  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.
