Bond Graphs III: Bond Graphs and Electrical Networks

Electrical networks are defined and a definition of when a bond graph and an electrical network are equivalent is given. Bond graphs and electrical networks are defined to be primitive if they contain no transformers or gyrators. A bond graph is defined to be realisable if it is equivalent to an electrical network and primitively realisable if it is equivalent to a primitive electrical network. It is shown how to construct a bond graph equivalent to a given electrical network and how to construct an electrical network equivalent to a given bond graph. Chordless odd loops are defined and a characterisation of primitively realisable bond graphs in terms of chordless odd loops and forbidden induced subgraphs is given. It is shown how to construct a primitive network equivalent to a given primitively realisable bond graph.

[1]  Jim Lawrence,et al.  Oriented matroids , 1978, J. Comb. Theory B.

[2]  Alan S. Perelson,et al.  System Dynamics: A Unified Approach , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[3]  Hinrich R. Martens,et al.  A topological procedure for converting a bond graph to a linear graph , 1974 .

[4]  Pieter C. Breedveld,et al.  Bond graphs for engineers , 1992 .

[5]  Dean Karnopp,et al.  Introduction to physical system dynamics , 1983 .

[6]  Alan S. Perelson,et al.  Bond graphs and linear graphs , 1976 .

[7]  W. T. Tutte.  An algorithm for determining whether a given binary matroid is graphic. , 1960 .

[8]  Alan S. Perelson.  Bond Graph Sign Conventions , 1975 .

[9]  Douglas R. Woodall,et al.  Bond Graphs I: Acausal Equivalence , 1997, Discret. Appl. Math..

[10]  B. Neumann,et al.  On a class of abelian groups , 1953 .

[11]  Peter L. Hammer,et al.  Discrete Applied Mathematics , 1993 .

[12]  Robert E. Bixby,et al.  An Almost Linear-Time Algorithm for Graph Realization , 1988, Math. Oper. Res..

[13]  Wai-Kai Chen,et al.  Graph theory , 1972 .

[14]  B. Sturmfels.  Oriented Matroids , 1993 .

[15]  P. H. Roe,et al.  The mathematical foundations of bond graphs—I. Algebraic theory , 1989 .

[16]  P. E. Wellstead,et al.  Introduction to physical system modelling , 1979 .

[17]  W. T. Tutte.  A homotopy theorem for matroids. II , 1958 .

[18]  Douglas R. Woodall,et al.  Bond Graphs II: Causality and Singularity , 1997, Discret. Appl. Math..