When performing dynamic analysis of a constrained mechanical system, a set of index 3 Differential-Algebraic Equations (DAE) describes the time evolution of the system. The paper presents a state-space based method for the numerical solution of the resulting DAE. A subset of so called independent generalized coordinates, equal in number to the number of degrees of freedom of the mechanical system, is used to express the time evolution of the mechanical system. The second order statespace ordinary differential equations (SSODE) that describe the time variation of independent coordinates are numerically integrated using a Rosenbrock type formula. For stiff mechanical systems, the proposed algorithm is shown to significantly reduce simulation times when compared to state of the art existent algorithms. The better efficiency is due to the use of an L-stable integrator and a rigorous and general approach to providing analytical derivatives required by it.

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