Periodic solutions of strongly non-linear Mathieu oscillators |
| |
Authors: | Gamal M Mahmoud |
| |
Institution: | Department of Mathematics, Faculty of Science, University of Assiut, Assiut 71516, Egypt |
| |
Abstract: | The purpose of this paper is to continue our investigation into periodic solutions of strongly non-linear Mathieu oscillators. The modified version of the generalized averaging method which we developed recently is applied to derive highly accurate analytical expressions for these periodic solutions. These analytical results are used, together with the perturbation methods of multiple time scaling, to obtain second order expressions for the stability regions of these periodic solutions. The analytical research results are verified with numerical computations. Very good agreement is found, which shows the applicability of the modified version of the generalized averaging method to this kind of strongly non-linear oscillators. These oscillators may be used to model the beam-beam interaction in particle accelerators. |
| |
Keywords: | strongly non-linear Mathieu oscillators periodic solutions stability frequency |
本文献已被 ScienceDirect 等数据库收录! |
|