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Triad Resonance for Weakly Coupled, Slowly Varying Oscillators
Author(s) -
Grimshaw R.
Publication year - 1987
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/sapm19877711
Subject(s) - explosive material , resonance (particle physics) , singularity , sign (mathematics) , nonlinear system , physics , energy exchange , action (physics) , coupling (piping) , algebraic number , triad (sociology) , normal mode , classical mechanics , interaction model , interaction energy , mathematics , mathematical analysis , quantum mechanics , chemistry , vibration , materials science , computer science , molecule , psychology , world wide web , organic chemistry , atmospheric sciences , psychoanalysis , metallurgy
A dynamical system with weak nonlinearity is considered for the situation when three modes come into resonance. Interaction equations are derived, and various analytical approximations and numerical results obtained. If is found that either the interaction is explosive, when all modes generally grow during the interaction, with the possibility of an algebraic singularity developing, or the interaction is contained, and the modes exchange action during the coupling. The explosive interaction requires both positive‐ and negative‐energy modes to participate, while the contained interaction can accommodate modes with the same‐sign or opposite‐sign energies.