The aim of this paper is to provide an intrinsic Hamiltonian jormulation of the equations of motion ofnetwork models of non-resistive physical systems. A recently developed extension of the classical Hamiltonian equations of motion considers systems with state space given by Poisson manifolds endowed with degenerate Poisson structures, examples of which naturally appear in the reduction of' systems with symmetry. The link with network representations of non-resistive physical systems is established using the generalized bond graph formalism which has the essential feature of symmetrizing all the energetic network elements into a single class and introducing a coupling unit gyrator. The relation between the Hamiltonian formalism and network dynamics is then investtgated throqh the representation of the invariants of the system, either captured in the degeneracy of the Poisson structure or in the topological constraints at the ports of the gyrative type network structure. This provides a Hamiltonian formulation of dimension equal to the order of the physical system, in particular, for odd dimensional systems. A striking example is the direct Hamiltonian formulation of electrical LC networks.

Abstract-First, the dynamics of LC-circuits are formulated as a Hamiltonian system 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 KirchhoWs laws. Second, the antisymmetric relations defining the Poisson bracket are realized as a physical network using the gyrator element and 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 Hamiltonian system are deduced.

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In this paper we present a bond graph model of a continuous stirred tank reactor which represents the reaction kinetics as well as the heat and mass transport phenomena in the reactor. The consequences of reticulation of the phenomena and of the systematic use of the power conjugated variables on the formulation of the thermodynamic properties, the reaction kinetics and the energy and mass transport are shown. A classical example of chemical reaction is chosen to illustrate this approach: the equilibrated reaction of hydrogen and iodine in hydrogen iodide.

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