Interconnection and structure in physical systems' dynamics

This paper discusses the relation between the power continuous interconnection structure in network models and the geometric structure of Hamiltonian systems. Firstly the gyrative interconnection structure, characterizing interdomain coupling in physical systems, is related to the Poisson structure of Hamiltonian systems. Secondly, the concept of port interaction is used to define the interaction of Hamiltonian systems with their environment. Thirdly, different integrability assumptions, concerning the definition of interaction by interaction potentials and the Jacobi identities, are discussed Finally it is presented how the previous results may be generalized to power continuous interconnection structures encompassing as well the power exchanges internal to a physical model as well as the exchanges with its environment. In this case the power continuous interconnection is related with Dirac structure, a geometric structure generalizing the Poisson bracket to constrained and implicit Hamiltonian systems. Copyright (C) 1998 IFAC.