Nullcline Analysis as a Tool to Study the Spin-Up of Tethered Satellite Systems

As interest in exploring the extraterrestrial environment increases, the study of novel space systems will become more important. One such family of systems that has been investigated in depth over the past two decades is the tethered satellite system. These systems are comprised of two or more end bodies joined by a long, light-weight, flexible connector known as a tether. In addition to the standard gravitational, atmospheric, and radiation forces that aect the motion of typical satellites, tension forces are transferred along the tether and aect the motion of the end bodies relative to the Earth and relative to each other. The dynamics of such satellite systems in Earth orbit have been investigated since the 1960s. Since that time many potential applications of tethered satellites have been proposed. These applications include systems using the Skyhook orbital injection such as the Momentum Exchange and Electrodynamic Reboost vehicle (MXER). Also, a set of concepts designed to produce artificial gravity in space exist. Each of these applications relies heavily on the assumption that the dynamics of tethered satellite systems are well known, predictable, and controllable. In fact, simply determining the possible dynamics of tethered satellite motion has been the focus of many previous studies. This paper presents a technique which uses some analytical characteristics of the dierential equations of motion of tethered satellite systems in order to describe and predict tethered satellite motion.