Hostname: page-component-7b7567c8c-jswmv Total loading time: 0 Render date: 2026-11-15T20:48:00.040Z Has data issue: false hasContentIssue false
  • English
  • Français

A uniform description of an oscillator's resonant transition

Published online by Cambridge University Press:  17 February 2009

P. B. Chapman
P. B. Chapman
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, WA 6009.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

A uniform approximation to the description of a linear oscillator's slow resonant transition is calculated. If the time scale of the transition is ɛ−1, the approximation contains explicitly the 0(1) and 0(ɛ½) terms, and fixes a uniform 0(ɛ) error bound.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 32 , Issue 2 , October 1990, pp. 193 - 206
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Chapman, P. B. and Mahony, J. J., “Reflection of waves in a slowly varying medium”, SIAM J. Appl. Math. 34 (1978) 303–319.CrossRefGoogle Scholar
[2], H. and Jeffreys, B. S., Mathematical physics. 3rd Edition (University Press, Cambridge, 1956).Google Scholar
[3]Kevorkian, J., “Perturbation techniques for oscillatory systems with slowly varying coefficients”, SIAM Review 29 (1987) 391–460.CrossRefGoogle Scholar
[4]Krylov, N. and Bogoliubov, N. N., Introduction to nonlinear mechanics (Princeton University Press, Princeton, N. J. 1947).Google Scholar
[5]Olver, F. W. J., Asymptotics and special functions (Academic Press, N.Y., 1974).Google Scholar