Journal
JOURNAL OF GEOMETRY AND PHYSICS
Volume 42, Issue 1-2, Pages 166-194Publisher
ELSEVIER
DOI: 10.1016/S0393-0440(01)00083-3
Keywords
distributed-parameter systems; Hamiltonian systems; boundary variables; Dirac structures; Stokes' theorem; conservation laws
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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. (C) 2002 Elsevier Science B.V. All rights reserved.
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