Stabilized index-1 differential-algebraic formulations for sensitivity analysis of multi-body dynamics

Abstract

Convergence results are shown for the Hiller-Anantharaman stabilized index-1 differential algebraic equation (DAE) formulation of the DAE of motion of a multi-body system. The formulation is extended to the direct differentiation DAE and the adjoint (A) DAE resulting from the design sensitivity analysis of multi-body dynamics. Convergence of backward differential formula methods applied to the Hiller-Anantharaman formulation is proven not only for the DAE of motion but also for the differentiation DAE and the ADAE. The Hiller-Anantharaman formulation is attractive for multi-body dynamics because of its stabilization properties, resulting from a stabilized index reduction of the original index-3 DAE, and because it yields a DAE that includes the position and velocity constraint equations. In addition, the Hiller-Anantharaman index-1 DAE formulation has the advantage that the currently available index-1 DAE integrators are in a more mature phase than higher-index DAE integrators.