Nonlinear dynamic analysis of a three-body tethered satellite system with deployment/retrieval

Abstract

This paper analyzes the nonlinear dynamic behavior of a three-body tethered satellite system undergoing deployment and retrieval, considering a variable orbital radius for the instantaneous mass center of the three satellites. A deploying or retrieving satellite system is modeled as a two-piece dumbbell model with six degrees of freedom, which consists of three point masses and two straight massless tethers. The nonlinear equations of motion for this model are derived by applying Lagrange’s equations. Using these nonlinear equations, the dynamic behavior of a satellite system is analyzed for several initial satellite attitudes. For the case of a three-body tethered satellite system undergoing deployment or retrieval, the dynamic response and attitude dynamics of the system are studied. This study shows that the proposed equations of motion generate results that are significantly different from those of a previous study when the system parameters and conditions are chosen so that the orbital radius of the mass center changes considerably with time. It is also observed that the attitude of a tethered satellite system stabilizes as the tethers are deployed and destabilizes as the tethers are retrieved.