Hamiltonian system and the Saint Venant problem in elasticity

Abstract

The traditional semi-inverse solution method of the Saint Venant problem, which is described in the Euclidian space under the Lagrange system formulation, is updated to be solved in the symplectic space under the conservative Hamiltonian system. 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.