This paper discusses the vibration phenomena of a rotor rubbing with a stator caused by an initial perturbation. The analytical model consists of a simple disc-shaft rotor and a fixed stator. The perturbation is an instantaneous change of the radial velocity when the rotor is rotating in its normal steady state. It is found that under certain conditions, the rotor will remain rubbing with the stator, even if the initial perturbation no longer exists. In the case of no friction on the contact surface between the rotor and the stator, the full rubbing behaves as forward whirling. When friction is present, the full rubbing behaves as backward whirling.