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Solution of the Duffing Equation

  • George Adomian
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 60)

Abstract

Consider the Duffing equation with variable excitation and constant coefficients α, β, γ
$$\begin{gathered} {\text{u''}} + \alpha u' + \beta u + \gamma {u^3} = \delta (t) \hfill \\ u(0) = {c_0}{\text{ u'(0) = }}{{\text{c}}_1} \hfill \\ \end{gathered} % MathType!End!2!1! $$
δ(t) will be written as a series δ(t) = Σ n=0 δntn. Let L = d2/dt2. Then L−1 will be the two-fold integration from 0 to t.

Keywords

Excitation Frequency White Noise Excitation Decomposition Solution DUFFING Equation Sine Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Suggested Reading

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    A. Blaquière, Nonlinear System Analysis, Academic Press (1988).Google Scholar
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    J. Hale, Oscillations in Nonlinear Systems, McGraw-Hill (1963).Google Scholar
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    C. Hyashi, Nonlinear Oscillations in Physical Systems, McGraw-Hill (1964).Google Scholar
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    G. Duffing, Erzwungene Schwingungen bei Veränderlicher Eigenfrequenz und ihre technische Bedeutung, Vieweg (1918).Google Scholar
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    Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations,Springer-Verlag (1983).Google Scholar
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    K. Kreith, Oscillation Theory, Springer-Verlag (1973).Google Scholar
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    P. Hagedorn, Nonlinear Oscillations, 2nd ed., Clarendon (1988).Google Scholar
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    J. D. Cole, Perturbation Methods in Applied Mathematics, Blaisdell (1968).Google Scholar
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    A. A. Andronov, A. A. Vitt, and S. E. Khaikin, F. Immirzi, transl., Theory of Oscillators, Addison-Wesley (1966).Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • George Adomian
    • 1
  1. 1.General Analytics CorporationAthensUSA

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