约束自治广义Birkhoff系统平衡稳定性的梯度系统方法

Stability of equilibrium for autonomous generalized Birkhoffian system with constraints by gradient system

摘要: 建立约束自治广义Birkhoff系统的微分方程.给出约束自治广义Birkhoff系统转化为梯度系统的条件.利用梯度系统的特性来研究约束自治广义Birkhoff系统的稳定性.最后举例说明结果的应用.

Abstract: The differential equations of the autonomous generalized Birkhoffian system with constraints have been established in our research.The conditions for an autonomous generalized Birkhoffian system with constraints being translated into a gradient system have been given.Weve studied the stability of equilibrium for autonomous generalized Birkhoffian system with constraints by the characteristic of the gradient system.In the end,an example has been given to illustrate the application of the results.