Dai, Shiqiang Asymptotic analysis of strongly nonlinear oscillators. (English) Zbl 0585.34039 Appl. Math. Mech., Engl. Ed. 6, 409-415 (1985). In the paper the asymptotic method is applied for the analysis of a strongly nonlinear autonomous oscillator characterised by the differential equation \(\ddot u+g(u)=\epsilon f(u,\dot u)\) with a small parameter \(\epsilon >0\). The equations for the amplitude and phase factor are obtained and the amplitude and stability of the corresponding limit cycles are determined. Reviewer: J.Mika Cited in 1 ReviewCited in 4 Documents MSC: 34E15 Singular perturbations for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 34C29 Averaging method for ordinary differential equations 34D15 Singular perturbations of ordinary differential equations Keywords:second order differential equation; strongly nonlinear autonomous oscillator; phase factor; limit cycles PDFBibTeX XMLCite \textit{S. Dai}, Appl. Math. Mech., Engl. Ed. 6, 409--415 (1985; Zbl 0585.34039) Full Text: DOI References: [1] Chien Wei-zang (ed.),Singular Perturbation Theory and Its Applications in Mechanics, Science Press, Beijing (1981). (in Chinese). [2] Kevorkian, J. and J. D. Cole,Perturbation Methods in Applied Mathematics, Springer-Verlag, New York (1981). · Zbl 0456.34001 [3] Kuzmak, G. E., Asymptotic solutions of nonlinear second order diffential equations with variable cofficients,PMM (USSR),23 (1959), 515–526 (in Russian) [4] Luke, J. C., A perturbation method for nonlinear dispersive wave problems,Proc. Roy. Soc. Ser. A292 (1966), 403–412. · Zbl 0143.13603 · doi:10.1098/rspa.1966.0142 [5] Whitham, G. B.,Linear and Nonlinear Waves, John Wiley & Sons, Inc., New York (1974). · Zbl 0373.76001 [6] Burton, T. D., Non-linear oscillator limit cycle analysis using a time transformation approach,Int. J. Non-Linear Mech.,17 (1982), 7–19. · Zbl 0499.70031 · doi:10.1016/0020-7462(82)90033-6 [7] Bogoliubov, N. N. and Y. A. Mitropolsky,Asymptotic Methods in the Theory of Nonlinear Oscillations, 4th Ed., ”Nauka” Press, Moscow (1974). (in Russian). [8] Byrd, P. F. and M. D. Friedman,Handbook of Elliptic Integrals for Engineers and Scientists, 2nd Ed., Springer-Verlag, New York (1971). · Zbl 0213.16602 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.