In this paper we will outline a formulation for the dynamics of constrained systems. This formulation relies on the D’Alembert-Lagrange principle and the physically meaningful decomposition of the virtual displacements and the generalized velocities for the system where a redundant, non-minimum set of variables is used. The approach is valid for general constrained system with holonomic and/or nonholonomic constraints. We will also discuss a potential application of this formulation in improving the accuracy and stability of the simulation of constrained systems. This application will be demonstrated by an example drawn from space robotics.

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