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Time-frequency analysis of classical trajectories of polyatomic molecules

Vela-Arevalo, Luz V. and Wiggins, Stephen (2001) Time-frequency analysis of classical trajectories of polyatomic molecules. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 11 (5). pp. 1359-1380. ISSN 0218-1274. https://resolver.caltech.edu/CaltechAUTHORS:20170408-162326245

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Abstract

We present a new method of frequency analysis for Hamiltonian Systems of 3 degrees of freedom and more. The method is based on the concept of instantaneous frequency extracted numerically from the continuous wavelet transform of the trajectories. Knowing the time-evolution of the frequencies of a given trajectory, we can define a frequency map, resonances, and diffusion in frequency space as an indication of chaos. The time-frequency analysis method is applied to the Baggott Hamiltonian to characterize the global dynamics and the structure of the phase space in terms of resonance channels. This 3-degree-of-freedom system results from the classical version of the quantum Hamiltonian for the water molecule given by Baggott [1988]. Since another first integral of the motion exists, the so-called Polyad number, the system can be reduced to 2 degrees of freedom. The dynamics is therefore simplified and we give a complete characterization of the phase space, and at the same time we could validate the results of the time-frequency analysis.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1142/S0218127401002766DOIArticle
Additional Information:© 2001 World Scientific Publishing Co. Received June 20, 2000; Revised July 25, 2000. This research was partially supported by Consejo Nacional de Ciencia y Tecnologia (CONACYT México); and by the National Science Foundation Grant DMS-9704759.
Funders:
Funding AgencyGrant Number
Consejo Nacional de Ciencia y Tecnología (CONACYT)UNSPECIFIED
NSFDMS-9704759
Issue or Number:5
Record Number:CaltechAUTHORS:20170408-162326245
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170408-162326245
Official Citation:TIME-FREQUENCY ANALYSIS OF CLASSICAL TRAJECTORIES OF POLYATOMIC MOLECULES LUZ V. VELA-AREVALO and STEPHEN WIGGINS International Journal of Bifurcation and Chaos 2001 11:05, 1359-1380
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76175
Collection:CaltechAUTHORS
Deposited By: 1Science Import
Deposited On:09 Aug 2017 21:12
Last Modified:03 Oct 2019 16:58

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