Controllability from rest to arbitrary position of the nonhomogeneous Timoshenko beam

The controllability of a slowly rotating beam clamped to a disc is considered. It is assumed that at the beginning the beam remains at the position of rest and it is supposed to rotate by the given angle to achieve a desired position. The movement is governed by the system of two differential equations with nonhomogeneous coefficients: mass density, rotary inertia, flexural rigidity and shear stiffness. The problem of controllability is reduced to the moment problem that is, in turn, solved with the use of the asymptotics of the spectrum of the operator connected with the movement.