Oscillators in resonance p:q:r

M. Arribas, A. Elipe, L. Floría and A. Riaguas

Chaos, Solitons & Fractals, 2006, vol. 27, issue 5, 1220-1228

Abstract: A canonical transformation is proposed to handle Hamiltonian systems made of the addition or subtraction of three harmonic oscillators in p:q:r resonance. This transformation is an extension of the classical Lissajous transformation for the 1:1 resonance. Our extended Lissajous variables consist of three pairs of action-angle variables, which makes possible the application of perturbation theories without encountering small divisors. A set of functions, related with the Lissajous variables, are found, and are used to describe the phase flow of reduced space after normalization.

Date: 2006
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:27:y:2006:i:5:p:1220-1228

DOI: 10.1016/j.chaos.2005.04.085

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