An Elliptic Lindstedt-Poincaré Method for Certain Strongly Non-Linear Oscillators

Nonlinear Dynamics

Volumn 12, Issue 3, 1997, Pages 199-213

  Chen, S H ^a   Cheung, Y K ^b  

^a SUN YAT SEN UNIVERSITY   (China)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Elliptic functions; L P method; Strongly non linear oscillators

Indexed keywords

DIFFERENTIAL EQUATIONS; DYNAMICS; HARMONIC ANALYSIS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; PERTURBATION TECHNIQUES;

ELLIPTIC FUNCTIONS; LINDSTEDT-POINCARE METHOD; MULTIPLE TIME SCALES (MTS) METHODS; VAN DER POL EQUATION;

NONLINEAR SYSTEMS;

EID: 0031095817     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008267817248     Document Type: Article

References (13)

1. Nayfeh, A. H., Introduction to Perturbation Techniques, Wiley, New York, 1981.
2. Mickens, R. E., Nonlinear Oscillations, Cambridge University Press, New York, 1981.
3. Mickens, R. E. and Oyedeji, K., 'Construction of approximate analytical solutions to a new class of non-linear oscillator equation', Journal of Sound and Vibration 102, 1985, 579-582.
4. Yuste, S. B. and Bejarano, J. D., 'Construction of approximate analytical solutions to a new class of non-linear oscillator equations', Journal of Sound and Vibration 110, 1986, 347-350.
5. Margallo, J. G., Bejarano, J. D. and Yuste, S. B., 'Generalized Fourier series for the study of limit cycles', Journal of Sound and Vibration 125, 1988, 13-21.
6. Margallo, J. G. and Bejarano, J. D., 'Generalized Fourier series and limit cycles of generalized Van der Pol oscillators', Journal of Sound and Vibration 136, 1990, 453-466.
7. Yuste, S. B. and Bejarano, J. D., 'Extension and improvement to the Krylov-Bogoliubov methods using elliptic functions', International Journal of Control 49, 1989, 1127-1141.
8. Coppola, V. T. and Rand, R. H., 'Averaging using elliptic functions: Approximations of limit cycle', Acta Mechanica 81, 1990, 125-142.
9. Chen, S. H. and Cheung, Y. K., 'An elliptic-perturbation method for certain strongly non-linear oscillators', Journal of Sound and Vibration, to be published.
10. Kuzmak, G. E., 'Asymptotic solutions of nonlinear second order differential equations with variable coefficients', Journal of Applied Mathematics and Mechanics 23, 1959, 730-744.
11. Kevorkian, J. and Cole, J. D., 'Perturbation methods in applied mathematics', in Applied Mathematical Sciences, Vol. 34, Springer-Verlag, New York, 1981.
12. Byrd, P. F. and Friedman, M. D., Handbook of Elliptic Integrals for Engineers and Physicists, Springer-Verlag, Berlin, 1954.
13. Nayfeh, A. H. and Mook, D. T., Nonlinear Oscillations, Wiley, New York, 1979.