Depending on the speed of rotation, a gyroscopic system may lose or gain stability. The paper characterizes the critical angular velocities at which a conservative gyroscopic system may change from a stable to an unstable state, and vice versa, in terms of the eigenvalues of a high-order matrix pencil. A numerical method for evaluation of all possible candidates for such critical velocities is developed.
Stability Boundaries of a Conservative Gyroscopic System
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Oct. 7, 2001; final revision, Apr. 29, 2002. Associate Editor: O. O’ Reilly. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Department of Mechanical and Environmental Engineering University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Gladwell, G. M. L., Khonsari, M. M., and Ram, Y. M. (August 25, 2003). "Stability Boundaries of a Conservative Gyroscopic System ." ASME. J. Appl. Mech. July 2003; 70(4): 561–567. https://doi.org/10.1115/1.1574062
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