Constrained mechanical systems and gradient systems with strong Lyapunov functions

• The characteristics of gradient systems with strong Lyapunov functions are studied.
• The conditions for the transformation to a gradient system are given.
• The stability of the mechanical systems is studied.
• Some examples are given to illustrate the application of the results.

The characteristics of stationary and non-stationary gradient systems with strong Lyapunov functions are studied. The conditions under which holonomic mechanical systems, generalized Birkhoff systems and generalized Hamilton systems can be considered as gradient systems are given. The characteristics of the gradient systems can be used to study the stability of the mechanical systems. Some examples are given to illustrate the application of the results.