Hamiltonian formulation of distributed-parameter systems with boundary energy flow

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

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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
    Place of PublicationEnschede
    PublisherUniversity of Twente, Faculty of Mathematical Sciences
    Number of pages30
    Publication statusPublished - 2001

    Publication series

    NameMemorandum / Faculty of Mathematical Sciences
    PublisherUniversity of Twente, Faculty of Mathematical Sciences
    No.1586
    ISSN (Print)0169-2690

    Keywords

    • MSC-35B37
    • MSC-35Q60
    • MSC-70H05
    • IR-65773
    • MSC-93C20
    • EWI-3406
    • MSC-76N10

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