A parallel O(N) formulation for general multibody dynamics

A new methodology for dynamical analyses applicable to a very large class of rigid and flexible multibody systems is presented. It is based on a variable-gain error correction method with scaling, and has the following distinctive features: (i) All kinds of holonomic and nonholonomic equality constraints can be treated in a plain and unified manner; (ii) Stability of the constraints is always attained; (iii) The formulation has an order N computational cost in terms of both the constrained and unconstrained degrees of freedom, regardless of the system topology; (iv) Unlike the traditional recursive order N algorithms, it is quite amenable to parallel computation; (v) Since no matrix operations are involved, it can be implemented to very simple general-purpose simulation programs. Versatility, dynamical validity and efficiency of the approach are checked through numerical studies of several particular systems.