Abstract: Considering that the algorithm of the equations of motion of multibody systems is the base for the analysis of dynamics, the discrete null space method for the Newmark integration is proposed. The procedure is essentially based upon the following steps. The equations of motion of constrained multibody systems are directly discretized by the Newmark time stepping scheme. The discrete Lagrange multipliers are eliminated by using a discrete null space matrix and the discrete d’Alembert-type formulation is obtained. The number of unknowns is reduced further by employing specific local reparametrizations. It is shown that the developed method can not only reduce the dimension of the equations of motion, thus improving the computational efficiency, but also obtain the good results with less constraint violation.

Key words: Constraint violation, Differential algebra equations, Discrete null space, Dynamics of multibody systems, Newmark