On controlled rotation of an elastic rod

Abstract Plane rotational motions of an elastic rod loaded by a perfectly rigid body and acted upon by a controlling moment of forces, are considered. A system of integrodifferential equations with initial and boundary conditions is obtained. The problems of control are studied, which carried the system from some initial state to a given angular state with damping of elastic oscillations or to a state when the system rotates as a whole with fixed angular velocity. These formulations appear in the course of considering a whole series of practical problems of controlling the systems with elastic constraints such as robots and manipulators, weight lifting machines, etc. The asymptotic methods are used to obtain the solution of the control problems stated, close to the two limiting cases: 1) the case of weightless rod (quasistatic approximation) and 2) the case of high flexural rigidity. The problems of dynamics and control of oscillating systems with distributed parameters were studied in /1–11/ et al.