摘要
Mathieu方程x^+(δ+2εcos2t)x=0是重要的参数激振问题非线性微分方程,其稳定特性分析是研究中的一个重要问题.抛开以往约束参数法和Hill无限行列式法,提出了确定稳定区域的精确的数值分析方法,并经过计算研究,给出了该方程的精确的稳定区域.获得了与以往分析结果不同的更为符合真实问题的解.同时,给出了稳定和不稳定两种情况的响应和相图.
Mathieu equation x + (δ + 2εcos2t)x = 0 is parameter vibration differential equation. Its stability analysis is important question. In this paper, a new numerical method is studied. Comparing with constrain parameter method and Hill unlimited determinant method, this method is used to compute correct result. Stable and unstable zone are well decided, and stable demonstrating figures are given. Respond and phase diagram are showed.
出处
《辽宁大学学报（自然科学版）》
CAS
2004年第1期31-33,共3页
Journal of Liaoning University：Natural Sciences Edition
