Energy-conserving formulation of RLC-circuits with linear resistors

In this paper firstly, the dynamics of LC-circuits without excess elements is expressed in terms of contact systems encompassing in a single formulation the Hamiltonian formulation and the pseudo-gradient formulation called the Brayton-Moser equations. Indeed the contact formulation encompasses both the Hamiltonian system and its the adjoint variational system. Secondly we express the dynamics of RLC-circuits with linear resistors in the contact formalism by extending the state space to an associated space of Thermodynamic phase which again encompasses as well the Hamiltonian formulation with dissipation as the BraytonMoser formulation.