Trajectories of an unguided probe with a damping cable

Abstract

The relative orbital motion of two point masses connected by a flexible nonexpadable weightless cord with shock contacts is considered. This system models, for example, the dynamics of a satellite and a probe connected by a cable. The orbit of the center of mass is assumed to be circular. The motion of the probe relative to the center of mass can be presented as a series of portions of free motion between successive contacts, i.e., as the probe recedes from the satellite to a distance equal to the cable length. At the time of establishing contact, there is shock interaction, which can be of various nature — perfectly elastic, perfectly inelastic, and with partial absorption of energy.