Introduction to Hamiltonian fluid dynamics and stability theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2000
|
| Schriftenreihe: | Chapman & Hall/CRC monographs and surveys in pure and applied mathematics
102 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 274 S. |
| ISBN: | 1584880236 |
Internformat
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| 650 | 7 | |a Fluides, Dynamique des |2 ram | |
| 650 | 4 | |a Hamiltonian sistemler | |
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Datensatz im Suchindex
| _version_ | 1804127857953210368 |
|---|---|
| adam_text | Titel: Introduction to Hamiltonian fluid dynamics and stability theory
Autor: Swaters, Gordon E
Jahr: 2000
Contents
1 Introduction 1
2 The nonlinear pendulum 9
2.1 Model formulation.....................9
2.2 Canonical Hamiltonian formulation..............10
2.3 Least Action Principle ...................12
2.4 Symplectic Hamiltonian formulation .............14
2.5 Mathematical properties of the J matrix ...........16
2.6 Poisson bracket formulation.................18
2.7 Steady solutions of a canonical Hamiltonian system ......26
2.8 Linear stability of a steady solution .............28
2.9 Nonlinear stability of a steady solution............35
3 The two dimensional Euler equations 43
3.1 Vorticity equation formulation................43
3.2 Hamiltonian structure for partial differential equations .....50
3.3 Hamiltonian structure of the Euler equations .........56
3.4 Reduction of the canonical Poisson bracket ..........69
3.5 Casimir functionals.....................80
3.6 Noether s Theorem.....................83
3.7 Exercises .........................91
4 Stability of steady Euler flows 93
4.1 Steady solutions of the vorticity equation...........93
4.2 Linear stability problem .................100
4.3 Normal mode equations for parallel shear flows .......101
4.4 Linear stability theorems .................105
4.5 Nonlinear stability theorems................114
4.6 Andrews s Theorem ...................123
4.7 Flows with special symmetries...............127
4.8 Exercises ........................141
5 The Charney-Hasegawa-Mima equation 143
5.1 A derivation of the CHM equation.............145
5.2 Hamiltonian structure ..................151
5.3 Steady solutions.....................155
5.4 Stability of steady solutions................158
5.5 Steadily-travelling solutions................181
5.6 Exercises........................202
6 The KdV equation 205
6.1 A derivation of the Ad V equation .............205
6.2 Hamiltonian structure ..................212
6.3 Periodic and soliton solutions ...............220
6.4 Variational principles...................224
6.4 Linear stability .....................227
6.5 Nonlinear stability....................239
6.6 Exercises........................260
References .........................263
Index............................269
|
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| author | Swaters, Gordon E. |
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| ctrlnum | (OCoLC)42659450 (DE-599)BVBBV013157737 |
| dewey-full | 532/.05 514.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics 514 - Topology |
| dewey-raw | 532/.05 514.74 |
| dewey-search | 532/.05 514.74 |
| dewey-sort | 3532 15 |
| dewey-tens | 530 - Physics 510 - Mathematics |
| discipline | Physik Mathematik |
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| id | DE-604.BV013157737 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:40:01Z |
| institution | BVB |
| isbn | 1584880236 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008965034 |
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| physical | 274 S. |
| publishDate | 2000 |
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| publisher | Chapman & Hall/CRC |
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| series | Chapman & Hall/CRC monographs and surveys in pure and applied mathematics |
| series2 | Chapman & Hall/CRC monographs and surveys in pure and applied mathematics |
| spelling | Swaters, Gordon E. Verfasser aut Introduction to Hamiltonian fluid dynamics and stability theory Gordon E. Swaters Boca Raton [u.a.] Chapman & Hall/CRC 2000 274 S. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC monographs and surveys in pure and applied mathematics 102 Dinâmica dos fluídos larpcal Fluides, Dynamique des ram Hamiltonian sistemler Stabilite Stabilité ram Systèmes hamiltoniens ram Sıvı dinamiği Fluid dynamics Hamiltonian systems Stability Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 s Hamiltonsches System (DE-588)4139943-2 s Stabilität (DE-588)4056693-6 s DE-604 Chapman & Hall/CRC monographs and surveys in pure and applied mathematics 102 (DE-604)BV013350872 102 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008965034&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Swaters, Gordon E. Introduction to Hamiltonian fluid dynamics and stability theory Chapman & Hall/CRC monographs and surveys in pure and applied mathematics Dinâmica dos fluídos larpcal Fluides, Dynamique des ram Hamiltonian sistemler Stabilite Stabilité ram Systèmes hamiltoniens ram Sıvı dinamiği Fluid dynamics Hamiltonian systems Stability Strömungsmechanik (DE-588)4077970-1 gnd Stabilität (DE-588)4056693-6 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| subject_GND | (DE-588)4077970-1 (DE-588)4056693-6 (DE-588)4139943-2 |
| title | Introduction to Hamiltonian fluid dynamics and stability theory |
| title_auth | Introduction to Hamiltonian fluid dynamics and stability theory |
| title_exact_search | Introduction to Hamiltonian fluid dynamics and stability theory |
| title_full | Introduction to Hamiltonian fluid dynamics and stability theory Gordon E. Swaters |
| title_fullStr | Introduction to Hamiltonian fluid dynamics and stability theory Gordon E. Swaters |
| title_full_unstemmed | Introduction to Hamiltonian fluid dynamics and stability theory Gordon E. Swaters |
| title_short | Introduction to Hamiltonian fluid dynamics and stability theory |
| title_sort | introduction to hamiltonian fluid dynamics and stability theory |
| topic | Dinâmica dos fluídos larpcal Fluides, Dynamique des ram Hamiltonian sistemler Stabilite Stabilité ram Systèmes hamiltoniens ram Sıvı dinamiği Fluid dynamics Hamiltonian systems Stability Strömungsmechanik (DE-588)4077970-1 gnd Stabilität (DE-588)4056693-6 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| topic_facet | Dinâmica dos fluídos Fluides, Dynamique des Hamiltonian sistemler Stabilite Stabilité Systèmes hamiltoniens Sıvı dinamiği Fluid dynamics Hamiltonian systems Stability Strömungsmechanik Stabilität Hamiltonsches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008965034&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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