The linearized ph approximation to the time dependent Reynolds equation is solved simultaneously with the equations of motion for a rotating journal shaft supported by a rigidly mounted bearing sleeve. Given the two bearing parameters Λ=6μωR2paC2 and Ω=MCω2πpaDL a critical operating eccentricity ratio is determined below which the bearing is unstable and above which the bearing is stable. Whirl frequency at the threshold point is computed to be equal to or slightly less than one-half rotor speed.
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J. S. Ausman (1963) studied this question.