The relationship between recursive multibody dynamics and discrete-time optimal control

A recursive algorithm, based on a Newton-Euler formulation, is developed for the solution of the simulation-dynamics problem for a chain of rigid bodies. Arbitrary joint constraints are permitted, that is, joints may allow translational and/or rotational degrees of freedom. The recursive procedure is shown to be identical to that encountered in a discrete-time optimal-control problem. For each relevant quantity in the multibody-dynamics problem, there exists an analog in the context of optimal control. The performance index that is minimized in the control problem is identified as Gibbs´ function for the chain of bodies