On the dynamics of spinning tethered space vehicles

Extensive work on the development of high–fidelity models of tethered systems has been carried out over the past three decades in support of the various space–tether missions flown to date. Although many of these models account for the full six–degrees–of–freedom motions of the end bodies, they did not consider a spinning tether. The reason is that most of the investigations are believed to focus on specific mission configurations such as the shuttle–based and space station–based applications. They addressed the particular features for that class of tethered systems and a spinning tether was not one of those features. However, from the flight of Canadian OEDIPUS–A (Observations of Electric–field Distributions in an Ionospheric Plasma – a Unique Strategy) mission, which was the first to involve a spinning tether, it is clear that the spin of the tether is an important factor that must be included in the modelling. This is especially true for a wire–like tether which has a finite bending stiffness. In this paper, a set of nonlinear equations of motion is formulated for a spacecraft comprising two rigid payloads with flexible booms and connected by a tether that is spinning at the same nominal rate as the end bodies. Additionally, closed–form infinitesimal and quasi–stability conditions that provide very useful design equations for a spinning tethered spacecraft are presented. One of the main findings of this work is the dominant role played by the subtle effects of the tether root bending on the dynamics of a spinning tethered spacecraft, particularly at high spin rates. Using our model, we show that these effects lead to the dynamics anomaly observed in the OEDIPUS–A mission, when the aft payload exhibited an unexpectedly rapid and large divergence of the coning angle.