Abstarct: The guding concept of a Hamiltonian system of differential equation forms the basis of much of the more advanced work in classical mechanics, including motion of rigid bodies, celestial mechanics, quantization theory and so on. More recently, Hamiltonian methods have become increasingly important in the study of the equations of continuum mechanics, including fluids, plasmas and elastic media.This method is coordinate-free and is applicable for any given system such as PDE and ODE.