Approximate controllability of a rotating Kirchhoff plate model

In this paper, we consider a mechanical system consisting of a rigid body with a thin elastic plate. The plate vibration is governed by the Kirchhoff plate theory. We derive the equations of motion as a system of ordinary and partial differential equations and consider the angular acceleration as a control parameter. The dynamical equations are transformed into an infinite set of ordinary differential equations with respect to modal coordinates. It is shown that such a system is not controllable in general. Hence, the approximate controllability problem is set out for the dynamics restricted to an invariant manifold. Then sufficient conditions for the approximate controllability are proposed. Simulation results are presented to illustrate the spillover effect.