### Abstract

Original language | English |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Faculty of Mathematical Sciences |

Number of pages | 30 |

Publication status | Published - 2001 |

### Publication series

Name | Memorandum / Faculty of Mathematical Sciences |
---|---|

Publisher | University of Twente, Faculty of Mathematical Sciences |

No. | 1586 |

ISSN (Print) | 0169-2690 |

### Fingerprint

### Keywords

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

### Cite this

*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.

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*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.

Research output: Book/Report › Report › Other research output

TY - BOOK

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

AU - van der Schaft, A.J.

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

CY - Enschede

ER -