Generalized gradient representation of holonomic mechanical systems

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.