The Mathematical Foundations of Bond Graphs-IV. Matrix Representations and Causality

The development of a mathematical theory for bond graphs continues with an analysis qf two areas crucial to the derivation of system equations,from a bond graph model. Matri.y representations of bond graph matroids ure exumined and used to provide a rigorous proof of the mathematical equivalence sf‘ the linear graph and bond graph modelling methods. The procedure of selecting causality by the method of’ cuusal strokes is discussed. This is shown to he a device,for choosing a base of the cycle matroid of a bond gruph, und u s@cient condition is proved for when the method gives u base. An example is given of’s bond graph with u cuusul loop which corresponds to a vulid causal assi,gnment. Various combinatorial ,finmulue are proved concerning ranks und dimensions. Formulae ,for the ranks of’@rt and flow matrices and the number of independent equutions obtained ,from u bond graph are consequences of’ the results.