Hamiltonian formulation of distributed-parameter systems with boundary energy flow

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

Research output: Book/ReportReportOther research output

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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

Fingerprint

distributed parameter systems
formulations
ideal fluids
energy
traction
conservation laws
Maxwell equation
transmission lines
strings

Keywords

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

Cite this

van der Schaft, A. J., & Maschke, B. M. (2001). Hamiltonian formulation of distributed-parameter systems with boundary energy flow. (Memorandum / Faculty of Mathematical Sciences; No. 1586). Enschede: University of Twente, Faculty of Mathematical Sciences.
van der Schaft, A.J. ; Maschke, B.M. / Hamiltonian formulation of distributed-parameter systems with boundary energy flow. Enschede : University of Twente, Faculty of Mathematical Sciences, 2001. 30 p. (Memorandum / Faculty of Mathematical Sciences; 1586).
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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.",
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van der Schaft, AJ & Maschke, BM 2001, Hamiltonian formulation of distributed-parameter systems with boundary energy flow. Memorandum / Faculty of Mathematical Sciences, no. 1586, University of Twente, Faculty of Mathematical Sciences, Enschede.

Hamiltonian formulation of distributed-parameter systems with boundary energy flow. / van der Schaft, A.J.; Maschke, B.M.

Enschede : University of Twente, Faculty of Mathematical Sciences, 2001. 30 p. (Memorandum / Faculty of Mathematical Sciences; No. 1586).

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - Hamiltonian formulation of distributed-parameter systems with boundary energy flow

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AU - Maschke, B.M.

N1 - Imported from MEMORANDA

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

KW - MSC-35B37

KW - MSC-35Q60

KW - MSC-70H05

KW - IR-65773

KW - MSC-93C20

KW - EWI-3406

KW - MSC-76N10

M3 - Report

T3 - Memorandum / Faculty of Mathematical Sciences

BT - Hamiltonian formulation of distributed-parameter systems with boundary energy flow

PB - University of Twente, Faculty of Mathematical Sciences

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van der Schaft AJ, Maschke BM. Hamiltonian formulation of distributed-parameter systems with boundary energy flow. Enschede: University of Twente, Faculty of Mathematical Sciences, 2001. 30 p. (Memorandum / Faculty of Mathematical Sciences; 1586).