A State-Space Dynamical Representation Based on a Subsystem Newton-Euler Recursive Method for General Multibody Systems

Computer-oriented dynamical equations are derived for general multibody systems based on the law of moment of momentum with respect to subsystem joints, graph theory, and a recursive formulation. The 6 × 6 transformation matrices, a path transfer matrix, a loop transfer matrix, and a series of combined rotation-translation (R-T) matrices are defined to obtain the equations in a compact matrix form, which is reduced to state-space form by defining the mode matrices for joints in terms of a minimal set of relative velocity (or quasivelocity) state variables. The recursive method of calculation is used for efficient computation. Applying the singular value decomposition (SVD) for a loop system to eliminate constraint forces, a minimal set of dynamical equations is obtained, in terms of independent loop relative quasivelocity state variables.