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Periodic solutions of strongly quadratic non-linear oscillators by the elliptic Lindstedt-Poincaré method. (English) Zbl 1235.70110
Summary: The elliptic Lindstedt-Poincaré method is used to study the periodic solutions of quadratic strongly nonlinear oscillators of the form x ¨+c 1 x+c 2 x 2 =ϵf(x,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,x ˙)=μ 0 +μ 1 x-μ 2 x 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:
70K42Equilibria and periodic trajectories (nonlinear dynamics)
70K60General perturbation schemes (nonlinear dynamics)
34C25Periodic solutions of ODE