The anti-Lagrangian equations: A missing network description

Abstract

The explicit topological formulation of dynamic equations in terms of scalar functions for RM (M-memristor) networks, called the anti-Lagrangian equations, is introduced. In general, two scalar functions are needed to set the anti-Lagrangian equations. The differential operators acting on these functions bear a certain anti-symmetry relationship with respect to the operators occuring in the standard Lagrangian equations for LC networks. The well-known stationary principles for pure R networks, as well as new quasi-stationary principles for pure M networks are shown to emerge naturally from anti-Lagrangian equations. The form of transformation of variables leaving the form of equations invariant is also studied. © 1979.