Bond graphs I: Acausal equivalence Original Research Article

This paper and its successor(s) aim to derive a mathematical description of bond graphs in general and of their junction structures in particular. It also introduces bond graphs to mathematicians that have no previous knowledge of them. In this introductory paper, a definition of bond graphs is given and the concept of acausal equivalence is introduced. Fifteen basic operations are defined and proved to be acausal equivalence operations. It is proved that these basic operations form a complete set, in the sense that, if two bond graphs are acausally equivalent, then each can be converted into the other by a sequence of these operations and their inverses. In the course of the proof it is shown that every bond graph is acausally equivalent to one in a standard form. These standard bond graphs are used to demonstrate various mathematical properties of bond graphs, and to derive a new procedure for testing whether or not a given set of input variables uniquely determines the corresponding set of output variables. This should be of interest to mathematicians and engineers alike.