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An analytic approximate approach for free oscillations of self-excited systems. (English) Zbl 1348.34071

Summary: A new analytic approximate technique for non-linear problems, namely the homotopy analysis method, is employed to propose an approach for free oscillations of self-excited systems. Different from perturbation methods on this topic, this approach does not depend upon any small/large parameters at all and therefore is valid for free oscillations of all self-excited systems. Besides, unlike other analytic techniques, this approach provides us with a convenient way to control the convergence of approximation series and adjust convergence regions when necessary. Two examples are employed to illustrate the validity and flexibility of this approach.

MSC:

34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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