Ullrich conditions and smoothness of reachable states of a rotating beam

We consider a Timoshenko beam slowly rotating in a horizontal plane. For this model we study the problem of description of all states reachable from a position of rest. This problem is equivalent to a non-Fourier trigonometric problem with respect to a system with two asymptotically close families of exponentials. Technically such a problem can be analyzed in terms of divided differences of the moment sequences. It turns out however that the set of reachable states admits an essentially more convenient analytical description in terms of smoothness of final states.