Three-Dimensional Multi-Tethered Satellite Formation with the Elements   Moving Along Lissajous Curves
  This note presents a novel approach to maintain three-dimensional multi-tethered satellite formation in space. For a formation consisting of a main body connected by tethers with several deputy satellites (the so-called "hub-and-spoke" configuration) we demonstrate that under proper choice of the system's parameters the deputy satellites can move along Lissajous curves in the plane normal to the local vertical with all tethers stretched, the total force due to the tension forces acting on the main satellite is balanced in a way allowing it to be in relative equilibrium strictly below or strictly above the system's center of mass. We analyze relations between the system's essential parameters and obtain conditions under which the proposed motion does take place. We also study analytically the motion stability for different configurations and whether the deputy satellites can collide or the tethers can entangle. Our theoretical findings are corroborated and validated by numerical experiments. 
D. Yarotsky, V. Sidorenko, D. Pritykin
math.OC