On controllability of a rotating string

We consider the problem of controllability of a rotating string. We say that a set of initial data of the string is controllable if, for any initial data of this set by suitable manipulation of the exterior force, the string goes to rest. The main result of the paper is a description of controllable sets of initial data. The equation is not strongly hyperbolic. To get exact controllability of such equation in the sharp time interval, we use control functions from Sobolev spaces with noninteger indices. To prove our results, we apply the method of moments that has been widely used in control theory of distributed parameter systems since the classical papers of H.O. Fattorini and D.L. Russell. We use recent results about exponential bases in Sobolev spaces with noninteger indices.