Three-phase motion of systems with elastic members

This paper deals with a three-phase motion of dynamical systems with elastic members. Such motions consist of a phase during which the motion is defined as unconstrained, a phase during which the motion is defined as constrained, and a transition phase, during which constraints are imposed or removed from the motion. In general, the elastic properties of a system with elastic members undergoing a three-phase motion change during the transition. It is shown in this paper that equations governing the motion of the system in the unconstrained phase can be used, in conjunction with the theory of imposition and removal of constraints, to generate equations governing the entire three-phase motion; and that the changes in the elastic properties of the system associated with the transition are taken care of automatically. The indicated theory is used to generate equations governing the capture of a satellite by a space robot with flexible links.