A conservative augmented Lagrangian algorithm for the dynamics of constrained mechanical systems

The motion of many practical mechanical systems is often constrained. An important example is the dynamics of multibody systems, where the numerical solution of this type of systems faces several difficulties. A strategy to solve this type of problem is the augmented Lagrange formulation, which allows the use of numerical integrators for ODEs, combined with an update scheme for the algebraic variables, accomplishing exact fulfillment of the constraints. 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.