Lagrange's Equations versus Bond Graph Modeling Methodology by an Example of a Mechanical System

Abstract

The bond graph modeling method was discovered by Henry Painter in 1959 and has quickly become a wide spread method all over the modeling engineering world. The method is based on the analysis of power circulation in systems and has some indisputable advantages over other modeling methods, based in principle on mathematical aspects. The paper proposes a comparison between the bond graph method and Lagrange's equations method, by applying both methods to model a mechanical system. The bond graph model is a graphical model. There are three possibilities to exploit the bond-graph diagram. The first one consists in deducing a system of differential or algebraic-differential equations from the diagram. The second one consists in obtaining the block diagram model from the bond graph diagram, without additionally writing any equations, followed by the block diagram implementation in the appropriate software, which permits to perform simulations at once. The third one consists in implementing the bond graph diagram directly in the appropriate software, where simulations can immediately run. The advantages and the disadvantages of the methods are emphasized, but the decision about the most appropriate method is up to the modeler.