Two-Bar Model for the Dynamics and Stability of Electrodynamic Tethers

Abstract. Previously a new dynamic instability that affected electrodynamic tethers in inclined orbits was studied, with a simple one-bar model that neglected the contribution of the tether lateral dynamics. The \u8f exibility of the tether (lateral dynamics), however, plays an important role in the overall motion of the system as shown by numerical simulations of a bare-tether generator in a circular inclined orbit. The same analytical techniques of the previous work are now applied to investigate the dynamics and stability of an electrodynamic tether system modeled by two articulated bars that account for the lowest lateralmodes of the tether. The analysis,which can be directly extended to any electrodynamic tether system, has been focused on two particular, but important cases: the combination of a conductive and a nonconductive leader tether (as in the PropulsiveSmall Expendable Deployment System) and a homogeneous, conductive tether. The lateral dynamics is extremely rich, with skip rope motion, instability peaks, and chains of bifurcations for different regions of the parameter space. The same energy pumpingmechanism that destabilizes the rigid model (one bar) is found to drive an even faster instability of the lateral modes. Damping, which has not been included in the analysis, could change this unstable behavior