SYNTHESIS OF A GENERATING-SYSTEM IN THE PROBLEM OF CONTROLLING AN ELASTIC ROD

The controlled motions of an elastic rod are investigated using the ex ample of a discrete model. The model consists of an arbitrary finite n umber of absolutely rigid links with elastic connections between them. For sufficiently high stiffness, the motions of an elastic system con tain different frequency components: the fast motions of the elastic p art and the slow motions of the system as a solid body. The motion of such systems is described by singularly perturbed equations. On changi ng to the standard form of Poincare systems with a small parameter on the right-hand side of the equations of motion, the generating system which describes the motion of the elastic part may turn out to be cons ervative and the vibrational motions of the elastic part will be prese rved in the system. A procedure for synthesizing the equations is prop osed which enables one to form a generating system with the required p roperties. The effect which arises is of a substantially non-linear fo rm. A theorem on the asymptotic stability of the steady state of the g enerating system as a whole is proved.