Abstract: The traditional semi inverse solution method of the Saint Venant problem and the Saint Venant principle,which were described in the Euclidian space under the Lagrange system formulation,are updated to be solved in the symplectic space under the conservative Hamiltonian system. Thus,the Saint Venant problem and the Saint Venant principle have been unified by the direct method. It is proved in the present paper that all the Saint Venant solutions can be obtained directly via the zero eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian operator matrix and the Saint Venant principle corresponds to neglect the non zero eigenvalue solutions,where the non zero eigenvalues give the decay rates. 

Key words:  , Hamiltonian system；Saint Venant problem；Saint Venant principle；Symplectic；Eigenvalue problem