The generalized Lagrange formulation for nonlinear RLC networks

Based on the concept of generalized Euler-Lagrange equations, this paper develops a Lagrange formulation of networks of considerably broad scope. It is shown that the generalized Lagrange equations along with a set of compatibility constraint equations represents a set of governing differential equations of order equal to the order of complexity of the network. In this method the generalized coordinates include capacitor charges and inductor fluxes and the generalized velocities are comprised of an independent set of capacitor voltages and inductor currents. The generalized Hamilton equations are also developed and the connection with the Brayton-Moser equations is established.