On a Special Class of Self-Sustained Oscillations

[+] Author and Article Information
K. Klotter

Stanford University, Stanford, Calif.

E. Kreyszig

Ohio State University, Columbus, Ohio

J. Appl. Mech 27(3), 568-574 (Sep 01, 1960) (7 pages) doi:10.1115/1.3644042 History: Received June 18, 1959; Online September 16, 2011


This paper deals with the “modified van der Pol differential equations” q̈ − (sgn q̇) (δ/2)q̇2 h(q) + κ2 f(q) = 0, where h(q) and f(q) are suitable functions. It is shown that there exists a unique limit cycle. For the limit amplitude both lower and upper bounds are established in the case of unrestricted values δ. For small values δ the limit amplitude can be calculated immediately.

Copyright © 1960 by ASME
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