Stability of two tethered unsymmetrical earth- pointing bodies.

This investigation deals with the motion, in a circular orbit, of a flexible satellite consisting of two identical, but unsymmetrical, rigid bodies connected together by a single tether. The differential equations governing the motions of this assembly, regarded as having nine degrees of freedom (the motion of the composite mass center presumed known and the mass of the tether neglected), are presented. An "earth-pointing" motion, which corresponds to a particular solution to the set of differential equations, is accomplished when the assembly moves such that the rigid end bodies are at rest in the orbital reference frame and such that the connecting tether remains coincident with the line joining the center of the earth and the mass center of the satellite. A procedure for predicting the instabilities of such a motion is developed and employs the method of Routhian arrays. Some general conclusions concerning the influence of the tether on vehicle stability are reported. In particular, it is established that the elastic and damping properties of the tether are immaterial, while the tether length and tethering geometry at the end bodies are of principal importance.