将梯度系统推广到包含时间的情形,称之为广义梯度系统.给出完整力学成为梯度系统的条件.如果广义梯度系统的势函数可以成为Lyapunov函数,那么可用Lyapunov定理来研究系统的稳定性.
A gradient system is generalized to a system in which the time appears in the potential function, and the system is called generalized gradient system. The condition under which a holonomic mechanical system can be considered as a generalized gradient system is given. If the potential function of the system can be considered as a Lyapunov function,then the Lyapunov theorems can be used to study the stability of the system.