The Poincaré method for an oscillator with quadratic nonlinearity

Abstract

In [2], to evaluate free oscillation period of an undamped oscillator with large cubic restoring nonlinearity, a modified Poincare method has been proposed. There, in the neighborhood of the free oscillation of interest, the strongly nonlinear system under consideration is assumed to be near certain linear one with unknown (to be evaluated) frequency.

In the present paper, we deal with the case of quadratic non-linearity. An additional modification is introduced consisting in the elimination of constant derivation and second harmonic terms. The results obtained show that the domain of application of the Poincare method can be enlarged.