Methods of studying the motion of flexibly connected space objects are considered and some issues of their practical use are described. Particular attention is paid to the study of qualitative structures and bifurcations of dynamic systems that determine the movement of the ligament, and the characterization of the basic laws of movement of connected objects with a constant and adjustable length of the cable. Stationary modes of ligament movement are considered taking into account mechanical properties of connecting cable and main characteristics of its movement at sounding of upper layers of atmosphere, performance of orbital maneuvers, descent from orbit and creation of artificial gravity.