MACSYMA Program to Implement Averaging Using Elliptic Functions

  • Vincent T. Coppola
  • Richard H. Rand
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 28)


The method of averaging is applied to the system:
$$ x'' + \alpha (\tau )x + \beta (\tau ){x^3} + \in g(x,x',\tau ) = 0 $$
where τ = ∈t is slow time, and where ∈ << 1. This involves the laborous manipulation of Jacobian elliptic functions, a process which is most easily and accurately accomplished using computer algebra. We present the listing of a MACSYMA program which implements the method to 0(), as well as the results of a run for which g(x, x′, τ) is taken as a general cubic polynomial in x and x′.


Nonlinear Oscillator Elliptic Function Computer Algebra Order Average Simple Harmonic Oscillator 
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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Copyright information

© Springer-Verlag New York Inc. 1991

Authors and Affiliations

  • Vincent T. Coppola
    • 1
  • Richard H. Rand
    • 1
  1. 1.Department of Theoretical and Applied MechanicsCornell UniversityIthacaUSA

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