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Semi‐Resonant Interactions and Frequency Dividers
Author(s) -
Ablowitz, M. J.,
Funk B. A.,
Newell A. C.
Publication year - 1973
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm197352151
Subject(s) - quadratic growth , duffing equation , nonlinear system , dissipation , physics , natural frequency , control theory (sociology) , energy (signal processing) , process (computing) , mathematics , statistical physics , classical mechanics , mathematical analysis , computer science , quantum mechanics , vibration , control (management) , artificial intelligence , operating system
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.