Lagrangian reduction by stages:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
2001
|
| Series: | Memoirs of the American Mathematical Society
722 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Volume 152, Number 722 (third of 5 numbers) |
| Physical Description: | IX, 108 S. |
| ISBN: | 0821827154 |
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Record in the Search Index
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| adam_text | Contents
Chapter 1. Introduction 1
1.1. Background 1
1.2. The Main Results of This Paper. 3
1.3. Future Work and Related Issues. 4
Chapter 2. Preliminary Constructions 7
2.1. Notation and general assumptions. 7
2.2. Connections on Principal Bundles. 8
2.3. Associated Bundles. 10
2.4. The Bundles TQ/G and T(Q/G) 0 jj 14
Chapter 3. The Lagrange Poincare Equations 17
3.1. The Geometry of Variations 17
3.2. The Euler Lagrange and Euler Poincare Operators 21
3.3. The Lagrange Poincare Operator 28
3.4. The Reduced Variational Principle 34
Chapter 4. Wong s Equations and Coordinate Formulas 37
4.1. Wong s Equations 37
4.2. The Local Vertical and Horizontal Equations 38
Chapter 5. The Lie Algebra Structure on Sections of the Reduced Bundle 43
5.1. The Bundle T(Q/G) 0 0 Revisited 43
5.2. The Lie Algebra of Sections of T(Q/G) © 0 45
Chapter 6. Reduced Tangent Bundles 51
6.1. The Geometry of Lagrange Poincare Bundles 52
6.2. Reduction of Lagrange Poincare Bundles 61
6.3. Reduction by Stages of objects of £«P 71
6.4. The Subcategory WI and Reduction by Stages of Variational
Principles on TQ. 78
Chapter 7. Further Examples 85
7.1. Semidirect Products 85
7.2. Central Extensions 86
7.3. Rigid Body with Rotors 88
7.4. Systems Depending on a Parameter 88
Chapter 8. The Category £*p* and Poisson Geometry 95
8.1. The Poisson Bracket on Duals of Objects of £ P 95
vii
viii CONTENTS
8.2. Poisson Reduction in the Category £^3* Viewed as Dual to Reduction
in the Category £ P 100
Bibliography 103
|
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| author | Cendra, Hernán 1943- Marsden, Jerrold E. 1942-2010 Ratiu, Tudor S. 1950- |
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| id | DE-604.BV013868537 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:53:27Z |
| institution | BVB |
| isbn | 0821827154 |
| language | English |
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| physical | IX, 108 S. |
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| spelling | Cendra, Hernán 1943- Verfasser (DE-588)1146330146 aut Lagrangian reduction by stages Hernán Cendra ; Jerrold E. Marsden ; Tudor S. Ratiu Providence, RI American Mathematical Society 2001 IX, 108 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 722 Volume 152, Number 722 (third of 5 numbers) Differenzierbare Mannigfaltigkeit - Lagrange-Bewegungsgleichungen Variationsprinzip (DE-588)4062354-3 gnd rswk-swf Lagrange-Gleichungen (DE-588)4166461-9 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Variationsprinzip (DE-588)4062354-3 s Lagrange-Gleichungen (DE-588)4166461-9 s Differenzierbares dynamisches System (DE-588)4137931-7 s DE-604 Marsden, Jerrold E. 1942-2010 Verfasser (DE-588)124171141 aut Ratiu, Tudor S. 1950- Verfasser (DE-588)172325838 aut Memoirs of the American Mathematical Society 722 (DE-604)BV008000141 722 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009485974&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cendra, Hernán 1943- Marsden, Jerrold E. 1942-2010 Ratiu, Tudor S. 1950- Lagrangian reduction by stages Memoirs of the American Mathematical Society Differenzierbare Mannigfaltigkeit - Lagrange-Bewegungsgleichungen Variationsprinzip (DE-588)4062354-3 gnd Lagrange-Gleichungen (DE-588)4166461-9 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| subject_GND | (DE-588)4062354-3 (DE-588)4166461-9 (DE-588)4137931-7 |
| title | Lagrangian reduction by stages |
| title_auth | Lagrangian reduction by stages |
| title_exact_search | Lagrangian reduction by stages |
| title_full | Lagrangian reduction by stages Hernán Cendra ; Jerrold E. Marsden ; Tudor S. Ratiu |
| title_fullStr | Lagrangian reduction by stages Hernán Cendra ; Jerrold E. Marsden ; Tudor S. Ratiu |
| title_full_unstemmed | Lagrangian reduction by stages Hernán Cendra ; Jerrold E. Marsden ; Tudor S. Ratiu |
| title_short | Lagrangian reduction by stages |
| title_sort | lagrangian reduction by stages |
| topic | Differenzierbare Mannigfaltigkeit - Lagrange-Bewegungsgleichungen Variationsprinzip (DE-588)4062354-3 gnd Lagrange-Gleichungen (DE-588)4166461-9 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| topic_facet | Differenzierbare Mannigfaltigkeit - Lagrange-Bewegungsgleichungen Variationsprinzip Lagrange-Gleichungen Differenzierbares dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009485974&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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