An efficient approach for the numerical simulation of multibody systems

The field of kinematics and dynamics of mechanical systems has progressed from a manual graphics art to a highly developed discipline in analytical geometry and dynamics. Various general purpose formulations for the dynamic analysis of Constrained Mechanical Systems (CMS) lead to mixed Differential-Algebraic Equations (DAEs) called the Euler-Lagrange equations. During the past fifteen years many contributions have been made to the theory of computational kinematics and dynamics of CMS (also called Mutibody dynamics). The recent advances in computer hardware and software have tremendously revolutionized the analysis of CMS. There are various numerical approaches for solving general vector fields. In the previous paper [Appl. Math. Comput. 92 (1998) 153–193] a complete and detailed analysis of various approaches for the numerical solution of vector fields is given. In this paper we extend the algorithms presented in the above mentioned reference to solve the Euler-Lagrange equations of motion for CMS. The numerical experiments suggest that perturbation approach performs ‘better’ than the other approaches.