摘要
研究广义Birkhoff系统的平衡稳定性问题.建立了自治广义Birkhoff系统的平衡方程;给出了自治广义Birkhoff系统的一次近似方程,利用Lyapunov一次近似理论,建立了系统平衡状态稳定性的判据;构建了Lyapunov函数,利用Lyapunov直接法,建立了自治广义Birkhoff系统平衡状态稳定性的判据.给出了若干算例以说明结果的应用.
The stability problem of equilibrium for a generalized Birkhoffian system is studied. The equations ot equilibrium tor the autonomous generalized Birkhoffian system are established. The equations of first approximation of the system are given, and the criterion of stability for equilibrium state of the system is established by using the Liapunov＇s first approximation theory. The Liapunov＇s function is constructed, and the criterion of stability for equilibrium state of the system is established by using the Liapunov＇s direct method. Some examples are given to illustrate the application of the results.
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2010年第1期20-24,共5页
Acta Physica Sinica
基金
国家自然科学基金(批准号:10972151)
江苏省高校自然科学基金(批准号:08KJB130002)资助的课题~~
关键词
广义BIRKHOFF系统
平衡稳定性
一次近似法
直接法
generalized Birkhoffian system, stability of equilibrium, first approximation method, direct method
