Using linear graph theory and the principle of orthogonality to model multibody, multi-domain systems

This paper presents a unified formulation capable of systematically generating the governing symbolic equations for multibody, multi-domain systems. The formulation is based on the principle of orthogonality, a powerful concept that serves as a generalization of the principle of virtual work and virtual power. Since it is a graph-theoretic approach, the formulation also provides significant flexibility with respect to the system’s modeling variables. This allows the user to model the mechanical portion of the system using joint, absolute, absolute angular, or some hybrid set of coordinates. To demonstrate the robustness of the approach, the paper compares the algorithm’s results for a forward dynamic analysis of a flexible parking lot barrier to those in the literature. The parking lot barrier model includes a three-phase induction motor, a six bar mechanism and a flexible beam.