Generalized Hamiltonian model can give dynamics mechanism of inner parameters connected, however, it will meet many difficult while an actual physical system is converted to Generalized Hamiltonian model. And due to complexity of the structure matrix and damping matrix of high order Hamiltonian system, analysis and application to inner parameters connected mechanism is not ease and convenience. In this paper one kind of Hamiltonian model, four order and single input affine nonlinear system, is given basic form, it is a formulation formulize form, that is generalize Hamiltonian model can be directly derived by formulate calculation. The hydro turbine Hamiltonian model is taken as case to introduce this modeling method. At last, a simulation simplified method based-physical background is proposed, and used to simplify the hydro turbine Hamiltonian model.