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# MACSYMA Program to Implement Averaging Using Elliptic Functions

Chapter

## Abstract

The method of averaging is applied to the system: where τ =

$$ x'' + \alpha (\tau )x + \beta (\tau ){x^3} + \in g(x,x',\tau ) = 0 $$

*∈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′.*## Keywords

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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© Springer-Verlag New York Inc. 1991