Solution of the Duffing Equation

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


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.


Excitation Frequency White Noise Excitation Decomposition Solution DUFFING Equation Sine Series 
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Suggested Reading

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    A. Blaquière, Nonlinear System Analysis, Academic Press (1988).Google Scholar
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Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

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

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