Energy-momentum conserving integration of multibody dynamics

A rotationless formulation of multibody dynamics is presented, which is especially beneficial to the design of energy-momentum conserving integration schemes. The proposed approach facilitates the stable numerical integration of the differential algebraic equations governing the motion of both open-loop and closed-loop multibody systems. A coordinate augmentation technique for the incorporation of rotational degrees of freedom and associated torques is newly proposed. Subsequent to the discretization, size-reductions are performed to lower the computational costs and improve the numerical conditioning. In this connection, a new approach to the systematic design of discrete null space matrices for closed-loop systems is presented. Two numerical examples are given to evaluate the numerical properties of the proposed algorithms.