Alternative Causality Assignment Procedures in Bond Graph for Mechanical Systems

Abstract

This paper proposes to extend the set of causality assignment procedures. The proposed alternative procedures are mainly inspired by formulations developed in the mechanical domain. They enable Lagrange equations, Hamilton equations, and Boltzmann-Hamel equations to be obtained, as well as formulations with the Lagrange multipliers. In the context of system modeling a varied set of mechanical oriented equations are available in a systematic way from the bond graph representation and the proposed corresponding procedures provide an algorithmic frame for programming these mathematical formulations. The graphical features of the bond graph tool and the causality stroke concept enable formulations to be methodically obtained, formulations that can otherwise be very awkward to express. Also these procedures emphasize certain interesting properties of the bond graph tool e.g.: there is a clear distinction between the energy topology of a system and its dynamic equations; it also enables graphic structural analyses to be undertaken; and finally it can play a pedagogical role in engineering education.