BOND GRAPHS .1. ACAUSAL EQUIVALENCE

This paper and its successor(s) aim to derive a mathematical descripti on of bond graphs in general and of their junction structures in parti cular. It also introduces bond graphs to mathematicians that have no p revious knowledge of them. In this introductory paper, a definition of bond graphs is given and the concept of acausal equivalence is introd uced. Fifteen basic operations are defined and proved to be acausal eq uivalence operations. It is proved that these basic operations form a complete set, in the sense that, if two bond graphs are acausally equi valent, then each can be converted into the other by a sequence of the se operations and their inverses. In the course of the proof it is sho wn that every bond graph is acausally equivalent to one in a standard form. These standard bond graphs are used to demonstrate Various mathe matical properties of bond graphs, and to derive a new procedure for t esting whether or not a given set of input variables uniquely determin es the corresponding set of output variables. This should be of intere st to mathematicians and engineers alike.