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Zbl 1235.70110
Chen, S.H.; Yang, X.M.; Cheung, Y.K.
Periodic solutions of strongly quadratic non-linear oscillators by the elliptic Lindstedt-Poincaré method. (English)
[J] J. Sound Vib. 227, No. 5, 1109-1118 (1999). ISSN 0022-460X

Summary: The elliptic Lindstedt-Poincaré method is used to study the periodic solutions of quadratic strongly nonlinear oscillators of the form $\ddot x+c_1x+c_2x^2=\epsilon f(x,\dot x)$, in which the Jacobian elliptic functions are employed instead of the usual circular functions in the classical Lindstedt-Poincaré method. The generalized van der Pol equation with $f(x,\dot x)=\mu_0+\mu_1x-\mu_2x^2$ is studied in detail. Comparisons are made with the solutions obtained using the Lindstedt-Poincaré method and the Runge-Kutta method to show the efficiency of the present method.

MSC 2000:: *70K42 Equilibria and periodic trajectories
70K60 General perturbation schemes
34C25 Periodic solutions of ODE

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Zentralblatt MATH Berlin [Germany]