Stationary (near-stationary) modes of the unbalanced rotor rotation in the case of axis vibration with a frequency equal to (close to) the rotational frequency are investigated. Using the approach of vibration mechanics of Prof. Blechman the explanations of the mechanism of vibrational capture (VC) of rotation of an unbalanced rotor are given. The proposed interpretation of the effect allows to understand better the known results. Characteristic features of the mode are formulated. The possibility of occurrence of slow velocity oscillations of the unbalanced rotor is substantiated. For cases when the VC mode is not established, the applicability of the slow motion equation is demonstrated and an expression for the vibrational torque is obtained. This expression is also valid for the mode preceding the occurrence of VC. The effect of vibrational braking of an inertial vibration exciter at start-up is explained by its VC by resonant oscillations of the system. It is shown that self-synchronization of inertial vibration exciters is also a VC. It is demonstrated that practical problems of self-synchronisation of inertial vibroexciters can be solved by the method of VC research.