ON THE GENERALIZED AVERAGING METHOD OF A CLASS OF STRONGLY NONLINEAR FORCED OSCILLATORS

We present a modified version of the generalized averaging method for studying the periodic solutions of a class of strongly nonlinear force d oscillators of the form x + omega2x + epsilonf(x) P(OMEGAt) = 0, whe re f(x) is a nonlinear function of x, P(OMEGAt) is a periodic function of t, epsilon need not be small, and omega is a constant parameter. T his equation can be used to describe, e.g., a pendulum with a vibratin g length or the displacements of colliding particle beams in high ener gy accelerators. The new version is based on defining a new parameter alpha = alpha(epsilon) and a linear transformation of the time. This v ersion is applied for the cases f(x) = x3 and f(x) = x4 with P(OMEGAt) = cost and excellent agreement is found with the results of numerical experiments, for large values of epsilon.