Stabilization of a rotating geometrically exact rod

The problem of stabilization of the uniform rotation of a geometrically exact rod is investigated. A three dimensional, geometrically exact rod model including shear, extension, torsion and flexure is stabilized by means of a feedback torque applied to the boundary. The energy-momentum method of stability analysis is used as the basis of the feedback control design. The result shows that there exist critical rotation rates associated with the internal vibrations which cannot be removed by torque feedback. An example is presented for the case of uniform axial rotation