The conserved constrained dynamical system derives to differentialalgebraic equation. Solving the constrained differentialalgebraic equation via introducing the Lagrange parametric differential equation to treat the constraint, there is the differential index problem，which enlarges the variables to be solved. The existing solution methodology is always via the FDM. The symplectic preservation of the finite difference scheme is considered, however, the projection operation onto the constraint manifold still brings problems. The present paper applies the methodology of analytical structural mechanics. The independent displacements at the integration points are treated as primary variables to be solved, and the constraint conditions are satisfied strictly at the integration points. The timedomain finite element linear interpolation function is applied to approximate the orbit to generate the action function of the timeinterval.