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A recursive, free-body approach to the estimation of joint torques associated with observed motion in linkage mechanisms has recently been shown to be computationally more efficient than any other known approach to this problem. This paper applies this method to the analysis of human postural dynamics and shows how it can also be used to compute accelerations for specified joint torques. The latter calculation, referred to here as the direct dynamics problem, has until now involved symbolic complexity to such an extent as to generally limit computer simulation studies of postural control to very simple models. The model presented in this paper is both straightforward and general, and removes this obstacle to the investigation of possible neural control mechanisms by means of computer simulation. A computationally oriented linearization procedure for the direct dynamics problem is also included in the paper. Finally, example simulation results and corresponding measured body motions for human subjects are presented to validate the method.