Causality in vector bond graphs and its application to modeling of multi-body dynamic systems

Applications of bond graph to the modeling of dynamic systems with one dimensional topology have been proved to be efficient and effective. In applications where multi-power bonds are required to express the physics of the elements, the multi-dimensional topology of the system needs to be resolved into scalar forms. This makes the technique difficult to use and results in complex graphical models. Vector bond graphs have been introduced to tackle the modeling of these systems. However, due to the limitations in the causality assignment in vector bond graphs, their applications have been mostly limited to graphical presentations of multi-dimensional systems. In this paper, we introduce a new procedure for the causality assignment that eliminates the need for converting the bond graphs into scalar forms. The approach not only simplifies the modeling phase but it provides a systematic way similar to scalar bond graphs to derive the equations of motion directly from the vector bond graphs model.