Lagrangian & Hamiltonian dynamics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford University Press
2018
|
| Ausgabe: | First edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | xiv, 538 Seiten Illustrationen, Diagramme (teilweise farbig) |
| ISBN: | 9780198822370 9780198822387 |
Internformat
MARC
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| 245 | 1 | 0 | |a Lagrangian & Hamiltonian dynamics |c Peter Mann, University of St Andrews |
| 246 | 1 | 3 | |a Langrangian and Hamiltonian dynamics |
| 250 | |a First edition | ||
| 264 | 1 | |a Oxford |b Oxford University Press |c 2018 | |
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Datensatz im Suchindex
| _version_ | 1804178477263355904 |
|---|---|
| adam_text | Contents
A
Preface xiii
PART I NEWTONIAN MECHANICS
1 Newton’s Three Laws 3
1.1 Phase Space 7
1.2 Systems of Particles 8
1.3 The N-body Problem 11
Chapter summary 13
2 Energy and Work 15
Chapter summary 22
3 Introductory Rotational Dynamics 24
Chapter summary 33
4 The Harmonic Oscillator 34
Chapter summary 38
5 Wave Mechanics fe Elements of Mathematical Physics 44
PART II LAGRANGIAN MECHANICS
6 Coordinates 8z Constraints 55
Chapter summary 59
7 The Stationary Action Principle 61
7.1 The Inverse Problem 70
7.2 Higher-Order Theories the Ostrogradsky Equation 72
7.3 The Second Variation 73
7.4 Functions Functionals 74
7.5 Boundary Conditions 76
7.6 Variations 78
7.7 Weierstrass-Erdmann Conditions for Broken Extremals 79
7.8 Hamilton-Suslov Principle 79
Chapter summary 80
8 Constrained Lagrangian Mechanics 89
8.1 Holonomic Constraints 89
viii Contents
8.2 Non-Holonomic Constraints 93
Chapter summary 96
9 Point Transformations in Lagrangian Mechanics 100
Chapter summary 103
10 The Jacobi Energy Function 107
Chapter summary 112
11 Symmetries Lagrangian-Hamilton-Jacobi Theory 115
11.1 Noether’s Theorem 115
11.2 Gauge Theory 120
11.3 Isotropic Symmetries 122
11.4 Caratheodory-Hamilton-Jacobi theory 123
Chapter summary 124
12 Near-Equilibrium Oscillations 130
12.1 Normal Modes 137
Chapter summary 140
13 Virtual Work d’Alembert’s Principle 147
13.1 Gauss’s Least Constraint Jourdain’s Principle 153
13.2 The Gibbs-Appell Equations 156
Chapter summary 158
PART III CANONICAL MECHANICS
14 The Hamiltonian Phase Space 167
Chapter summary 172
15 Hamilton’s Principle in Phase Space 174
Chapter summary 178
16 Hamilton’s Equations Routhian Reduction 179
16.1 Phase Space Conservation Laws 181
16.2 Routhian Mechanics 183
17 Poisson Brackets ; Angular Momentum 190
17.1 Poisson Brackets Angular Momenta 195
17.2 Poisson Brackets Symmetries 197
Chapter summary 200
18 Canonical ; Gauge Transformations 202
18.1 Canonical Transformations I 202
18.2 Canonical Transformations II 206
Contents ix
18.3 Infinitesimal Canonical Transformations 211
Chapter summary 214
19 Hamilton-Jacobi Theory 217
19.1 Hamilton-Jacobi Theory I 217
19.2 Hamilton-Jacobi Theory II 224
Chapter summary 229
20 Liouville’s Theorem ; Classical Statistical Mechanics 237
20.1 Liouville’s Theorem k the Classical Propagator 237
20.2 Koopman-von Neumann Theory 244
20.3 Classical Statistical Mechanics 246
20.4 Symplectic Integrators 255
Chapter summary 259
21 Constrained Hamiltonian Dynamics 267
Chapter summary 274
22 Autonomous Geometrical Mechanics 277
22.1 A Coordinate-Free Picture 284
22.2 Poisson Manifolds k Symplectic Reduction 291
22.3 Geometrical Lagrangian Mechanics 296
22.4 Elements of Constrained Geometry 300
Chapter summary 303
23 The Structure of Phase Space 309
23.1 Time-Dependent Geometrical Mechanics 313
23.2 Picturing Phase Space 319
Chapter summary 322
24 Near-Integrable Systems 325
24.1 Canonical Perturbation Theory 325
24.2 KAM Theory k Elements of Chaos 333
PART IV CLASSICAL FIELD THEORY
25 Lagrangian Field Theory 345
Chapter summary 350
26 Hamiltonian Field Theory 353
27 Classical Electromagnetism 357
Chapter summary 365
x Contents
28 Noether’s Theorem for Fields
Chapter summary
29 Classical Path-Integrals
29.1 Configuration Space Integrals
29.2 Phase Space Integrals
PART V PRELIMINARY MATHEMATICS
30 The (Not So?) Basics
31 Matrices
32 Partial Differentiation
33 Legendre Transforms
34 Vector Calculus
35 Differential Equations
36 Calculus of Variations
PART VI ADVANCED MATHEMATICS
37 Linear Algebra
38 Differential Geometry
PART VII EXAM-STYLE QUESTIONS
Appendix A Noether’s Theorem Explored
Appendix B The Action Principle Explored
B.l Geodesics
Appendix C Useful Relations
Appendix D Poisson ; Nambu Brackets Explored
D.l Symplectic Notation Nambu Brackets
Appendix E Canonical Transformations Explored
Appendix F Action-Angle Variables Explored
Appendix G Statistical Mechanics Explored
G.l The Boltzmann Factor
G.2 Fluctuations
369
376
385
385
386
397
400
406
419
422
437
443
453
460
487
491
491
494
496
497
502
506
511
511
512
Contents xi
Appendix H Biographies 514
H.l Sir Isaac Newton 514
H.2 Leonhard Euler 515
H.3 Jean d’Alembert 516
H.4 Joseph-Louis Lagrange 517
H.5 Carl Gustav Jacobi 519
H.6 Sir William Hamilton 520
H.7 Siméon Denis Poisson 522
H.8 Amalie Emmy Noether 522
H.9 Ludwig Eduard Boltzmann 524
H.10 Edward Routh 525
H.ll Hendrika van Leeuwen 526
Bibliography
Index
527
533
An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics with a
relaxed and self-contained setting, for those unacquainted with mathematics or university level
physics. Lagrangian and Hamiltonian dynamics is the continuation of Newton’s classical physics
into new formalisms, each highlighting novel aspects of mechanics and gradually building in
complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian
dynamics also acts as a gateway to more abstract concepts rooted in differential geometry
and field theories and can be used to introduce these subject areas to newcomers.
Journeying in a self-contained manner from the very basics, through the fundamentals
and onwards to the cutting edge of the subject, along the way the reader is supported by
all the necessary background mathematics, fully worked examples and thoughtful and
vibrant illustrations, as well as an informal narrative and numerous fresh, modern and
interdisciplinary applications.
The book contains some unusual topics for a classical mechanics textbook: notable examples
include the classical wavefunction’, Koopman-von Neumann theory, classical density functional
theories, the ‘vakonomic’ variational principle for non-holonomic constraints, the Gibbs-Appell
equations, classical path integrals. Nambu brackets and the full framing of mechanics in the
language of differential geometry. Alongside these is a very detailed and explicit account of
Lagrangian and Hamiltonian dynamics, an account that ventures above and beyond that
presented in most undergraduate courses.
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| discipline | Physik |
| edition | First edition |
| format | Book |
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| id | DE-604.BV044913482 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:04:35Z |
| institution | BVB |
| isbn | 9780198822370 9780198822387 |
| language | English |
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| oclc_num | 1037947443 |
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| physical | xiv, 538 Seiten Illustrationen, Diagramme (teilweise farbig) |
| publishDate | 2018 |
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| publisher | Oxford University Press |
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| spelling | Mann, Peter Verfasser (DE-588)1169874851 aut Lagrangian & Hamiltonian dynamics Peter Mann, University of St Andrews Langrangian and Hamiltonian dynamics First edition Oxford Oxford University Press 2018 xiv, 538 Seiten Illustrationen, Diagramme (teilweise farbig) txt rdacontent n rdamedia nc rdacarrier Lagrange-Formalismus (DE-588)4316154-6 gnd rswk-swf Hamilton-Formalismus (DE-588)4376155-0 gnd rswk-swf Theoretische Mechanik (DE-588)4185100-6 gnd rswk-swf Theoretische Mechanik (DE-588)4185100-6 s Lagrange-Formalismus (DE-588)4316154-6 s Hamilton-Formalismus (DE-588)4376155-0 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030306943&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030306943&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Mann, Peter Lagrangian & Hamiltonian dynamics Lagrange-Formalismus (DE-588)4316154-6 gnd Hamilton-Formalismus (DE-588)4376155-0 gnd Theoretische Mechanik (DE-588)4185100-6 gnd |
| subject_GND | (DE-588)4316154-6 (DE-588)4376155-0 (DE-588)4185100-6 |
| title | Lagrangian & Hamiltonian dynamics |
| title_alt | Langrangian and Hamiltonian dynamics |
| title_auth | Lagrangian & Hamiltonian dynamics |
| title_exact_search | Lagrangian & Hamiltonian dynamics |
| title_full | Lagrangian & Hamiltonian dynamics Peter Mann, University of St Andrews |
| title_fullStr | Lagrangian & Hamiltonian dynamics Peter Mann, University of St Andrews |
| title_full_unstemmed | Lagrangian & Hamiltonian dynamics Peter Mann, University of St Andrews |
| title_short | Lagrangian & Hamiltonian dynamics |
| title_sort | lagrangian hamiltonian dynamics |
| topic | Lagrange-Formalismus (DE-588)4316154-6 gnd Hamilton-Formalismus (DE-588)4376155-0 gnd Theoretische Mechanik (DE-588)4185100-6 gnd |
| topic_facet | Lagrange-Formalismus Hamilton-Formalismus Theoretische Mechanik |
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