Equivalence of the generalized Lie-Hori method and the method of averaging

Details Equivalence of the generalized Lie-Hori method and the method of averaging Equivalence of the generalized Lie-Hori method and the method of averaging

May 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984cemec..33....1a&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 33, May 1984, p. 1-20.

Mathematics

Celestial Mechanics, Lie Groups, Perturbation Theory, Average, Canonical Forms, Equivalence, Orbit Calculation, Periodic Functions, Transformations (Mathematics)

Scientific paper

In this investigation, a comparison is made of two methods for developing perturbation theories for non-canonical dynamical systems. The methods compared are the generalized Lie-Hori method and the method of averaging. In the comparison presented here, the equivalence of the methods up to the second order in the small parameter is shown. However, the approach used can be extended to demonstrate the equivalence for higher orders. To illustrate the equivalence Duffing's equation, the van der Pol equation and the oscillator with quadratic damping problem are solved using each method.

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