Uniform Expansions of Periodic Solutions for the Third Superharmonic Resonance View Full Text


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Article Info

DATE

2004-08

AUTHORS

Ivan S. Gandzha, Vasyl P. Lukomsky

ABSTRACT

A new method of uniform expansions of periodic solutions to ordinary differential equations has recently been proposed to study quasi-harmonic processes in non-linear dynamical systems, in particular, when a small parameter of non-linearity is absent. The main idea of the method consists in using the ratio of the amplitudes of higher harmonics to the amplitude of the first harmonic of a periodic solution as a small formal parameter that appears due to descending the amplitudes of harmonics monotonically with increasing their number (this is the condition that the term ‘quasi-harmonic’ implies). In this paper, the method is generalized for the third superharmonic resonance (when the first and the third harmonics become of the same magnitude) in a harmonically forced oscillator with arbitrary odd polynomial non-linearity. More... »

PAGES

171-179

Journal

TITLE

Nonlinear Dynamics

ISSUE

3

VOLUME

37

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1023/b:nody.0000044679.09631.bf

DOI

http://dx.doi.org/10.1023/b:nody.0000044679.09631.bf

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1047637503


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