Controllable velocity projection for constraint stabilization in multibody dynamics

The direct numerical solution of the index-3 algebraic-differential equation system (DAE) associated with the constrained dynamics of a multibody system poses several computational difficulties mainly related to stability. Specially in long simulations, the instability is related to the drift of the solution from the velocity constraint manifold. One of the techniques proposed in the literature to overcome this problem is the velocity projection, which is a post-stabilization method that brings the solution back to the invariant manifold. This projection introduce a nonnegative artificial dissipation of energy when performed with the system mass matrix, which can affect the long term quality of the solution. This paper proposes a novel controllable velocity projection procedure capable of meeting certain requirements in the projected solution; namely, a maximum constraint value or a maximum dissipated energy. Several issues related to the efficiency of the implementation are discussed and two numerical simulations are presented. These simulations illustrate the performance of the proposed methodology and provide interesting insights about the relevance of the accuracy of the projection in the stabilization effect.