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In their paper, Drs. Jones and Evans discuss the calculus of variations which describes the methods used to minimize definite integrals of certain scalar functions, and is the mathematical foundation for studying a wide class of problems.
The applicability of the calculus of variations to these problems has always been hampered by the fact that the classical extremum principles, such as Hamilton's Principle, are only suitable for systems that conserve energy, and this certainly arose from the fact that dissipative elements are not describable in terms of energy functions. In this paper the authors suggest ways of removing this fundamental restriction by bringing together the classical formalism of variational mechanics and the topological properties of electrical networks.
Historically, variational mechanics developed from particle mechanics in which mass was considered to be the only energy storage device. In electrical networks, however, there are two distinct classes of storage device; capacitors and inductors. The existence of electrical network analogies for mechanical systems with one degree of freedom suggests a possible extension of the classical variational formulation.
Electrical networks possess a property unique amongst physical systems, namely that their actual physical structure is isomorphic to their abstract topological structure, represented by a linear graph. These linear graphs have the property that, from a selection of a "tree" of elements, two sets of independent variables are instantly presented. This is in contrast to classical variational analysis where such a set of independent variables is not always easily chosen. These variables may then be classified according to their physical and mathematical properties, and fitted to a simple morphological
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