A GENERAL FORMULATION IN RIGID MULTIBODY DYNAMICS

The dynamics of rigid multibodies is traditionally formulated by means of either minimal or redundant co-ordinates methods. An alternative approach is here proposed whereby a highly redundant set of coordinates is adopted. As a result, the equations of motion of the constrained bodies are decoupled. Several meaningful parameters are directly available and the constraint conditions are enforced in a very natural way. The first part of the paper presents the basic meanings and the theoretical developments of the formulation. The second develops a numerical approximation for the methodology proposed in the first part. The non-linear system of differential-algebraic equations governing the motion of the multibody is reduced to its weak form. It is linearized by applying a Newton-Raphson procedure and approximated through the method of finite elements in time. The details of the numerical application of-this method are discussed and a solution procedure is presented. Finally, some numerical examples involving tree and closed loop topologies prove the capability of the present formulation in handling multibody dynamics.