Classical mechanics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hingham, MA [u.a.]
Infinity Science Press
2008
|
| Series: | Physics series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 576 S. |
| ISBN: | 9781934015322 |
Staff View
MARC
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| 100 | 1 | |a Finn, J. Michael |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Classical mechanics |c J. Michael Finn |
| 264 | 1 | |a Hingham, MA [u.a.] |b Infinity Science Press |c 2008 | |
| 300 | |a XV, 576 S. | ||
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Record in the Search Index
| _version_ | 1804138025421111296 |
|---|---|
| adam_text | Contents
Preface
xi
Chapter
1.
Review of Newtonian Particle Mechanics
1
1.1
Introduction to Classical Mechanics
1
1.2
Historical Context
3
1.3
Newton s
Principia
11
1.4
Motion of a System of Particles
26
1.5
Solution of the Initial Value Problem
33
1.6
One-Dimensional Motion
36
1.7
Summary
49
1.8
Exercises
51
Chapter
2.
Vector Spaces and Coordinate Systems
57
2.1
Points and Vectors
57
2.2
Inner Product Spaces
59
2.3
Vector Operators
71
2.4
Curvilinear Coordinate Systems
76
2.5
Manifolds
84
2.6
*Covariant Differentiation
90
2.7
Summary
98
2.8
Exercises
100
Chapter
3.
Lagrangian and Hamiltonian Dynamics
105
3.1
Generalized Coordinates and Constraints
105
3.2
Principle of Virtual Work
112
3.3
Lagrange s Equations of Motion
116
3.4
Electromagnetic Interactions
127
3.5
Hamilton s Equations of Motion
128
3.6
Routh s Procedure for Eliminating Cyclic Variables
137
3.7
Summary
138
3.8
Exercises
140
vii
viii
Contents
Chapter
4.
Hamilton s Principle
4.1
Hamilton s Action Principle
147
4.2
Role of the Action in Quantum Field Theory
148
4.3
Calculus of Variations
149
4.4
Lagrange s Method of Undetermined Multipliers
158
4.5
Noether s Theorem
164
4.6 *
Symmetry and Scale in Experimental Design
170
4.7
Summary
175
4.8
Exercises I76
Chapter
5.
Central Force Motion
183
5.1
Central Force Interactions
183
5.2
Lagrangian Formulation of the Two Body Problem
184
5.3
Inverse-Square Force Law
200
5.4
Restricted Three-Body Problem
211
5.5
Gravitation Field Sources
222
5.6
Precession of the Planetary Orbits
224
5.7
Summary
225
5.8
Exercises
227
Chapter
6.
Small Oscillations
231
6.1
Small Oscillations about an Equilibrium Configuration
231
6.2
Review of the One-Dimensional Problem
232
6.3
Normal Mode Analysis of Coupled Oscillators
234
6.4
Finite Lattice Structures
252
6.5
Forced and Damped Oscillations
260
6.6
Summary
264
6.7
Exercises
265
Chapter
7.
Rotational Geometry and Kinematics
273
7.1
Rotational Geometry of Euclidean Space
273
7.2 Pauli
Spin Algebra
287
7.3
Vector Algebra Notation
292
7.4
Rotating Frames of Motion
300
7.5
Kinematics of Rotating Bodies
308
7.6
Summary
316
7.7
Exercises
317
Chapter
8.
Rigid Body Motion
323
8.1
General Motion of a Rigid Body
323
8.2
Rotational Kinetic Energy of a Rigid Body
326
Contents IX
8.3
Moment of Inertia Tensor
328
8.4
Euler s Equation of Motion
338
8.5
Lagrangian Formulation
345
8.6
*Precession of Magnetic Dipoles
355
8.7
Summary
358
8.8
Exercises
360
Chapter
9.
Canonical Transformation Theory
367
9.1
Generalizing the Action
367
9.2
Poisson
Brackets
370
9.3
Generating Functions
377
9.4
Infinitesimal Canonical Transformations
392
9.5
Lie Algebra of the Rotation Group
396
9.6
Symplectic Structure of the Theory
401
9.7
*Elevating Time to a Coordinate
407
9.8
Summary
410
9.9
Exercises
412
Chapter
10.
Hamilton-Jacobi Theory
415
10.1
Hamilton-Jacobi Equation
415
10.2
Bohm
Interpretation of Quantum Mechanics
427
10.3
Action-Angle Variables
430
10.4
Adiabatic Invariants
441
10.5
Summary
444
10.6
Exercises
446
Chapter
11.
Special Relativity
451
11.1
Unifying Space and Time
451
11.2
Minkowski Space
455
11.3
Geometric Structure of Spacetime
462
11.4
Proper
Lorentz
Transformations
468
11.5
Relativistic Particle Dynamics
476
11.6
Impulse Approximation
482
11.7
Relativistic Lagrangians
489
11.8
Summary
502
11.9
Exercises
505
Chapter
12.
Waves, Particles, and Fields
509
12.1
Introduction to the Classical Theory of Fields
509
12.2
Non
Relativistic Wave Equation
520
12.3
Non-linear Sine-Gordon Equation
527
x
Contents
12.4
Electromagnetic Waves
532
12.5 *
Gravitational Field Theory
537
12.6
Summary
540
12.7
Exercises
542
Appendix A. International System of Units and Conversion Factors
545
A.I
CGS
Units
547
A.2 Conversion Factors between Various Electromagnetic
548
Systems of Units
A.3 Dimensionless Units
- 550
Appendix B. Physical Constants and Solar System Data
553
Appendix C. Geometric Algebras in
N
Dimensions
557
References
561
Index
567
|
| adam_txt |
Contents
Preface
xi
Chapter
1.
Review of Newtonian Particle Mechanics
1
1.1
Introduction to Classical Mechanics
1
1.2
Historical Context
3
1.3
Newton's
Principia
11
1.4
Motion of a System of Particles
26
1.5
Solution of the Initial Value Problem
33
1.6
One-Dimensional Motion
36
1.7
Summary
49
1.8
Exercises
51
Chapter
2.
Vector Spaces and Coordinate Systems
57
2.1
Points and Vectors
57
2.2
Inner Product Spaces
59
2.3
Vector Operators
71
2.4
Curvilinear Coordinate Systems
76
2.5
Manifolds
84
2.6
*Covariant Differentiation
90
2.7
Summary
98
2.8
Exercises
100
Chapter
3.
Lagrangian and Hamiltonian Dynamics
105
3.1
Generalized Coordinates and Constraints
105
3.2
Principle of Virtual Work
112
3.3
Lagrange's Equations of Motion
116
3.4
Electromagnetic Interactions
127
3.5
Hamilton's Equations of Motion
128
3.6
Routh's Procedure for Eliminating Cyclic Variables
137
3.7
Summary
138
3.8
Exercises
140
vii
viii
Contents
Chapter
4.
Hamilton's Principle
4.1
Hamilton's Action Principle
147
4.2
Role of the Action in Quantum Field Theory
148
4.3
Calculus of Variations
149
4.4
Lagrange's Method of Undetermined Multipliers
158
4.5
Noether's Theorem
164
4.6 *
Symmetry and Scale in Experimental Design
170
4.7
Summary
175
4.8
Exercises I76
Chapter
5.
Central Force Motion
183
5.1
Central Force Interactions
183
5.2
Lagrangian Formulation of the Two Body Problem
184
5.3
Inverse-Square Force Law
200
5.4
Restricted Three-Body Problem
211
5.5
Gravitation Field Sources
222
5.6
Precession of the Planetary Orbits
224
5.7
Summary
225
5.8
Exercises
227
Chapter
6.
Small Oscillations
231
6.1
Small Oscillations about an Equilibrium Configuration
231
6.2
Review of the One-Dimensional Problem
232
6.3
Normal Mode Analysis of Coupled Oscillators
234
6.4
Finite Lattice Structures
252
6.5
Forced and Damped Oscillations
260
6.6
Summary
264
6.7
Exercises
265
Chapter
7.
Rotational Geometry and Kinematics
273
7.1
Rotational Geometry of Euclidean Space
273
7.2 Pauli
Spin Algebra
287
7.3
Vector Algebra Notation
292
7.4
Rotating Frames of Motion
300
7.5
Kinematics of Rotating Bodies
308
7.6
Summary
316
7.7
Exercises
317
Chapter
8.
Rigid Body Motion
323
8.1
General Motion of a Rigid Body
323
8.2
Rotational Kinetic Energy of a Rigid Body
326
Contents IX
8.3
Moment of Inertia Tensor
328
8.4
Euler's Equation of Motion
338
8.5
Lagrangian Formulation
345
8.6
*Precession of Magnetic Dipoles
355
8.7
Summary
358
8.8
Exercises
360
Chapter
9.
Canonical Transformation Theory
367
9.1
Generalizing the Action
367
9.2
Poisson
Brackets
370
9.3
Generating Functions
377
9.4
Infinitesimal Canonical Transformations
392
9.5
Lie Algebra of the Rotation Group
396
9.6
Symplectic Structure of the Theory
401
9.7
*Elevating Time to a Coordinate
407
9.8
Summary
410
9.9
Exercises
412
Chapter
10.
Hamilton-Jacobi Theory
415
10.1
Hamilton-Jacobi Equation
" 415
10.2
Bohm
Interpretation of Quantum Mechanics
427
10.3
Action-Angle Variables
430
10.4
Adiabatic Invariants
441
10.5
Summary
444
10.6
Exercises
446
Chapter
11.
Special Relativity
451
11.1
Unifying Space and Time
451
11.2
Minkowski Space
455
11.3
Geometric Structure of Spacetime
462
11.4
Proper
Lorentz
Transformations
468
11.5
Relativistic Particle Dynamics
476
11.6
Impulse Approximation
482
11.7
Relativistic Lagrangians
489
11.8
Summary
502
11.9
Exercises
505
Chapter
12.
Waves, Particles, and Fields
509
12.1
Introduction to the Classical Theory of Fields
509
12.2
Non
Relativistic Wave Equation
520
12.3
Non-linear Sine-Gordon Equation
527
x
Contents
12.4
Electromagnetic Waves
532
12.5 *
Gravitational Field Theory
537
12.6
Summary
540
12.7
Exercises
542
Appendix A. International System of Units and Conversion Factors
545
A.I
CGS
Units
547
A.2 Conversion Factors between Various Electromagnetic
548
Systems of Units
A.3 Dimensionless Units
- 550
Appendix B. Physical Constants and Solar System Data
553
Appendix C. Geometric Algebras in
N
Dimensions
557
References
561
Index
567 |
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| id | DE-604.BV035075436 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:05:24Z |
| indexdate | 2024-07-09T21:21:38Z |
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| isbn | 9781934015322 |
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| physical | XV, 576 S. |
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| spelling | Finn, J. Michael Verfasser aut Classical mechanics J. Michael Finn Hingham, MA [u.a.] Infinity Science Press 2008 XV, 576 S. txt rdacontent n rdamedia nc rdacarrier Physics series Mechanics Mechanik (DE-588)4038168-7 gnd rswk-swf Mechanik (DE-588)4038168-7 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016743769&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Finn, J. Michael Classical mechanics Mechanics Mechanik (DE-588)4038168-7 gnd |
| subject_GND | (DE-588)4038168-7 |
| title | Classical mechanics |
| title_auth | Classical mechanics |
| title_exact_search | Classical mechanics |
| title_exact_search_txtP | Classical mechanics |
| title_full | Classical mechanics J. Michael Finn |
| title_fullStr | Classical mechanics J. Michael Finn |
| title_full_unstemmed | Classical mechanics J. Michael Finn |
| title_short | Classical mechanics |
| title_sort | classical mechanics |
| topic | Mechanics Mechanik (DE-588)4038168-7 gnd |
| topic_facet | Mechanics Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016743769&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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