Some stability results in the theory of whirling

The whirling motion of a fixed-free viscoelastic shaft, whose model is based on the spring and dashpot (Kelvin element), is considered. We develop a precise determination of the system's stability by first obtaining its eigenvalues. It is shown that asymptotic stability exists as long as the angular speed of the shaft is below a certain critical value. On the other hand, the degree of stability first increases as the speed is increased but eventually decreases again.