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Meminductors and memcapacitors do not allow a Lagrangian formulation in theclassical sense since these elements are nonconservative in nature and theassociated energies are not state functions. To circumvent this problem, adifferent configuration space is considered that, instead of the usual loopcharges, consist of time-integrated loop charges. As a result, thecorresponding Euler-Lagrange equations provide a set of integrated Kirchhoffvoltage laws in terms of the element fluxes. Memristive losses can be includedvia a second scalar function that has the dimension of action. A dualvariational principle follows by considering variations of the integrated nodefluxes and yields a set of integrated Kirchhoff current laws in terms of theelement charges. Although time-integrated charge is a somewhat unusual quantityin circuit theory, it may be considered as the electrical analogue of amechanical quantity called absement. Based on this analogy, simple mechanicaldevices are presented that can serve as didactic examples to explainmemristive, meminductive, and memcapacitive behavior.

Memory Elements: A Paradigm Shift in Lagrangian Modeling of Electrical Circuits