Semi-Resonant Interactions and Frequency Dividers

M. J. Ablowitz, B. A. Funk, Alan C Newell

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

A theory describing the behavior of a system as it evolves slowly through internal nonlinear resonances is presented. The energy sharing process is seen to be quite complex as it depends crucially on both nonlinear and frequency detuning effects. Two phenomena are discussed in detail although the general ideas are applicable to many situations. Firstly we examine the interaction between the quadratically coupled oscillators whose natural frequencies are in the ratio 2:1 for a limited period of time. Such a system is shown to be an extremely useful switching device. Secondly we examine the time dependent Duffing equation and find that smooth forward and reverse transitions occur without the presence of dissipation.

Original languageEnglish (US)
Pages (from-to)51-74
Number of pages24
JournalStudies in Applied Mathematics
Volume52
Issue number1
DOIs
StatePublished - Mar 1 1973
Externally publishedYes

Fingerprint

Natural frequencies
Nonlinear Resonance
Internal Resonance
Duffing Equation
Coupled Oscillators
Natural Frequency
Period of time
Interaction
Dissipation
Reverse
Sharing
Energy

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Semi-Resonant Interactions and Frequency Dividers. / Ablowitz, M. J.; Funk, B. A.; Newell, Alan C.

In: Studies in Applied Mathematics, Vol. 52, No. 1, 01.03.1973, p. 51-74.

Research output: Contribution to journalArticle

Ablowitz, M. J. ; Funk, B. A. ; Newell, Alan C. / Semi-Resonant Interactions and Frequency Dividers. In: Studies in Applied Mathematics. 1973 ; Vol. 52, No. 1. pp. 51-74.
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