Nonlinear oscillations of a triatomic molecule

Abstract

ude decreases if the difference of the frequency of the two modes is reduced. We consider the simplest case of a symmetric rectilinear molecule where the coupling has a cubic nonlinearity in addition to a linear restoring force. Approximate analytical results are in good agreement with numerical simulations of the exact equations of motion, although in some cases the actual behavior fundamentally deviates from the perturbative theory. Two physical demonstrations of the instability are described, where the apparatus are a system of gliders coupled by springs and magnets on an air track. Possible quantum mechanical implications are discussed. This work is a fundamental generalization of the parametric instability of two linearly coupled nonlinear oscillators that was reported in a previous investigation.