Spatial operator algebra for multibody system dynamics

Abstract

This paper describes a new spatial operator algebra for the dynamics of general-topology rigid multibody systems. Spatial operators allow a concise and systematic formulation of the dynamical equations of motion of multibody systems and the development of efficient computational algorithms. Equations of motion are developed for progressively more complex systems: serial chains, topological trees, and closed-loop systems. New operator factorizations and expressions for the mass matrix and its inverse are derived and used to obtain efficient, spatially recursive computational algorithms. The algorithms can be easily reconfigured in response to changes in the constraints and the topology of constituent bodies. Thus, they are particularly suited for time-varying multibody systems. References are provided for extensions to flexible multibody systems. Spatially recursive algorithms, based on the sequential filtering and smoothing methods encountered in optimal estimation theory, provide the computational infrastructure to mechanize the spatial operators.