On the method of strained parameters and the method of averaging
Author:
D. P. Mason
Journal:
Quart. Appl. Math. 42 (1984), 77-85
MSC:
Primary 34C29
DOI:
https://doi.org/10.1090/qam/736507
MathSciNet review:
736507
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Abstract: The method of multiple scales can be modified to remove remaining undesirable features in the perturbation solution by expanding available parameters in the equation(s) (Veronis [1]). Corresponding modifications to the Lindstedt-Poincaré method of strained parameters and the method of averaging are investigated and illustrated using the Duffing equation. It is found that a solution to the Duffing equation with no secular terms in either the amplitude or the frequency can be obtained simply by expanding the parameter in the equation without making the near-identity transformation of the independent variable associated with the Lindstedt-Poincaré technique.
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N. Krylov and N. N. Bogoliubov, Introduction to nonlinear mechanics, Princton Univ. Press, Princeton, 1947
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- Ali Hasan Nayfeh, Introduction to perturbation techniques, Wiley-Interscience [John Wiley & Sons], New York, 1981. A Wiley-Interscience Publication. MR 597894
G. Veronis, A note on the method of multiple scales, Quart. Appl. Maths. 38, 363–368 (1980)
A. H. Nayfeh, Perturbation methods, Wiley, New York, 1973, pp. 165, 168
N. Krylov and N. N. Bogoliubov, Introduction to nonlinear mechanics, Princton Univ. Press, Princeton, 1947
N. N. Bogoliubov and Y. A. Mitropolsky, Asymptotic methods in the theory of nonlinear oscillations, Gordon and Breach, New York, 1961, p. 412
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A. H. Nayfeh, Introduction to perturbation techniques, Wiley, New York, 1981, pp. 113, 139
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Article copyright:
© Copyright 1984
American Mathematical Society