PERIODIC-SOLUTIONS OF STRONGLY NONLINEAR MATHIEU OSCILLATORS

The purpose of this paper is to continue our investigation into period ic solutions of strongly non-linear Mathieu oscillators. The modified version of the generalized averaging method which we developed recentl y is applied to derive highly accurate analytical expressions for thes e periodic solutions. These analytical results are used, together with the perturbation methods of multiple time scaling, to obtain second o rder expressions for the stability regions of these periodic solutions . The analytical research results are verified with numerical computat ions. Very good agreement is found, which shows the applicability of t he modified version of the generalized averaging method to this kind o f strongly non-linear oscillators. These oscillators may be used to mo del the beam-beam interaction in particle accelerators. (C) 1997 Elsev ier Science Ltd.