevention of parametric excitation instability of the system.