ORIENTATION AND STABILIZATION OF A FLEXIBLE BEAM ATTACHED TO A RIGID BODY - PLANAR MOTION

We consider a flexible structure modeled as a rigid body which rotates in inertial space; a light flexible beam is clamped to the rigid body at one end and free at the other. We assume that the flexible beam perform only planar motion. The equations of motion are obtained by using free body diagrams. We pose two control problems, namely, the orientation and stabilization of the system. It is shown that suitable boundary controls applied to the free end of the beam and suitable control torques applied to the rigid body solve the problems posed above. The proofs are obtained by using the energy of the system as a Lyapunov functional.