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Analysis of Nonlinear Systems by Truncated Point Mappings

[+] Author and Article Information
Ramesh S. Guttalu, Henryk Flashner

Department of Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453, USA

Appl. Mech. Rev 42(11S), S83-S92 (Nov 01, 1989) doi:10.1115/1.3152412 History: Online June 03, 2009

Abstract

This paper summarizes results obtained by the authors regarding the utility of truncated point mappings which have been recently published in a series of papers. The method described here is applicable to the analysis of multidimensional, multiparameter, periodic nonlinear systems by means of truncated point mappings. Based on multinomial truncation, an explicit analytical expression is determined for the point mapping in terms of the states and parameters of the system to any order of approximation. By combining this approach with analytical techniques, such as the perturbation method employed here, we obtain a powerful tool for finding periodic solutions and for analyzing their stability. The versatility of truncated point mapping method is demonstrated by applying it to study the limit cycles of van der Pol and coupled van der Pol oscillators, the periodic solutions of the forced Duffing’s equation and for a parametric analysis of periodic solutions of Mathieu’s equation.

Copyright © 1989 by The American Society of Mechanical Engineers
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