Comments on Stability Properties of Conservative Gyroscopic Systems

[+] Author and Article Information
P. Lancaster

Department of Mathematics and Statistics, The University of Calgary, Calgary, Alberta, T2N 1N4 Canada

W. Kliem

Department of Mathematics, Technical University of Denmark, DK-2800 Lyngby, Denmark

J. Appl. Mech 66(1), 272-273 (Mar 01, 1999) (2 pages) doi:10.1115/1.2789160 History: Received August 27, 1997; Revised December 10, 1997; Online October 25, 2007


A conjecture of Renshaw and Mote concerning gyroscopic systems with parameters predicts the eigenvalue locus in the neighborhood of a double-zero eigenvalue. In the present paper, this conjecture is reformulated in the language of generalized eigenvectors, angular splitting, and analytic behavior of eigenvalues. Two counter-examples for systems of dimension two show that the conjecture is not generally true. Finally, splitting or analytic behavior of eigenvalues is characterized in terms of expansion of the eigenvalues in fractional powers of the parameter.

Copyright © 1999 by The American Society of Mechanical Engineers
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