AN INTRINSIC HAMILTONIAN-FORMULATION OF THE DYNAMICS OF LC-CIRCUITS

First, the dynamics of LC-circuits are formulated as a Hamiltonian sys tem defined with respect to a Poisson bracket which may be degenerate, i.e., nonsymplectic. This Poisson bracket is deduced from the network graph of the circuit and captures the dynamic invariants due to Kirch hoff's laws. Second, the antisymmetric relations defining the Poisson bracket are realized as a physical network using the gyrator element a nd partially dualizing the network graph constraints. From the network realization of the Poisson bracket, the reduced standard Hamiltonian system as well as the realization of the embedding standard Hamiltonia n system are deduced.