Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-22T08:45:54.059Z Has data issue: false hasContentIssue false

Perturbations of nonlinear autonomous oscillators

Published online by Cambridge University Press:  17 February 2009

P. B. Chapman
Affiliation:
Mathematics Department, University of Western Australia, Nedlands, 6009, Western Australia.
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 general theory is given for autonomous perturbations of non-linear autonomous second order oscillators. It is found using a multiple scales method. A central part of it requires computation of Fourier coefficients for representation of the underlying oscillations, and these coefficients are found as convergent expansions in a suitable parameter.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Bourland, F. J. and Haberman, R., “Separatrix crossing: Time invariant potentials with dissipation”, SIAM J. Appl Math. 50 (1990) 17161744.CrossRefGoogle Scholar
[2]Bourland, F. J., Haberman, R. and Kath, W., “Averaging methods for the phase shift of arbitrarily perturbed nonlinear oscillators with application to capture”, SIAM J. Appl. Math. 52 (1991) 11501167.CrossRefGoogle Scholar
[3]Guckenheimer, J. and Holmes, P., Nonlinear oscillations, dynamical systems, and bifurcations of vector fields (Springer-Verlag, New York, 1983).CrossRefGoogle Scholar
[4]Kuzmak, G. E., “Asymptotic solutions of second order differential equations with variable coefficients”, P. M. M. J. Appl. Math. Mech. 23 (1959) 730744.CrossRefGoogle Scholar
[5]Meirovitch, L., Methods of analytical dynamics (McGraw-Hill, New York, 1970).Google Scholar
[6]Milne-Thomson, L. M., Theoretical hydrodynamics (Macmillan, London, 1960).Google Scholar
[7]Morse, P. M. and Feshbach, H., Methods of theoretical physics, Volume 1 (McGraw-Hill, New York, 1953).Google Scholar
[8]Nayfeh, A., Perturbation methods (Wiley, New York, 1973).Google Scholar
[9]Nekrasov, A. I., “On waves of permanent type”, Izv. Ivanov-Vosnosonk. Politehn. Inst. 6 (1922) 155171.Google Scholar
[10]Whittaker, E. T. and Watson, G. N., Modern analysis, 4th ed. (The University Press, Cambridge, 1958).Google Scholar