On the constraints violation for forward multibody dynamics : application of the Baumgarte stabilization method

Abstract

This work deals with the study of the constraints violation for forward dynamic analysis of constrained multibody systems. For this purpose, the well-known Baumgarte Stabilization method formulation is revised and applied. The influence of the some variables that affect the constraints violation, such as, the Baumgarte parameters and the time step, are discussed. In the sequel of this process, the main issues associated with the methodologies of the rigid multibody systems are reviewed. The generalized Cartesian coordinates are utilized to describe the bodies’ degrees-of-freedom. The adopted formulation of the equations of motion relies on the Newton-Euler approach, augmented with the constraint equations that lead to a set of differential algebraic equations. The presented approach is applied to two planar multibody systems, a four-bar linkage and a biomechanical model for human gait analysis. It was carried out a set of simulations with and without stabilization method, i.e., with Baumgarte parameters α and β equal to 5 and equal to 0, respectively. The resuts depict that the Baumgarte stabilization method is an efficient and simple way for correcting the constraints violation and, hence, for avoinding alterations on the initial coordinates of the multi body systems.