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Strongly non-linear oscillators with slowly varying parameters

โœ Scribed by Jianping Cai; Y.P Li

Book ID
104030951
Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
260 KB
Volume
275
Category
Article
ISSN
0022-460X

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โœฆ Synopsis

A multiple scales method, which gives the approximate solution in terms of elliptic functions, is used for the study of strongly non-linear oscillators with slowly varying parameters. As an application, quadratic and cubic non-linear oscillators are studied in detail. Two examples are considered: a generalized Van der Pol oscillator and a pendulum with variable length. Comparisons are also made with numerical results to show the efficiency of the present method.

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A non-linear scales method is presented for the analysis of strongly non-linear oscillators of the form Y: + g(x) = ef (x, d:), where g(x) is an arbitrary non-linear function of the displacement x. We assumed that x(t,~) x0(~,,7) + m-, m T~ = ~,~=~ e'~xn(~) + O(e'~), where d~/dt = ~,~=1 e'~R~(~) , d