Coordinates Reduction and Numerical Integration of Models of Constrained Multibody Systems

The authors present a variation of the constraint orthogonalization method proposed by Kim and Vanderploeg [1] for constrained multibody systems. Firstly the theoretical bases of the QTZ decomposition are presented, then it is reported how to apply this methodology to reduce the constraints number and define the independent velocities. A section is dedicated to three different solution methods based upon the QTZ decomposition. The first one leads to the reduced system of equation of motion, the other two methods allow to rearrange the Differential-Algebraic-Equations system into state space form by means of independent accelerations and a minimum set of coordinates, respectively. Finally two numerical examples based on the methodology herein proposed are reported. The results obtained by means of the in house developed multibody code NumDyn3D, based on QTZ decomposition, are compared to the ones obtained by means of the commercial software Working Model.