Direct Application of the Loop Rule to Bond Graphs

Abstract

The Shannon-Mason loop rule permits direct reduction of a linear constant-parameter signal flow graph to a transfer function. Signal flow graphs can be constructed from bond graphs or sets of equations. Application of the loop rule to the parent bond graphs, however, with the aid of certain rules, is shown to be quicker and less prone to error. Also, four invariant classes of bond graph meshes are distinguished, with implications in physical analogies and in computation.