A Note on Symplectic Algorithm for the Equations of Dynamics

In this paper, we discover that the methods of direction integration are of similar shortcoming of the usual numerical methods, such as unstability, short-term action of computation, especially, the numerical damping by simulations being traced, and so on. Illustration shows that implicit direction methods are not unconditionally stable, nor of a higher precision as viewed before. The symplectic methods are stability and less quantity of computation. If the implicit direction methods try to reach the same stability of symplectic integrations, we must increase computation quantities in a smaller steplength. At last, we conclude that symplectic integrations are promising in applying to structural dynamics for forecasting.