Utilization of Euler-Lagrange Equations in Circuits with Memory Elements

It is well known that the equation of motion of a system can be set up using the Lagrangian and the dissipation function, which describe the conservative and dissipative parts of the system. However, this procedure, consisting in a systematic differentiation of the above state functions, cannot be used for circuits containing simultaneously conventional nonlinear elements such as the resistor, capacitor, and inductor, and their nonlinear memory versions the memristor, memcapacitor, and meminductor. The paper provides a general solution to this problem and demonstrates it on the example of modeling Josephson's junction.