Analytical study of the superiority of the momentum equations of motion for impulsive loads

In the step-by-step computing the response to an impulsive loading, the application of the Newmark explicit method to solve the momentum equations of motion is much better than to solve the force equations of motion. The main cause to this effect is theoretically verified and confirmed by a series of numerical illustrations. The original form of the Newmark explicit method is generally require to select an appropriate step size largely dependent upon the shape of an impulse, especially the ending value of the impulse. On the other hand, it is almost shape independent for the use of the integral form of the Newmark explicit method. In fact, a much larger time step can be employed by the integral form of the Newmark explicit method to have the same accuracy of solutions when compared to the original form. Numerical experiments show that the integral form of the other members of the Newmark method also has this improved property.