D. Negrut, R. Rampalli, G. Ottarsson, A. Sajdak, "On the use of the HHT Method in the Context of Index 3 Differential Algebraic Equations of Multibody Dynamics," Preprint ANL/MCS-P1278-0805, August 2005. [pdf]
The paper presents theoretical and implementation aspects related to a numerical integrator used for the simulation of large mechanical systems with flexible bodies and contact/impact. The proposed method is based on the Hilber-Hughes-Taylor (HHT) implicit formula and is tailored to answer the challenges posed by the numerical solution of index 3 Differential Algebraic Equations that govern the time evolution of a multibody system. One of the salient attributes of the algorithm is the good conditioning of the Jacobian matrix associated with the implicit integrator. Error estimation, integration step-size control, and nonlinear system stopping criteria are discussed in detail. The simulations of an engine model, a model with contacts, and a model with flexible bodies confirm a 2 to 3/, X speed-up factor when compared with the integrators currently available in MSC.ADAMS, a commercial mechanical system simulation package.