The theory of classical dynamics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Ausgabe: | Digitally printed version |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Originally published: 1985 |
| Beschreibung: | XIV, 315 S. graph. Darst. |
Internformat
MARC
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| 245 | 1 | 0 | |a The theory of classical dynamics |c J. B. Griffiths |
| 250 | |a Digitally printed version | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a XIV, 315 S. |b graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
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Datensatz im Suchindex
| _version_ | 1804138123384324096 |
|---|---|
| adam_text | CONTENTS
Preface
ix
Introduction
xi
1
The Newtonian method
1
1.1
The technique of mathematical modelling
1
1.2
The testing of models and theories
5
1.3
The primitive base of classical dynamics
10
1.4
The character of the theory
13
2
Space, time and vector notation
16
2.1
Space
16
2.2
Time
19
2.3
Scalar and vector notation
22
2.4
Position and Euclidean space
25
2.5
Velocity and acceleration
28
2.6
Kinematics: examples
31
Exercises
34
3
Force, mass and the law of motion
35
3.1
The concept of a particle
35
3.2
The law of inertia
37
3.3
The concept of force
39
3.4
Mass and the magnitude of a force
43
3.5
The law of motion and its application
47
3.6
Rectilinear motion and projectiles: examples
53
Exercises
62
3.7
Comments on other axiomatic formulations
64
4
Newtonian relativity
67
4.1
Relative motion
68
4.2
Inerţial
frames of reference
72
4.3
Motion relative to the earth: examples
76
Exercises
81
4.4
The search for an
inerţial
frame
82
4.5
Absolute rotation or Mach s principle
83
5
Newtonian gravitation
86
5.1
Kepler s laws
86
5.2
An intermediate theory of planetary motion
90
VI
Contents
5.3
Newton s theory of universal gravitation
91
5.4
Observational evidence
94
5.5
Gravitational and
inerţial
mass
97
5.6
The general relativistic correction
98
5.7
Weight 10°
6
Particle dynamics
103
6.1
Kinetic energy, work and the activity equation
104
6.2
Irrotational fields
105
6.3
Conservative fields and potential energy
108
6.4
The energy integral
112
6.5
Gravitational fields
116
6.6
Momentum and angular momentum
119
6.7
Impulsive motion
121
6.8
Standard examples
123
Exercises
130
7
Systems of several particles
132
7.1
Systems of several particles as a model
132
7.2
Centroide:
examples
135
Exercises
137
7.3
Energy and angular momentum
137
7.4
Equations of motion
140
7.5
η
-body
problems: examples
147
Exercises
150
7.6
Motion of bodies with variable mass
150
7.7
Rocket motion: examples
152
Exercises
154
7.8
Constraints and degrees of freedom
155
7.9
An approach to the dynamics of fluids
159
8
Rigid body dynamics I66
8.1
The concept of a rigid body
166
8.2
The possible motions of a rigid body
168
8.3
Moments of inertia
170
8.4
Evaluating moments of inertia: examples
1
Exercises I83
8.5
Equations for motion in a plane ^
8.6
2D rigid body motion: examples 1°6
Exercises
193
8.7
Moments and products of inertia
194
8.8
Principal axes of inertia
198
8.9
The inertia tensor: examples
203
Exercises
207
8.10
Equations of motion 208
8.11
The energy integral 212
Contents
vii
8.12 3D
rigid body motion: examples
214
Exercises
228
8.13
Impulsive motion
229
8.14
Impulses: examples
231
Exercises
234
9
Analytical dynamics
236
9.1
Generalised coordinates
236
9.2
Kinetic energy and the generalised momentum components
239
9.3
Virtual work and the generalised force components
242
9.4
Lagrange s equations for a holonomic system
246
9.5
First integrals of Lagrange s equations
250
9.6
Holonomic systems: examples
255
Exercises
260
9.7
The fundamental equation
261
9.8
Systems subject to constraints
264
9.9
Lagrange s equations for impulsive motion
269
9.10
Nonholonomic and impulsive motion: examples
271
Exercises
275
10
Variational principles
276
10.1
Hamilton s principle
276
10.2
Deductions from Hamilton s principle
279
10.3
The principle of least action
282
11
Hamilton-Jacobi theory
286
11.1
Hamilton s equations of motion
287
11.2
Integrals of Hamilton s equations
291
11.3
The Hamiltonian approach: examples
293
Exercises
294
11.4
Hamilton s principal function
295
11.5
The Hamilton-Jacobi equation
297
11.6
Hamilton s characteristic function
301
11.7
The Hamilton-Jacobi approach: examples
303
Exercises
306
Appendix: list of basic results and definitions
308
Suggestions for further reading
311
Index
312
|
| adam_txt |
CONTENTS
Preface
ix
Introduction
xi
1
The Newtonian method
1
1.1
The technique of mathematical modelling
1
1.2
The testing of models and theories
5
1.3
The primitive base of classical dynamics
10
1.4
The character of the theory
13
2
Space, time and vector notation
16
2.1
Space
16
2.2
Time
19
2.3
Scalar and vector notation
22
2.4
Position and Euclidean space
25
2.5
Velocity and acceleration
28
2.6
Kinematics: examples
31
Exercises
34
3
Force, mass and the law of motion
35
3.1
The concept of a particle
35
3.2
The law of inertia
37
3.3
The concept of force
39
3.4
Mass and the magnitude of a force
43
3.5
The law of motion and its application
47
3.6
Rectilinear motion and projectiles: examples
53
Exercises
62
3.7
Comments on other axiomatic formulations
64
4
Newtonian relativity
67
4.1
Relative motion
68
4.2
Inerţial
frames of reference
72
4.3
Motion relative to the earth: examples
76
Exercises
81
4.4
The search for an
inerţial
frame
82
4.5
Absolute rotation or Mach's principle
83
5
Newtonian gravitation
86
5.1
Kepler's laws
86
5.2
An intermediate theory of planetary motion
90
VI
Contents
5.3
Newton's theory of universal gravitation
91
5.4
Observational evidence
94
5.5
Gravitational and
inerţial
mass
97
5.6
The general relativistic correction
98
5.7
Weight 10°
6
Particle dynamics
103
6.1
Kinetic energy, work and the activity equation
104
6.2
Irrotational fields
105
6.3
Conservative fields and potential energy
108
6.4
The energy integral
112
6.5
Gravitational fields
116
6.6
Momentum and angular momentum
119
6.7
Impulsive motion
121
6.8
Standard examples
123
Exercises
130
7
Systems of several particles
132
7.1
Systems of several particles as a model
132
7.2
Centroide:
examples
135
Exercises
137
7.3
Energy and angular momentum
137
7.4
Equations of motion
140
7.5
η
-body
problems: examples
147
Exercises
150
7.6
Motion of bodies with variable mass
150
7.7
Rocket motion: examples
152
Exercises
154
7.8
Constraints and degrees of freedom
155
7.9
An approach to the dynamics of fluids
159
8
Rigid body dynamics I66
8.1
The concept of a rigid body
166
8.2
The possible motions of a rigid body
168
8.3
Moments of inertia
170
8.4
Evaluating moments of inertia: examples
1'"
Exercises I83
8.5
Equations for motion in a plane ^
8.6
2D rigid body motion: examples 1°6
Exercises
193
8.7
Moments and products of inertia
194
8.8
Principal axes of inertia
198
8.9
The inertia tensor: examples
203
Exercises
207
8.10
Equations of motion 208
8.11
The energy integral 212
Contents
vii
8.12 3D
rigid body motion: examples
214
Exercises
228
8.13
Impulsive motion
229
8.14
Impulses: examples
231
Exercises
234
9
Analytical dynamics
236
9.1
Generalised coordinates
236
9.2
Kinetic energy and the generalised momentum components
239
9.3
Virtual work and the generalised force components
242
9.4
Lagrange's equations for a holonomic system
246
9.5
First integrals of Lagrange's equations
250
9.6
Holonomic systems: examples
255
Exercises
260
9.7
The fundamental equation
261
9.8
Systems subject to constraints
264
9.9
Lagrange's equations for impulsive motion
269
9.10
Nonholonomic and impulsive motion: examples
271
Exercises
275
10
Variational principles
276
10.1
Hamilton's principle
276
10.2
Deductions from Hamilton's principle
279
10.3
The principle of least action
282
11
Hamilton-Jacobi theory
286
11.1
Hamilton's equations of motion
287
11.2
Integrals of Hamilton's equations
291
11.3
The Hamiltonian approach: examples
293
Exercises
294
11.4
Hamilton's principal function
295
11.5
The Hamilton-Jacobi equation
297
11.6
Hamilton's characteristic function
301
11.7
The Hamilton-Jacobi approach: examples
303
Exercises
306
Appendix: list of basic results and definitions
308
Suggestions for further reading
311
Index
312 |
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| index_date | 2024-07-02T22:26:41Z |
| indexdate | 2024-07-09T21:23:11Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016807120 |
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| spelling | Griffiths, Jeremy B. 1947- Verfasser (DE-588)137355262 aut The theory of classical dynamics J. B. Griffiths Digitally printed version Cambridge [u.a.] Cambridge Univ. Press 2008 XIV, 315 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Originally published: 1985 Dynamics Mechanik (DE-588)4038168-7 gnd rswk-swf Dynamik (DE-588)4013384-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Dynamik (DE-588)4013384-9 s DE-604 Mechanik (DE-588)4038168-7 s 1\p DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016807120&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 |
| spellingShingle | Griffiths, Jeremy B. 1947- The theory of classical dynamics Dynamics Mechanik (DE-588)4038168-7 gnd Dynamik (DE-588)4013384-9 gnd |
| subject_GND | (DE-588)4038168-7 (DE-588)4013384-9 (DE-588)4123623-3 |
| title | The theory of classical dynamics |
| title_auth | The theory of classical dynamics |
| title_exact_search | The theory of classical dynamics |
| title_exact_search_txtP | The theory of classical dynamics |
| title_full | The theory of classical dynamics J. B. Griffiths |
| title_fullStr | The theory of classical dynamics J. B. Griffiths |
| title_full_unstemmed | The theory of classical dynamics J. B. Griffiths |
| title_short | The theory of classical dynamics |
| title_sort | the theory of classical dynamics |
| topic | Dynamics Mechanik (DE-588)4038168-7 gnd Dynamik (DE-588)4013384-9 gnd |
| topic_facet | Dynamics Mechanik Dynamik Lehrbuch |
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