A Study of Coupled Mathieu Equations by Use of Infinite Determinants

[+] Author and Article Information
Ti-Chiang Lee

Aeronautical Research Laboratory, Taichung, Taiwan, Republic of China

J. Appl. Mech 43(2), 349-352 (Jun 01, 1976) (4 pages) doi:10.1115/1.3423838 History: Received February 01, 1975; Revised September 01, 1975; Online July 12, 2010


Hill’s method of infinite determinant is applied to solving a system of Mathieu-type equations. Expansion of the converging infinite determinant then leads to the criterion for stability of the solution. Numerical results are then presented in graphs for two examples. Good agreements between the present results and the existing solutions are observed. The criterion therefore is useful to predict the stability properties of a finite number of coupled Mathieu equations.

Copyright © 1976 by ASME
Topics: Equations , Stability
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