On the Stability of Gyroscopic Systems

[+] Author and Article Information
P. Lancaster, P. Zizler

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

J. Appl. Mech 65(2), 519-522 (Jun 01, 1998) (4 pages) doi:10.1115/1.2789085 History: Received June 17, 1997; Revised September 24, 1997; Online October 25, 2007


Gyroscopic systems considered here have the form Aÿ + Gẏ + Ky = 0 where A, G, K are real n × n matrices with A > O, GT = −G, KT = K, and the stiffness matrix K has some negative eigenvalues; i.e., the equilibrium position is unstable (when G = 0). A new necessary condition for stability is established. It is also shown that gyroscopic systems with K < 0 and G singular are always unstable for G sufficiently large.

Copyright © 1998 by The American Society of Mechanical Engineers
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