A Rosenbrock–Nystrom state space implicit approach for the dynamic analysis of mechanical systems: II—method and numerical examples

When performing dynamic analysis of a constrained mechanical system, a set of index three differential-algebraic equations (DAE) describes the time evolution of the system. A state–space based method for the numerical solution of the resulting DAE has also been developed. The numerical method uses a linearly implicit time stepping formula of the Rosenbrock type, which is suitable for medium accuracy integration of stiff systems. This paper discusses choices of method coefŽ cients and presents numerical results. For stiff mechanical systems, the proposed algorithm is shown to reduce signiŽ cantly simulation times when compared to state of the art existent algorithms. The better efŽ ciency is due to the use of an L-stable integrator, and a rigorous and general approach to providing analytical derivatives required by it.