SINGULARITY-FREE AUGMENTED LAGRANGIAN ALGORITHMS FOR CONSTRAINED MULTIBODY DYNAMICS

After a general review of the methods currently available for the dyna mics of constrained multibody systems in the context of numerical effi ciency and ability to solve the differential equations of motion in si ngular positions, we examine the acceleration based augmented Lagrangi an formulations, and propose a new one for holonomic and non-holonomic systems that is based on the canonical equations of Hamilton. This ne w one proves to be more stable and accurate that the acceleration base d counterpart under repetitive singular positions. The proposed algori thms are numerically efficient, can use standard conditionally stable numerical integrators and do not fail in singular positions, as the cl assical formulations do. The reason for the numerical efficiency and b etter behavior under singularities relies on the fact that the leading matrix of the resultant system of ODEs is sparse, symmetric, positive definite, and its rank is independent of that of the Jacobian of the constraint equations. The latter fact makes the proposed method partic ularly suitable for singular configurations.