The discrete null space method for the energy consistent integration of constrained mechanical systems. Part II: multibody dynamics

In the present work, rigid bodies and multibody systems are regarded as constrained mechanical systems at the outset. The constraints may be divided into two classes: (i) internal constraints which are intimately connected with the assumption of rigidity of the bodies, and (ii) external constraints related to the presence of joints in a multibody framework. Concerning external constraints lower kinematic pairs such as revolute and prismatic pairs are treated in detail. Both internal and external constraints are dealt with on an equal footing. The present approach thus circumvents the use of rotational variables throughout the whole time discretization. After the discretization has been completed a size-reduction of the discrete system is performed by eliminating the constraint forces. In the wake of the size-reduction potential conditioning problems are eliminated. The newly proposed methodology facilitates the design of energy–momentum methods for multibody dynamics. The numerical examples deal with a gyro top, cylindrical and planar pairs and a six-body linkage