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

Abstract

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

Libration Control of Bare Electrodynamic Tethers Considering Elastic–Thermal–Electrical Coupling

“…The physical properties of the microsatellite and the EDT system are listed in Table 1. As pointed out in [14], heavy subsatellites at the cathodic end have a positive effect on the dynamic stability of deorbit operation by EDT systems. In the current paper, the mass of the subsatellite is assumed to be two times the mass of the tether for the sake of stability.…”

“…Equations (13), (14), and (16) are highly nonlinear and must be solved numerically at each time step. Once the current i C is determined by Eq.…”

“…As mentioned by Pelaez et al [14], the dumbbell model cannot predict the elastic instability of tethers, which may develop faster than the libration instability and lead to the global instability of TSSs. Consequently, a two-bar tether model was proposed to capture the first mode of transverse motion of flexible tethers in order to assess the effect of tether transverse dynamics on the libration stability of tethers in circular and highly eccentric elliptic inclined orbits [14,18]. Later, the lumped mass model was proposed to capture the high-frequency modes of the transverse motion of tethers [6].…”

“…However, the periodic excitation of the electrodynamic force will lead to an unstable libration motion of the EDT system [12], leading to a tumbling motion if no control strategy is applied. Nevertheless, analyses in the published literature reveal that the libration instability is slow to grow compared with the instability of transverse motion of flexible tethers [13,14] and is substantially affected by the orbital eccentricity in elliptical orbits [15]. Therefore, it is imperative to 1) understand the EDT dynamics with a high-fidelity dynamic model by considering a tether's orbital, attitude, and elastic dynamics subject to realistic and comprehensive environmental perturbations; and 2) develop a simple and practical control strategy to stabilize the libration motion of EDT systems while maintaining their deorbit efficiency.…”

Mission-function control of tethered satellite/climber system

“…1 shows the model of TSS with a climber used in this study: tethered satellite/climber system (TSCS). This model is similar to the three-mass tethered satellite model [30,31] or two-bar model [32] except that the climber ascends and descends the tether, whereas the center satellite in the three-mass tethered satellite model [30,31] and the twobar model [32] do not. The climber is at a distance L 1 along the tether from the mother satellite, and the subsatellite is at a distance L 2 along the tether from the climber.…”