Classical mechanics:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Upper Saddle River, NJ
Pearson/Addison-Wesley
2002
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Pearson international edition
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 638 S. Ill., graph. Darst. |
| ISBN: | 9780321188977 |
Internformat
MARC
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| 264 | 1 | |a Upper Saddle River, NJ |b Pearson/Addison-Wesley |c 2002 | |
| 300 | |a XVIII, 638 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1808229327580430336 |
|---|---|
| adam_text |
Contents
1 ■
Survey of the Elementary Principles
1
1.1
Mechanics of a Particle
1
1.2
Mechanics of a System of Particles
5
1.3
Constraints
12
1.4
D' Alembert's Principle and Lagrange's Equations
16
1.5
Velocity-Dependent Potentials and the Dissipation Function
22
1.6
Simple Applications of the Lagrangian Formulation
24
2 ■
Variational Principles and Lagrange's Equations
34
2.1
Hamilton's Principle
34
2.2
Some Techniques of the Calculus of Variations
36
2.3
Derivation of Lagrange's Equations from Hamilton's Principle
44
2.4
Extending Hamilton's Principle to Systems with Constraints
45
2.5
Advantages of a Variational Principle Formulation
51
2.6
Conservation Theorems and Symmetry Properties
54
2.7
Energy Function and the Conservation of Energy
60
3 ■
The Central Force Problem
70
3.1
Reduction to the Equivalent One-Body Problem
70
3.2
The Equations of Motion and First Integrals
72
3.3
The Equivalent One-Dimensional Problem, and
Classification of Orbits
76
3.4
The Virial Theorem
83
3.5
The Differential Equation for the Orbit, and
Integrable
Power-Law Potentials
86
3.6
Conditions for Closed Orbits (Bertrand's Theorem)
89
3.7
The Kepler Problem: Inverse-Square Law of Force
92
3.8
The Motion in Time in the Kepler Problem
98
3.9
The Laplace-Runge-Lenz Vector
102
3.10
Scattering in a Central Force Field
106
3.11
Transformation of the Scattering Problem to Laboratory
Coordinates
114
3.12
The Three-Body Problem
121
vi
Contents
4 ■
The Kinematics of Rigid Body Motion
134
4.1
The Independent Coordinates of a Rigid Body
134
4.2
Orthogonal Transformations
139
4.3
Formal Properties of the Transformation Matrix
144
4.4
The
Euler
Angles
150
4.5
The Cayley-Klein Parameters and Related Quantities
154
4.6
Euler's Theorem on the Motion of a Rigid Body
155
4.7
Finite Rotations
161
4.8
Infinitesimal Rotations
163
4.9
Rate of Change of a Vector
171
4.10
The Coriolis Effect
174
5 ■
The Rigid Body Equations of Motion
184
5.1
Angular Momentum and Kinetic Energy of Motion
about a Point
184
5.2
Tensors
188
5.3
The Inertia Tensor and the Moment of Inertia
191
5.4
The Eigenvalues of the Inertia Tensor and the Principal
Axis Transformation
195
5.5
Solving Rigid Body Problems and the
Euler
Equations of
Motion
198
5.6
Torque-free Motion of a Rigid Body
200
5.7
The Heavy Symmetrical Top with One Point Fixed
208
5.8
Precession of the Equinoxes and of Satellite Orbits
223
5.9
Precession of Systems of Charges in a Magnetic Field
230
6 ■
Oscillations
238
6.1
Formulation of the Problem
238
6.2
The Eigenvalue Equation and the Principal Axis Transformation
241
6.3
Frequencies of Free Vibration, and Normal Coordinates
250
6.4
Free Vibrations of a Linear Triatomic Molecule
253
6.5
Forced Vibrations and the Effect of Dissipative Forces
259
6.6
Beyond Small Oscillations: The Damped Driven Pendulum and the
Josephson
Junction
265
7 ■
The Classical Mechanics of the
Special Theory of Relativity
276
7.1
Basic Postulates of the Special Theory
277
7.2
Lorentz
Transformations
280
7.3
Velocity Addition and Thomas Precession
282
7.4
Vectors and the Metric Tensor
286
Contents
vii
7.5 l-Forms and Tensors 289
7.6 Forces in
the
Special
Theory; Electromagnetism
297
7.7
Relativistic Kinematics of Collisions and Many-Particle
Systems
300
7.8
Relativistic Angular Momentum
309
7.9
The Lagrangian Formulation of Relativistic Mechanics
312
7.10
Covariant Lagrangian Formulations
318
7.11
Introduction to the General Theory of Relativity
324
8 ■
The Hamilton Equations of Motion
334
8.1
Legendre Transformations and the Hamilton Equations
of Motion
334
8.2
Cyclic Coordinates and Conservation Theorems
343
8.3
Routh's Procedure
347
8.4
The Hamiltonian Formulation of Relativistic Mechanics
349
8.5
Derivation of Hamilton's Equations from a
Variational Principle
353
8.6
The Principle of Least Action
356
9 ■
Canonical Transformations
368
9.1
The Equations of Canonical Transformation
368
9.2
Examples of Canonical Transformations
375
9.3
The Harmonic Oscillator
377
9.4
The Symplectic Approach to Canonical Transformations
381
9.5
Poisson
Brackets and Other Canonical Invariants
388
9.6
Equations of Motion, Infinitesimal Canonical Transformations, and
Conservation Theorems in the
Poisson
Bracket Formulation
396
9.7
The Angular Momentum
Poisson
Bracket Relations
408
9.8
Symmetry Groups of Mechanical Systems
412
9.9
Liouville's Theorem
419
10 ■
Hamilton-Jacobi Theory and Action-Angle Variables
430
10.1
The Hamilton-Jacobi Equation for Hamilton's Principal
Function
430
10.2
The Harmonic Oscillator Problem as an Example of the
Hamilton-Jacobi Method
434
10.3
The Hamilton-Jacobi Equation for Hamilton's Characteristic
Function
440
10.4
Separation of Variables in the Hamilton-Jacobi Equation
444
10.5
Ignorable
Coordinates and the Kepler Problem
445
10.6
Action-angle Variables in Systems of One Degree of Freedom
452
viii Contents
10.7
Action-Angle Variables for Completely Separable Systems
457
10.8
The Kepler Problem in Action-angle Variables
466
11 ■
Classical Chaos
483
11.1
Periodic Motion
484
11.2
Perturbations and the Kolmogorov-Arnold-Moser Theorem
487
11.3
Attractors
489
11.4
Chaotic Trajectories and Liapunov Exponents
491
11.5
PoincaréMaps
494
11.6
Hénon-Heiles Hamiitonian
496
11.7
Bifurcations, Driven-damped Harmonic Oscillator, and Parametric
Resonance
505
11.8
The Logistic Equation
509
11.9
Fractals and Dimensionality
516
12 ■
Canonical Perturbation Theory
526
12.1
Introduction
526
12.2
Time-dependent Perturbation Theory
527
12.3
Illustrations of Time-dependent Perturbation Theory
533
12.4
Time-independent Perturbation Theory
541
12.5
Adiabatic Invariants
549
13 ■
Introduction to the Lagrangian and Hamiitonian
Formulations for Continuous Systems and Fields
558
13.1
The Transition from a Discrete to a Continuous System
558
13.2
The Lagrangian Formulation for Continuous Systems
561
13.3
The Stress-energy Tensor and Conservation Theorems
566
13.4
Hamiitonian Formulation
572
13.5
Relativistic Field Theory
577
13.6
Examples of Relativistic Field Theories
583
13.7
Noether's Theorem
589
Appendix A
■
Euler
Angles in Alternate Conventions
and Cayley-Klein Parameters
601
Appendix
В
■
Groups and Algebras
605
Selected Bibliography
617
Author Index
623
Subject index
625 |
| any_adam_object | 1 |
| author | Goldstein, Herbert 1922-2005 Poole, Charles P. 1927-2015 Safko, John L. |
| author_GND | (DE-588)133613895 (DE-588)121716309 (DE-588)131909622 |
| author_facet | Goldstein, Herbert 1922-2005 Poole, Charles P. 1927-2015 Safko, John L. |
| author_role | aut aut aut |
| author_sort | Goldstein, Herbert 1922-2005 |
| author_variant | h g hg c p p cp cpp j l s jl jls |
| building | Verbundindex |
| bvnumber | BV019422759 |
| callnumber-first | Q - Science |
| callnumber-label | QA805 |
| callnumber-raw | QA805 |
| callnumber-search | QA805 |
| callnumber-sort | QA 3805 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | UF 1000 |
| classification_tum | PHY 200f |
| ctrlnum | (OCoLC)47056311 (DE-599)BVBBV019422759 |
| dewey-full | 531 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531 |
| dewey-search | 531 |
| dewey-sort | 3531 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 3. ed. |
| format | Book |
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| genre | 1\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV019422759 |
| illustrated | Illustrated |
| indexdate | 2024-08-24T01:11:07Z |
| institution | BVB |
| isbn | 9780321188977 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012884370 |
| oclc_num | 47056311 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-573 DE-355 DE-BY-UBR DE-188 |
| owner_facet | DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-573 DE-355 DE-BY-UBR DE-188 |
| physical | XVIII, 638 S. Ill., graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Pearson/Addison-Wesley |
| record_format | marc |
| series2 | Pearson international edition |
| spelling | Goldstein, Herbert 1922-2005 Verfasser (DE-588)133613895 aut Classical mechanics Herbert Goldstein ; Charles Poole ; John Safko 3. ed. Upper Saddle River, NJ Pearson/Addison-Wesley 2002 XVIII, 638 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pearson international edition Klassieke mechanica gtt Mechanics, Analytic Lagrange-Gleichungen (DE-588)4166461-9 gnd rswk-swf Hamilton-Jacobi-Theorie (DE-588)4278207-7 gnd rswk-swf Kraft (DE-588)4032651-2 gnd rswk-swf Schwingung (DE-588)4053999-4 gnd rswk-swf Kinematik (DE-588)4030664-1 gnd rswk-swf Theoretische Mechanik (DE-588)4185100-6 gnd rswk-swf Hamilton-Gleichungen (DE-588)4289066-4 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Mechanik (DE-588)4038168-7 s Theoretische Mechanik (DE-588)4185100-6 s 2\p DE-604 Schwingung (DE-588)4053999-4 s 3\p DE-604 Hamilton-Jacobi-Theorie (DE-588)4278207-7 s 4\p DE-604 Kinematik (DE-588)4030664-1 s 5\p DE-604 Hamilton-Gleichungen (DE-588)4289066-4 s 6\p DE-604 Lagrange-Gleichungen (DE-588)4166461-9 s 7\p DE-604 Kraft (DE-588)4032651-2 s 8\p DE-604 Poole, Charles P. 1927-2015 Verfasser (DE-588)121716309 aut Safko, John L. Verfasser (DE-588)131909622 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012884370&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 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 7\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 8\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Goldstein, Herbert 1922-2005 Poole, Charles P. 1927-2015 Safko, John L. Classical mechanics Klassieke mechanica gtt Mechanics, Analytic Lagrange-Gleichungen (DE-588)4166461-9 gnd Hamilton-Jacobi-Theorie (DE-588)4278207-7 gnd Kraft (DE-588)4032651-2 gnd Schwingung (DE-588)4053999-4 gnd Kinematik (DE-588)4030664-1 gnd Theoretische Mechanik (DE-588)4185100-6 gnd Hamilton-Gleichungen (DE-588)4289066-4 gnd Mechanik (DE-588)4038168-7 gnd |
| subject_GND | (DE-588)4166461-9 (DE-588)4278207-7 (DE-588)4032651-2 (DE-588)4053999-4 (DE-588)4030664-1 (DE-588)4185100-6 (DE-588)4289066-4 (DE-588)4038168-7 (DE-588)4123623-3 |
| title | Classical mechanics |
| title_auth | Classical mechanics |
| title_exact_search | Classical mechanics |
| title_full | Classical mechanics Herbert Goldstein ; Charles Poole ; John Safko |
| title_fullStr | Classical mechanics Herbert Goldstein ; Charles Poole ; John Safko |
| title_full_unstemmed | Classical mechanics Herbert Goldstein ; Charles Poole ; John Safko |
| title_short | Classical mechanics |
| title_sort | classical mechanics |
| topic | Klassieke mechanica gtt Mechanics, Analytic Lagrange-Gleichungen (DE-588)4166461-9 gnd Hamilton-Jacobi-Theorie (DE-588)4278207-7 gnd Kraft (DE-588)4032651-2 gnd Schwingung (DE-588)4053999-4 gnd Kinematik (DE-588)4030664-1 gnd Theoretische Mechanik (DE-588)4185100-6 gnd Hamilton-Gleichungen (DE-588)4289066-4 gnd Mechanik (DE-588)4038168-7 gnd |
| topic_facet | Klassieke mechanica Mechanics, Analytic Lagrange-Gleichungen Hamilton-Jacobi-Theorie Kraft Schwingung Kinematik Theoretische Mechanik Hamilton-Gleichungen Mechanik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012884370&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT goldsteinherbert classicalmechanics AT poolecharlesp classicalmechanics AT safkojohnl classicalmechanics |