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Modified Lindstedt-Poincaré methods for some strongly nonlinear oscillations. II: A new transformation. (English) Zbl 1116.34321
Summary: A modified Lindstedt-Poincaré method is proposed. In this technique, we introduce a new transformation of the independent variable. This transformation will also allow us to avoid the occurrence of secular terms in the perturbation series solution. Some examples are given here to illustrate its effectiveness and convenience. The results show that the obtained approximate solutions are uniformly valid on the whole solution domain, and they are suitable not only for weakly non-linear systems, but also for strongly nonlinear systems.
Part I, cf. ibid. 37, No. 2, 315–320 (2002; Zbl 1116.34320).

34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
70K60 General perturbation schemes for nonlinear problems in mechanics
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
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