In this paper we use the Birkhoff-Gustavson perturbation theory to analyze the vibrational modes of two linearly coupled Morse oscillators in the transition region from normal modes to local modes. Our study is based on: truncation of the Hamiltonian written in normal mode coordinates at the 4th order, transformation to normal form and analytical study; construction and use of the approximate integrals of motion of the exact Hamiltonian according to Birkhoff and Gustavson theory. By comparison with a previous analytical study, we demonstrate that perturbation theory, based either on local or normal modes can be used to accurately describe transition modes.
Characterization of Vibrational transition modes by use of normal form
ABBATE, Sergio;LONGHI, Giovanna
1993-01-01
Abstract
In this paper we use the Birkhoff-Gustavson perturbation theory to analyze the vibrational modes of two linearly coupled Morse oscillators in the transition region from normal modes to local modes. Our study is based on: truncation of the Hamiltonian written in normal mode coordinates at the 4th order, transformation to normal form and analytical study; construction and use of the approximate integrals of motion of the exact Hamiltonian according to Birkhoff and Gustavson theory. By comparison with a previous analytical study, we demonstrate that perturbation theory, based either on local or normal modes can be used to accurately describe transition modes.File | Dimensione | Formato | |
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