Hamiltonian formulation of distributed-parameter systems with boundary energy flow

A.J. van der Schaft, B.M. Maschke

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    399 Citations (Scopus)
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    Abstract

    A Hamiltonian formulation of classes of distributed-parameter systems is presented, which incorporates the energy flow through the boundary of the spatial domain of the system, and which allows to represent the system as a boundary control Hamiltonian system. The system is Hamiltonian with respect to an infinite-dimensional Dirac structure associated with the exterior derivative and based on Stokes' theorem. The theory is applied to the telegraph equations for an ideal transmission line, Maxwell's equations on a bounded domain with non-zero Poynting vector at its boundary, and a vibrating string with traction forces at its ends. Furthermore, the framework is extended to cover Euler's equations for an ideal fluid on a domain with permeable boundary. Finally, some properties of the Stokes-Dirac structure are investigated, including the analysis of conservation laws.
    Original languageEnglish
    Pages (from-to)166-194
    Number of pages29
    JournalJournal of geometry and physics
    Volume42
    Issue number1-2
    DOIs
    Publication statusPublished - May 2002

    Keywords

    • Stokes theorem
    • Boundary variables
    • Conservation laws
    • Distributed-parameter systems
    • Hamiltonian systems
    • Dirac structures
    • n/a OA procedure

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