Stability for manifolds of equilibrium state of generalized Hamiltonian system with additional terms

For a generalized Hamiltonian system with additional terms, stability for the manifolds of the equilibrium state is presented. Equilibrium equations, disturbance equations and the first approximate equations of the system are given. A theorem for the stability of the manifolds of the equilibrium state of a general autonomous system is used for the generalized Hamiltonian systems with additional terms, and three propositions on the stability of the manifolds of the equilibrium state of the system are obtained. An example is given to illustrate the application of the method and results. At last, we study the stability for manifolds of the equilibrium state of the Euler equations of a rigid body subjected to external moments of force, by using of the method in this paper.