广义Birkhoff系统稳定性对双参数的依赖关系  

Dependance of Stability of Generalized Birkhoff System on Two Parameters

作　　者：陈向炜[1] 曹秋鹏 梅凤翔[3] 

机构地区：[1]商丘师范学院物理与电气信息学院,商丘476000 [2]苏州科技大学数理学院,苏州215009 [3]北京理工大学宇航学院,北京100081

出　　处：《力学季刊》2017年第1期108-112,共5页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(11372169;10932002;11272050);河南省自然科学基金(112300410269)

摘　　要：研究双参数对广义Birkhoff系统稳定性的影响.分别给出广义Birkhoff系统和梯度系统的微分方程,得到广义Birkhoff系统转化成梯度系统的条件.在该条件下把广义Birkhoff系统化成梯度系统,利用梯度系统的性质研究了广义Birkhoff系统的稳定性随双参数变化关系.结果表明,随双参数变化广义Birkhoff系统的平衡稳定性可能是稳定的,或渐进稳定的,也可能是不稳定的,在参数平面上划出稳定性区域和不稳定区域.举例说明结果的应用.Dependance of stability of equilibrium of generalized Birkhoff system on two parameters is studied. The differential equations of the generalized Birkhoff system and the gradient system are given respectively, and the conditions for the transformation of the generalized Birkhoff system into a gradient system are obtained. Under the conditions the generalized Birkhoff system is considered as a gradient system, and the characteristic of the gradient system can be used to study the stability and its dependance on two parameters of the system. The results show that the equilibrium stability of the system is likely to be stable, or asymptotically stable, and may be unstable with the change of two parameters. The stability region and unstable region are drawn on the parameter plane. Some examples are given to illustrate the application of the results.

关 键 词：广义BIRKHOFF系统 梯度系统 稳定性 参数平面 

分 类 号：O316[理学—一般力学与力学基础]