Dynamics of a flexible multi-tethered satellite formation in a Halo orbit with uncertain parameters

Abstract

The nonlinear dynamics of a flexible rotating multi-tethered satellite formation in a Halo orbit with uncertain-but-bounded parameters are examined in this paper via an interval analysis method. In Hill's problem, equations of motion for the focused system are derived with the flexibility and extensibility of tethers involved. Not limited to the system of concern, the developed dynamic model could be generally applied to any N-body multi-tethered satellite system of arbitrary configurations. In addition, the space environmental perturbation of the thermal effect is considered in the dynamics modeling to improve accuracy. Based on interval descriptions, a bounds estimation problem is formulated for the station keeping phase of the system with uncertain interval parameters. Furthermore, an interval method of high efficiency, which utilizes the Chebyshev series for approximation, is presented to solve this problem by only using the lower and upper bounds of the uncertain parameters and avoiding a global search in numerical results. Finally, numerical simulations have been performed to demonstrate the effectiveness and feasibility of the proposed method and to evaluate the influences of the uncertain interval parameters on the dynamic behaviors of the system.