“…During the last few decades, the dynamics of many different types of dumbbell satellites have attracted wide attention of many researchers. We refer the reader to classical monographs [4,15,16,18,21,[27][28][29] for the existence of periodic oscillations of dumbbell satellite systems, [3,9,19,30] for the stability of periodic oscillations, [1,7,8,10,14,22,25] for the stability of equilibria points, and [23,24,26] for the dynamics and control. For example, Guirao et al [15] gave sufficient conditions for the existence of periodic motions about the dumbbell satellite's center of mass that are asymptotic to translational motion in an absolute coordinate system by the use of the averaging method.…”