On the computational methods for solving the differential-algebraic equations of motion of multibody systems

Abstract

In this investigation, different computational methods for the analytical development and the computer implementation of the differential-algebraic dynamic equations of rigid multibody systems are examined. The analytical formulations considered in this paper are the Reference Point Coordinate Formulation based on Euler Parameters (RPCF-EP) and the Natural Absolute Coordinate Formulation (NACF). Moreover, the solution approaches of interest for this study are the Augmented Formulation (AF) and the Udwadia-Kalaba Equations (UKE). As shown in this paper, the combination of all the methodologies analyzed in this work leads to general, effective, and efficient multibody algorithms that can be readily implemented in a general-purpose computer code for analyzing the time evolution of mechanical systems constrained by kinematic joints. This study demonstrates that multibody algorithm based on the combination of the NACF with the UKE turned out to be the most effective and efficient computational method. The conclusions drawn in this paper are based on the numerical results obtained for a benchmark multibody system analyzed by means of dynamical simulations.