The motion of many practical mechanical systems is often constrained. An important example is the dynamics of multibody systems, where these constraints arise from the modeling of joints that connect different bodies. The numerical solution of the dynamics of this type of systems faces several difficulties, mainly due to stability problems [
]. Different methods have been proposed in the literature to overcome these problems, based on different strategies for the constraints formulation.
One of these strategies is the augmented Lagrange formulation, which allows the use of numerical integrators for Ordinary Differential Equations, combined with an update scheme for the algebraic variables, accomplishing exact fulfillment of the constraints.
In this context, this work focuses on the design of a conservative version of this augmented Lagrangian formulation for holonomic constraints, proposing a numerical procedure that exhibits excellent stability, thus providing an interesting alternative for the dynamical analysis of these type of systems. A point of departure is a conservative formulation based in the penalty method [
], which exhibits good stability but does not accomplish exact fulfillment of the constraints.