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Internal Resonances in Weakly Nonlinearly Coupled Oscillators with Slowly Varying Parameters
Author(s) -
Shivamoggi B. K.
Publication year - 1987
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19870670106
Subject(s) - physics , coupling (piping) , adiabatic process , resonance (particle physics) , nonlinear system , classical mechanics , statistical physics , quantum mechanics , engineering , mechanical engineering
The present paper considers the problem of internal resonances in a system of two linear oscillators which are weakly nonlinearly coupled. The system parameters such as the uncoupled frequencies of the oscillators vary slowly in time so that internal resonances prevail only temporarily. One issue of interest in such problems is how the presence of nonlinear coupling affects the adiabatic invariance of the individual actions of the two oscillators. The purpose of this paper is to give a method to investigate this issue quite generally, without assuming special forms of temporal variations of the uncoupled frequencies of the two oscillators and without considering the details of the transition region corresponding to an internal resonance.