Dynamics of Non-Rigid Molecules: The Exploration of Phase Space Via Resonant and Sub-Resonant Coupling
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In systems of non-linear coupled oscillators, it is possible to specify initial distributions of excitation energy that cause the zero order frequencies of the oscillators to be in resonance. In the presence of coupling, these resonances mediate the exchange of energy between the zero order modes. The magnitude of this energy exchange is a measure of the width of the resonance. We show that for higher order resonances there exist sub-resonances that in other parts of phase space correspond to lower order resonances. These sub-resonances provide a mechanism for large amplitude, high frequency oscillatory excursions in phase space. They also induce sub-resonant modulation of the resonance widths. To analyse the dynamics of coupled non-linear oscillators, conventional methods typically treat the coupling as a small perturbation and“average”over rapidly oscillating non-resonant terms. This averaging neglects the effect of the sub-resonances which, for physically realistic couplings can have amplitudes as large or larger than the resonance. We discuss an alternative approach for the perturba-tive analysis of coupled non-linear oscillators designed to incorporate the effect of sub-resonances on the dynamics. We then show that for small values of coupling when first order perturbation theory is valid, the sub-resonances lead to new, nearly separable modes. However, for large coupling, sub-resonant effects cannot be transformed away and dominate phase space dynamics.
KeywordsAction Space Resonance Width Resonance Centre Fourier Series Expansion Resonance Surface
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