Adjoint sensitivity index-3 augmented Lagrangian formulation with projections

The interest on closed-form analytical sensitivity equations based on the classical forward dynamics formulations, started shortly after the equations were ready and became popular. A vast effort was devoted by the authors in the last years to derive the forward and adjoint sensitivity equations for some state-of-the-art formulations of practical interest. Recently, the forward sensitivity equations for the index-3 augmented Lagrangian formulation with projections (the ALI3-P formulation) have been derived. In this article, the ALI3-P adjoint sensitivity equations are derived and implemented in the MBSLIM library as a general code and tested in one academic example and one real-life multibody system.