Stability for manifolds of equilibrium states of generalized Hamiltonian systems

For a generalized Hamiltonian system, stability for the manifolds of equilibrium states is presented based on Lyapunov’s stability theories. Equilibrium equations, perturbation equations and first approximate equations of the system are given. A theorem for the stability of manifolds of equilibrium states of general autonomous system is used to the generalized Hamiltonian system, and three propositions on the stability of manifolds of equilibrium states of the system are obtained. Two examples are given to illustrate application of the method and results.