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.