Dynamics and rebound behavior analysis of flexible tethered satellite system in deployment and station-keeping phases

The tether deployment of a tethered satellite system involves the consideration of complex dynamic properties of the tether, such as large deformation, slack, and even rebound, and therefore, the dynamic modelling of the tether is necessary for performing a dynamic analysis of the system. For a variable-length tether element, the absolute nodal coordinate formulation (ANCF) in the framework of the arbitrary Lagrange-Euler (ALE) description was used to develop a precise dynamic model of a tethered satellite. The model considered the gravitational gradient force and Coriolis force in the orbital coordinate frame, and it was validated through numerical simulation. In the presence of dynamic constraints, a deployment velocity of the tether was obtained by an optimal procedure. In the simulation, rebound behavior of the tethered satellite system was observed when the ANCF-ALE model was employed. Notably, the rebound behavior cannot be predicted by the traditional dumbbell model. Furthermore, an improved optimal deployment velocity was developed. Simulation results indicated that the rebound phenomenon was eliminated, and smooth deployment as well as a stable state of the station-keeping process were achieved. Additionally, the swing amplitude in the station-keeping phase decreased when a deployment strategy based on the improved optimal deployment velocity was used.