The steady motions of a three-body system in weightlessness conditions

The stability of the steady motions by inertia of a combination of three point masses, forming an open chain, is investigated using the Routh–Lyapunov theorem. The problem is investigated in two different formulations: in the first formulation the mean mass is fixed with respect to a thread, and in the second it can move along that thread without friction, while constant tension of the thread is ensured by additional devices, consuming external energy. In steady motions, the configurations of the arrangement of the masses in both systems are similar, but the stability conditions are found to be different.