Multibody system order n dynamics formulation based on velocity transform method

In the multibody-simulation discipline, equations-of-motion formulations in which the number of calculations per integration step increase only linearly with the number n of bodies are called order it or 0(n) formulations. The development of such formulations is an area of current research because of their capability of yielding simulations that run much faster than conventional ones when n is large. This paper presents a new order n algorithm. It is applicable to systems of rigid or nonrigid bodies. It permits the bodies' interconnection joints to have an arbitrary number of degrees of freedom between 0 and 6. The system can have open-chain, tree, or closed-loop topology. Both absolute accelerations and relative accelerations are established by the technique. Closed topological loops are handled by the concept of cut joints. Constraint forces are calculated only at the cut joints, not at the uncut ones. The derivation of the algorithm uses a velocity transformation to eliminate the appearance of forces due to constraints at the uncut joints. The algorithm entails sequential computational passes—backward and forward—through the system of bodies.