Global Dynamics of a Ring-Tethered Three-Satellite System in Any Plane

This paper explores the global dynamics of a ring-tethered three-satellite formation in any plane to expand the potential application range of such satellite formations. A multidegree-of-freedom model for the formation is constructed, and orthogonal control forces perpendicular to the assigned motion plane are applied to maintain the tethered satellites operating within the desired plane. The effects of environmental perturbations, such as the Earth's oblateness (J2), atmospheric drag, and solar pressure, are also taken into account. Floquet theory is utilized to analyse the stability of the ring-tethered three-satellite formation. The impact of motion plan attitude and initial system states on the motion forms, including spin and irregular motions, is examined. Furthermore, a parametric analysis of the tether length, orbital altitude, and environmental perturbations is carried out. Finally, an effective proportional–differential control strategy is introduced to demonstrate that the system is stabilizable, even when its parameters are in the irregular region. The results show that the stability of the system can be maintained through appropriate control methods. This study provides important insights into the global dynamics of ring-tethered three-satellite formations and can serve as a useful reference for the design and operation of such systems.