Precise integration method for singular Hamilton matrix

There are n second-order ordinary differential equations (ODE) for structural dynamics of finite element method. It's obtained In first-order ODEs when the dynamic system is introduced into Hamilton system through the principle of general variation. The precise integration method is good for solving ODEs. It can give precise numerical results approaching to the exact solution at the integration points when it is applied to linear time-invariant dynamic system. The system matrix will be singular when the structure has rigid body displacement for non-homogeneous dynamic systems. A new method named complete pivot Gauss-Jordan elimination is proposed. It is used to derive to zero eigen-solutions for singular matrix. Based on this method, it is easy to separate the subspace corresponding to zero eigen-solutions from singular Hamilton matrix by using conjugate sympletic orthogonal normalization between Hamilton eigen-vectors. Then the singular portion can be excluded through projection. The singular solution is derived from analysis. The nonsingular solution is derived from the precise integration method. The numerical result demonstrates the validity and efficiency of the method.