Foundations of mechanics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
AMS Chelsea Publ.
2008
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Originally publ.: Reading, Mass. : Benjamin/Cummings Pub., 1978. Includes bibliographical references and index |
| Physical Description: | XXIV, 826 S. Ill., graph. Darst. |
| ISBN: | 9780821844380 |
Staff View
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| 100 | 1 | |a Abraham, Ralph |d 1936- |e Verfasser |0 (DE-588)115444254 |4 aut | |
| 245 | 1 | 0 | |a Foundations of mechanics |c Ralph Abraham ; Jerrold E. Marsden |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Providence, RI |b AMS Chelsea Publ. |c 2008 | |
| 300 | |a XXIV, 826 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 500 | |a Originally publ.: Reading, Mass. : Benjamin/Cummings Pub., 1978. | ||
| 500 | |a Includes bibliographical references and index | ||
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Record in the Search Index
| _version_ | 1804138012444983296 |
|---|---|
| adam_text | Contents
Preface
to the
AMS
Chelsea Edition
...................................xiii
Preface to the Second Edition
..........................................xv
Preface to the First Edition
............................................xvii
Introduction
............................................................xix
Preview
................................................................xx»·
PARTI PRELIMINARIES
1
Chapter
1.
Differential Theory
.........................3
1.1
Topology
..............................3
Exercises
..............................17
1.2
Finite-Dimensional Banach Spaces
...............17
Exercises
..............................19
1.3
Local Differential Calculus
...................20
Exercises
..............................30
1.4
Manifolds and Mappings
....................31
Exercises
..............................36
1.5
Vector Bundles
..........................37
Exercises
..............................41
1.6
The Tangent Bundle
.......................42
vil
vlil
CONTENTS
Exercises
..............................50
1.7 Tensors..............................52
Exercises
..............................59
Chapter
2.
Calculus on Manifolds
.....................60
2.1
Vector Fields as Dynamical Systems
..............60
Exercises
..............................78
2.2
Vector Fields as Differential Operators
.............78
Exercises
..............................98
2.3
Exterior Algebra
.........................101
Exercises
.............................109
2.4
Cartan s Calculus of Differential Forms
...........109
Exercises
.............................121
2.5
Orientable
Manifolds
......................122
Exercises
.............................131
2.6
Integration on Manifolds
....................131
Exercises
.............................143
2.7
Some Riemannian Geometry
..................144
Exercises
.............................156
PART II ANAL YTICAL DYNAMICS
159
Chapters. Hamiltonian and Lagrangian Systems
............161
3.1
Symplectic Algebra
.......................161
Exercises
.............................174
3.2
Symplectic Geometry
......................174
Exercises
.............................185
3.3
Hamiltonian Vector Fields and
Poisson
Brackets
......187
Exercises
.............................199
3.4
Integral Invariants, Energy Surfaces, and Stability
.....201
Exercises
.............................208
3.5
Lagrangian Systems
.......................208
Exercises
.............................217
3.6
The Legendre Transformation
.................218
Exercises
.............................223
3.7
Mechanics on Riemannian Manifolds
.............224
Exercises
.............................244
3.8
Variational Principles in Mechanics
..............246
Exercises
.............................252
Chapter
4.
Hamiltonian Systems with Symmetry
............253
4.1
Lie Groups and Group Actions
................253
Exercises
.............................271
CONTENTS
lx
4.2
The Momentum Mapping
...................276
Exercises
.............................295
4.3
Reduction of Phase Spaces with Symmetry
..........298
Exercises
.............................309
4.4
Hamiltonian Systems on Lie Groups and the Rigid Body
. .311
Exercises
............................. 338
4.5
The Topology of Simple Mechanical Systems
........338
Exercises
.............................359
4.6
The Topology of the Rigid Body
................360
Exercises
.............................368
Chapter
5.
Hamllton-Jacobi Theory and Mathematical Physics
.... 370
5.1
Time-Dependent Systems
....................370
Exercises
.............................378
5.2
Canonical Transformations and Hamilton-Jacobi Theory
. 379
Exercises
.............................400
5.3
Lagrangian Submanifolds
...................402
Exercises
.............................420
5.4
Quantization
...........................425
5.5
Introduction to Infinite-Dimensional Hamiltonian Systems
.453
Exercises
.............................486
5.6
Introduction to Nonlinear Oscillations
............489
PART III AN OUTLINE OF QUALITATIVE DYNAMICS
507
Chapter
6.
Topologica!
Dynamics
.....................509
6.1
Limit and Minimal Sets
.....................509
Exercises
.............................513
6.2
Recurrence
............................513
Exercises
.............................515
6.3
Stability
.............................515
Exercises
.............................519
Chapter
7.
Differentiable Dynamics
....................520
7.1
Critical Elements
........................520
Exercises
.............................525
7.2
Stable Manifolds
........................525
Exercises
.............................531
7.3
Generic Properties
........................531
Exercises
.............................534
7.4
Structural Stability
.......................534
Exercises
.............................536
ι
CONTENTS
7.5
Absolute Stability and Axiom A
................536
Exercises
.............................542
7.6
Bifurcations of Generic Arcs
..................543
Exercises
.............................548
7.7
A Zoo of Stable Bifurcations
..................548
7.8
Experimental Dynamics
....................570
Chapter
8.
Hamiltonian Dynamics
.....................572
8.1
Critical Elements
........................572
8.2
Orbit Cylinders
.........................576
Exercises
.............................579
8.3
Stability of Orbits
........................579
Exercises
.............................587
8.4
Generic Properties
........................587
8.5
Structural Stability
.......................592
8.6
A Zoo of Stable Bifurcations
..................595
8.7
The General Pathology
.....................606
8.8
Experimental Mechanics
....................610
PART IV CELESTIAL MECHANICS
617
ChapterD. The Two-Body Problem
....................619
9.1
Models for Two Bodies
.....................619
Exercises
.............................624
9.2
Elliptic Orbits and Kepler Elements
..............624
9.3
The Delaunay Variables
....................631
9.4 Lagrange
Brackets of Kepler Elements
............635
9.5
Whittaker s Method
.......................638
9.6
Poincaré
Variables
.......................647
Exercises
.............................652
9.7
Summary of Models
.......................652
Exercise
.............................656
9.8
Topology of the Two-Body Problem
.............656
Chapter
10.
The Three-Body Problem
...................663
10.1 Models for Three Bodies
....................663
Exercises
.............................673
10.2
Critical Points in the Restricted Three-Body Problem
. . . .675
Exercises
.............................687
10.3
Closed Orbits in the Restricted Three-Body Problem
.... 688
Exercises
.............................699
10.4
Topology of the Planar
л
-Body
Problem
...........699
CONTENTS xl
Appendix
The General Theory of Dynamical Systems and
Classical Mechanics by A.
N.
Kolmogorov
..........741
Bibliography
...................................759
Index
.......................................791
Glossary of Symbols
...................................................807
Errata
..................................................................809
|
| adam_txt |
Contents
Preface
to the
AMS
Chelsea Edition
.xiii
Preface to the Second Edition
.xv
Preface to the First Edition
.xvii
Introduction
.xix
Preview
.xx»·
PARTI PRELIMINARIES
1
Chapter
1.
Differential Theory
.3
1.1
Topology
.3
Exercises
.17
1.2
Finite-Dimensional Banach Spaces
.17
Exercises
.19
1.3
Local Differential Calculus
.20
Exercises
.30
1.4
Manifolds and Mappings
.31
Exercises
.36
1.5
Vector Bundles
.37
Exercises
.41
1.6
The Tangent Bundle
.42
vil
vlil
CONTENTS
Exercises
.50
1.7 Tensors.52
Exercises
.59
Chapter
2.
Calculus on Manifolds
.60
2.1
Vector Fields as Dynamical Systems
.60
Exercises
.78
2.2
Vector Fields as Differential Operators
.78
Exercises
.98
2.3
Exterior Algebra
.101
Exercises
.109
2.4
Cartan's Calculus of Differential Forms
.109
Exercises
.121
2.5
Orientable
Manifolds
.122
Exercises
.131
2.6
Integration on Manifolds
.131
Exercises
.143
2.7
Some Riemannian Geometry
.144
Exercises
.156
PART II ANAL YTICAL DYNAMICS
159
Chapters. Hamiltonian and Lagrangian Systems
.161
3.1
Symplectic Algebra
.161
Exercises
.174
3.2
Symplectic Geometry
.174
Exercises
.185
3.3
Hamiltonian Vector Fields and
Poisson
Brackets
.187
Exercises
.199
3.4
Integral Invariants, Energy Surfaces, and Stability
.201
Exercises
.208
3.5
Lagrangian Systems
.208
Exercises
.217
3.6
The Legendre Transformation
.218
Exercises
.223
3.7
Mechanics on Riemannian Manifolds
.224
Exercises
.244
3.8
Variational Principles in Mechanics
.246
Exercises
.252
Chapter
4.
Hamiltonian Systems with Symmetry
.253
4.1
Lie Groups and Group Actions
.253
Exercises
.271
CONTENTS
lx
4.2
The Momentum Mapping
.276
Exercises
.295
4.3
Reduction of Phase Spaces with Symmetry
.298
Exercises
.309
4.4
Hamiltonian Systems on Lie Groups and the Rigid Body
. .311
Exercises
. 338
4.5
The Topology of Simple Mechanical Systems
.338
Exercises
.359
4.6
The Topology of the Rigid Body
.360
Exercises
.368
Chapter
5.
Hamllton-Jacobi Theory and Mathematical Physics
. 370
5.1
Time-Dependent Systems
.370
Exercises
.378
5.2
Canonical Transformations and Hamilton-Jacobi Theory
. 379
Exercises
.400
5.3
Lagrangian Submanifolds
.402
Exercises
.420
5.4
Quantization
.425
5.5
Introduction to Infinite-Dimensional Hamiltonian Systems
.453
Exercises
.486
5.6
Introduction to Nonlinear Oscillations
.489
PART III AN OUTLINE OF QUALITATIVE DYNAMICS
507
Chapter
6.
Topologica!
Dynamics
.509
6.1
Limit and Minimal Sets
.509
Exercises
.513
6.2
Recurrence
.513
Exercises
.515
6.3
Stability
.515
Exercises
.519
Chapter
7.
Differentiable Dynamics
.520
7.1
Critical Elements
.520
Exercises
.525
7.2
Stable Manifolds
.525
Exercises
.531
7.3
Generic Properties
.531
Exercises
.534
7.4
Structural Stability
.534
Exercises
.536
ι
CONTENTS
7.5
Absolute Stability and Axiom A
.536
Exercises
.542
7.6
Bifurcations of Generic Arcs
.543
Exercises
.548
7.7
A Zoo of Stable Bifurcations
.548
7.8
Experimental Dynamics
.570
Chapter
8.
Hamiltonian Dynamics
.572
8.1
Critical Elements
.572
8.2
Orbit Cylinders
.576
Exercises
.579
8.3
Stability of Orbits
.579
Exercises
.587
8.4
Generic Properties
.587
8.5
Structural Stability
.592
8.6
A Zoo of Stable Bifurcations
.595
8.7
The General Pathology
.606
8.8
Experimental Mechanics
.610
PART IV CELESTIAL MECHANICS
617
ChapterD. The Two-Body Problem
.619
9.1
Models for Two Bodies
.619
Exercises
.624
9.2
Elliptic Orbits and Kepler Elements
.624
9.3
The Delaunay Variables
.631
9.4 Lagrange
Brackets of Kepler Elements
.635
9.5
Whittaker's Method
.638
9.6
Poincaré
Variables
.647
Exercises
.652
9.7
Summary of Models
.652
Exercise
.656
9.8
Topology of the Two-Body Problem
.656
Chapter
10.
The Three-Body Problem
.663
10.1 Models for Three Bodies
.663
Exercises
.673
10.2
Critical Points in the Restricted Three-Body Problem
. . . .675
Exercises
.687
10.3
Closed Orbits in the Restricted Three-Body Problem
. 688
Exercises
.699
10.4
Topology of the Planar
л
-Body
Problem
.699
CONTENTS xl
Appendix
The General Theory of Dynamical Systems and
Classical Mechanics by A.
N.
Kolmogorov
.741
Bibliography
.759
Index
.791
Glossary of Symbols
.807
Errata
.809 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Abraham, Ralph 1936- Marsden, Jerrold E. 1942-2010 |
| author_GND | (DE-588)115444254 (DE-588)124171141 |
| author_facet | Abraham, Ralph 1936- Marsden, Jerrold E. 1942-2010 |
| author_role | aut aut |
| author_sort | Abraham, Ralph 1936- |
| author_variant | r a ra j e m je jem |
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| bvnumber | BV035066162 |
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| callnumber-raw | QA805 |
| callnumber-search | QA805 |
| callnumber-sort | QA 3805 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 950 UF 1000 |
| classification_tum | PHY 200f |
| ctrlnum | (OCoLC)191847156 (DE-599)BVBBV035066162 |
| dewey-full | 531.01/515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531.01/515 |
| dewey-search | 531.01/515 |
| dewey-sort | 3531.01 3515 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| discipline_str_mv | Physik Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV035066162 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:02:20Z |
| indexdate | 2024-07-09T21:21:25Z |
| institution | BVB |
| isbn | 9780821844380 |
| language | English |
| lccn | 2008005206 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016734611 |
| oclc_num | 191847156 |
| open_access_boolean | |
| owner | DE-29T DE-703 DE-83 DE-91G DE-BY-TUM DE-20 DE-19 DE-BY-UBM DE-11 |
| owner_facet | DE-29T DE-703 DE-83 DE-91G DE-BY-TUM DE-20 DE-19 DE-BY-UBM DE-11 |
| physical | XXIV, 826 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | AMS Chelsea Publ. |
| record_format | marc |
| spelling | Abraham, Ralph 1936- Verfasser (DE-588)115444254 aut Foundations of mechanics Ralph Abraham ; Jerrold E. Marsden 2. ed. Providence, RI AMS Chelsea Publ. 2008 XXIV, 826 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Originally publ.: Reading, Mass. : Benjamin/Cummings Pub., 1978. Includes bibliographical references and index Géométrie différentielle Mécanique analytique Mécanique céleste Mechanics, Analytic Geometry, Differential Celestial mechanics Dynamik (DE-588)4013384-9 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Himmelsmechanik (DE-588)4127484-2 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Theoretische Mechanik (DE-588)4185100-6 gnd rswk-swf Theoretische Mechanik (DE-588)4185100-6 s DE-604 Mechanik (DE-588)4038168-7 s Mathematik (DE-588)4037944-9 s 1\p DE-604 Differentialgeometrie (DE-588)4012248-7 s 2\p DE-604 Himmelsmechanik (DE-588)4127484-2 s 3\p DE-604 Dynamik (DE-588)4013384-9 s 4\p DE-604 Marsden, Jerrold E. 1942-2010 Verfasser (DE-588)124171141 aut Erscheint auch als Online-Ausgabe 978-1-4704-1134-3 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016734611&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Abraham, Ralph 1936- Marsden, Jerrold E. 1942-2010 Foundations of mechanics Géométrie différentielle Mécanique analytique Mécanique céleste Mechanics, Analytic Geometry, Differential Celestial mechanics Dynamik (DE-588)4013384-9 gnd Mechanik (DE-588)4038168-7 gnd Differentialgeometrie (DE-588)4012248-7 gnd Himmelsmechanik (DE-588)4127484-2 gnd Mathematik (DE-588)4037944-9 gnd Theoretische Mechanik (DE-588)4185100-6 gnd |
| subject_GND | (DE-588)4013384-9 (DE-588)4038168-7 (DE-588)4012248-7 (DE-588)4127484-2 (DE-588)4037944-9 (DE-588)4185100-6 |
| title | Foundations of mechanics |
| title_auth | Foundations of mechanics |
| title_exact_search | Foundations of mechanics |
| title_exact_search_txtP | Foundations of mechanics |
| title_full | Foundations of mechanics Ralph Abraham ; Jerrold E. Marsden |
| title_fullStr | Foundations of mechanics Ralph Abraham ; Jerrold E. Marsden |
| title_full_unstemmed | Foundations of mechanics Ralph Abraham ; Jerrold E. Marsden |
| title_short | Foundations of mechanics |
| title_sort | foundations of mechanics |
| topic | Géométrie différentielle Mécanique analytique Mécanique céleste Mechanics, Analytic Geometry, Differential Celestial mechanics Dynamik (DE-588)4013384-9 gnd Mechanik (DE-588)4038168-7 gnd Differentialgeometrie (DE-588)4012248-7 gnd Himmelsmechanik (DE-588)4127484-2 gnd Mathematik (DE-588)4037944-9 gnd Theoretische Mechanik (DE-588)4185100-6 gnd |
| topic_facet | Géométrie différentielle Mécanique analytique Mécanique céleste Mechanics, Analytic Geometry, Differential Celestial mechanics Dynamik Mechanik Differentialgeometrie Himmelsmechanik Mathematik Theoretische Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016734611&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT abrahamralph foundationsofmechanics AT marsdenjerrolde foundationsofmechanics |