A method of analysis is developed for studying the whirl stability of rotor-bearing systems without the need to solve the governing differential-equations of motion of such systems. A mathematical model, comprised of an axially-symmetric appendage at the mid-span of a spinning shaft mounted on two dissimilar eight-coefficient bearings, is used to illustrate the method. Sufficient conditions for asymptotic stability of both the translational and rotational modes of motion of the system have been derived. The system's stability boundaries, ...