In this paper we consider the problem ofoptimal control of the model for a rotating body beam, whichdescribes the dynamics of motion of a beam attached perpendicularly to the center of a rigid cylinder and rotating with the cylinder.The control is applied on the cylinder via a torque to suppressthe vibrations of the beam.We prove that there exists at least one optimal control and derive anecessary condition for the control. Furthermore, on the basis ofiteration method, we proposenumerical approximation scheme to calculate theoptimal control and give numeric examples.
