Undesired vibrations due to mechanical imbalance is an inevitable phenomenon related to high speed rotating systems. In the absence of radial asymmetry, the steady state response of the rotor can be represented as a synchronous forward circular whirling motion. In this motion, the mass elements of the rotor do not carry relative accelerations since they all orbit in a circular motion of a constant radius and identical frequency. Therefore, in these steady state conditions, the flexible rotor can be regarded as a rigid rotor. Motivated by this observation, a rigid body analysis is utilized in order to derive a set of constraint relations that are required for inertial centering, namely, for a rotation about the rotor's center of mass and its principal axis. In order to force the existence of the inertial centering constraints, the shaft is supported by a set of active magnetic bearings (AMBs), and a suitable control system is developed. The performances of the developed controller are demonstrated via numerical simulations.