A unifying principle is presented whereby all finite lumped systems can be analyzed by a single technique, no matter how complex the system may be. This central principle is the existence of a linear graph which is isomorphic to the dynamical properties of the elementary parts of the system and which shows how the parts are connected together.
An analysis of a lumped system begins with a conceptual decomposition of the system into a number of simple parts, each of which has known dynamical properties. It is shown that if two types of scalar variables can be found such that (1) they define, with the aid of system parameters, the dynamical properties of each part of the system, (2) the first type obeys the MESH LAW, (3) the second obeys the INCIDENCE LAW, and (4) physical dimensions of appropriate products of the two types are consistent, then there exists a linear graph isomorphic with the dynamical properties of the system as described by the variables so selected. Trivial additions to the isomorphic graph yield a schematic diagram for the system. It is then shown that the algebraic properties of the schematic diagram can be used to generate in a straightforward manner a set of equations, on either the nodal or mesh basis, describing the dynamics of the system as a whole. The isomorphic graph is also the key ingredient in establishing complete analogy. Formal procedures for establishing complete analogies are presented.