广义Birkhoff系统与一类组合梯度系统

Generalized Birkhoff system and a kind of combined gradient system

提出一类组合梯度系统,即将梯度系统与斜梯度系统相加而组成的一个系统,并研究组合梯度系统的重要性质.将广义Birkhoff系统在一定条件下化成组合梯度系统,并利用组合梯度系统的性质来研究广义Birkhoff系统的积分和稳定性.

A combined gradient system which is obtained by adding a gradient system to a skew-gradient system is proposed.The property of the system is studied.Three results on its solution are obtained.Moreover,a criterion on the stability of the system is presented.The generalized Birkhoff system is a more extensive constrained mechanical system than Lagrange system,Hamilton system and Birkhoff system.The conditions under which a generalized Birkhoff system can be considered as a combined gradient system are given.When a generalized Birkhoff system is transformed into a combined gradient system,its integration and stability can be discussed by using the property.Finally,some examples are given to illustrate the application of our results.