Dynamics of multi-tethered satellite formations

The dynamics of certain multi-tethered satellite formations containing a central body are examined in this paper. Some simplifications are made prior to the analysis: the satellites are point-masses, the tethers are massless and straight, and the motion of the central body of the formations is prescribed. First, planar formations are investigated: these are termed hub-and- spoke (which comprises a central body (hub) from which stem tethers (spokes), each having a satellite at its end), and closed-hub-and- spoke (which has the same description but also has, in addition, tethers joining successive satellites). These formations are placed in the orbital plane, or in the Earth-facing plane normal to the orbit, and are given an initial spin rate about an axis orthogonal to their nominal plane. The ensuing motion is studied in order to ascertain the conditions under which the formations remain in dynamic stability. Later, the motion of three-dimensional configurations, whose initial spin vector is along the radial direction, is examined. These formations are deployed along the local vertical. They are: a closed-hub-and-spoke formation, which is found to be unstable and a double-pyramid configuration, which is found to be stable.