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- W1969445273 abstract "An analysis of the harmonic solutions of the Duffing equation can be accomplished by means of either the perturbation method or the method of iteration. However, this paper purports to study Duffing’s equation by using the method of van der Pol. In addition to providing an independent derivation of the response curves, this approach leads to a simplified discussion of the stability question. The variational equation takes the form of a Hill’s equation (in fact, the Mathieu equation). Hence, in order to investigate stability by the variational method one must study the boundedness properties of solutions of Mathieu’s equation. This need is obviated by using van der Pol’s method, since, in this case, the stability issue can be decided by applying the method of Andronow and Witt. That is, harmonic solutions are identified with the singular points of a first-order system of ordinary differential equations. Stability is then determined by utilizing Poincar~'s criteria for the classification of singularities of such systems." @default.
- W1969445273 created "2016-06-24" @default.
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- W1969445273 date "1992-09-01" @default.
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- W1969445273 title "An Alternative Analysis of Duffing’s Equation" @default.
- W1969445273 doi "https://doi.org/10.1137/1034088" @default.
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