A MODIFIED LINDSTEDT-POINCARE METHOD FOR CERTAIN STRONGLY NONLINEAR OSCILLATORS

A modified Lindstedt-Poincare' method is presented for extending the range of the validity of perturbation expansions to strongly non-linear oscillation of single degree-of-freedom systems. A new parameter alpha = alpha-(epsilon), which differs from Jones' and Burton's, is defined such that the value of alpha is always kept small regardless of the magnitude of the original parameter epsilon. Therefore, a strongly non-linear system with large parameter epsilon is transformed into a small parameter system with respect to alpha. This method is suitable for the system with even non-linearities as well as with odd non-linearities.