Hamiltonian formulation of distributed-parameter systems with boundary energy flow


Schaft, A.J. van der and Maschke, B.M. (2002) Hamiltonian formulation of distributed-parameter systems with boundary energy flow. Journal of Geometry and Physics, 42 (1-2). pp. 166-194. ISSN 0393-0440

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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.
Item Type:Article
Copyright:© 2002 Elsevier
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/69115
Official URL:https://doi.org/10.1016/S0393-0440(01)00083-3
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