Nonlinear normal modes for the Toda Chain

W. E. Ferguson, Hermann Flaschka, D. W. McLaughlin

Research output: Contribution to journalArticle

74 Citations (Scopus)

Abstract

The Toda Chain is a nonlinear mass-spring chain which can in principle be integrated analytically by the action-angle theory of classical mechanics. We show that the transformation from physical variables to action variables can be implemented very simply on a computer. We study the correspondence between action variables and the motions of the chain, and find the role of the action variables to be very similar to the role of normal-mode amplitudes in the harmonic chain. This similarity leads to a partly rigorous, partly heuristic normal-mode analysis for the Toda chain. New results are obtained when this normal-mode analysis is applied to certain perturbations of the Toda chain such as the Fermi-Pasta-Ulam chain or the Toda chain with a mass impurity.

Original languageEnglish (US)
Pages (from-to)157-209
Number of pages53
JournalJournal of Computational Physics
Volume45
Issue number2
DOIs
StatePublished - 1982

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Mechanics
Impurities
classical mechanics
harmonics
perturbation
impurities

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

Nonlinear normal modes for the Toda Chain. / Ferguson, W. E.; Flaschka, Hermann; McLaughlin, D. W.

In: Journal of Computational Physics, Vol. 45, No. 2, 1982, p. 157-209.

Research output: Contribution to journalArticle

Ferguson, W. E. ; Flaschka, Hermann ; McLaughlin, D. W. / Nonlinear normal modes for the Toda Chain. In: Journal of Computational Physics. 1982 ; Vol. 45, No. 2. pp. 157-209.
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