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TitleA methodology to eliminate the violation of the constraint equations for forward dynamics of constrained multibody systems
Author(s)Flores, Paulo
KeywordsConstraints violation
Baumgarte method
Penalty approach
Augmented lagrangian formulation
Multibody dynamics
Issue dateJun-2013
PublisherAssociação Portuguesa de Mecânica Teórica, Aplicada e Computacional (APMTAC)
Abstract(s)The dynamic equations of motion for constrained multibody systems are frequently formulated using the Newton-Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. It is known that the standard resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of three spatial multibody systems. The outcomes in terms of constraints violation and computational efficiency are analyzed and compared with those obtained with the Baumgarte stabilization method, the penalty approach and the augmented Lagrangian formulation.
TypeConference paper
AccessRestricted access (UMinho)
Appears in Collections:DEM - Publicações em actas de encontros científicos / Papers in conference proceedings

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