On the controlled rotation of a system of two rigid bodies with elastic elements

The problem of controlling the plane rotational motions of two rigid bodies connected by an elastic rod is studied. One end of the rod is attached to the support by a hinge with a spring, the latter modelling the elastic compliance of the fastening, and the other end is rigidly joined to the load. The Hamilton principle is used to obtain the integrodifferential equations and boundary conditions describing the motion of the system support — spring — rod — load. The following problem is posed: it is required to rotate the system by a given angle by means of the controlling force moment, with quenching of the relative oscillations of the load elements which appear as a result of the deformability of the rod and of the elastic torsion of the spring. Similar problem arise in the study of the dynamics and control of the motion of devices used in transporting loads through space (robots, manipulators, load lifting machines, etc.). In computing their control modes a significant part is played not only by the deformability of the elements, but also by the elastic compliance of the connecting joints. Asymptotic methods are used to botain a solution of the control problem in question for two limiting cases: 1) the mass of the load carried is much greater than the mass of the rod and support, and 2) the rod has high flexural rigidity