Infeld / Plebanski Motion and Relativity

1. Auflage 2013
ISBN: 978-1-4832-8038-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 230 Seiten, Web PDF

Motion and Relativity focuses on the methodologies, solutions, and approaches involved in the study of motion and relativity, including the general relativity theory, gravitation, and approximation. The publication first offers information on notation and gravitational interaction and the general theory of motion. Discussions focus on the notation of the general relativity theory, field values on the world-lines, general statement of the physical problem, Newton's theory of gravitation, and forms for the equation of motion of the second kind. The text then takes a look at the approximation method and the equations of motion and motion and the Newtonian and post-Newtonian approximation. Topics include general remarks on the approximation method, two forms of the equations of motion and integrability conditions, approximation method and coordinate system, and development of the metric field. The manuscript examines the variational principle and the equations of motion of the third kind and the one and two particle problems. The formulation of the problem, Lagrangian up the sixth order, motion of a test particle in the field of a heavy particle, two-body problem, and motion of rotating bodies are discussed. The text is a dependable reference for readers interested in the methodologies, solutions, and approaches involved in the study of motion and relativity.

Autoren/Hrsg.

Infeld, Leopold

Plebanski, Jerzy

Inhaltsverzeichnis

1;Front Cover;1
2;Motion and Relativity;4
3;Copyright Page;5
4;Table of Contents;6
5;INTRODUCTION;8
6;NOTATION;10
6.1;A. NOTATION OF GENERAL RELATIVITY THEORY;10
6.2;B. THE d FUNCTIONS;13
6.3;C. THE FIELD VALUES ON THE WORLD-LINES;13
6.4;D. THE COVARIANT CHARACTER OP THE d's. TENSORS ON WORLD-LINES;14
7;GEAVITATIONAL INTERACTION AND THE GENEEAL THEORY OF MOTION;15
7.1;1. GENERAL STATEMENT OF THE PHYSICAL PROBLEM. PARTICLES AND THE GRAVITATIONAL FIELD;15
7.2;2. NEWTON'S THEORY OP GRAVITATION;24
7.3;3. INTERACTION IN G. R. T. THE EQUATIONS OF MOTION OF THE FIRST AND SECOND KIND;30
7.4;4. THE EINSTEIN FIELD EQUATIONS;36
7.5;5. THE BIANCHI IDENTITIES;42
7.6;6. THE EQUATIONS OF MOTION ARE A CONSEQUENCE OF THE FIELD EQUATIONS;45
7.7;7. FORMS FOR THE EQUATIONS OF MOTION OF THE SECOND KIND;50
7.8;8. THE EQUATIONS OF MOTION IN GRAVITATIONAL AND NON-GRAVITATIONAL FIELDS;57
7.9;9. EQUATIONS OP MOTION IN DIFFERENT COORDINATE SYSTEMS;60
7.10;10. ON THE METHOD OF SOLUTION OF THE FIELD EQUATIONS WITH THE HELP OF THE DIPOLE PROCEDURE;64
8;CHAPTER III: THE APPBOXTMATION METHOD AND THE EQUATIONS OF MOTION;69
8.1;1. GENERAL REMARKS ON THE APPROXIMATION METHOD;69
8.2;2. ON THE DEVELOPMENT OP THE METBIC FIELD;72
8.3;3. ON THE THREE LEVELS OF OUR REASONING;74
8.4;4. THE APPROXIMATION METHOD AND THE COORDINATE SYSTEM;76
8.5;5. THE APPROXIMATION METHOD AND THE FIELD EQUATIONS;79
8.6;6. ON THE TWO FOEMS OF THE EQUATIONS OF MOTION AND THE INTEGBABILITY CONDITIONS;90
9;CHAPTER .II. THE NEWTONIAN AND POST-NEWTONIAN ...R..IMA....;97
9.1;1. THE NEWTONIAN APPROXIMATION;97
9.2;2. THE GRAVITATIONAL FIELD FOR THE POST-NEWTONIAN EQUATIONS OF MOTION;100
9.3;3. THE EQUATIONS OF MOTION IN THE POST-NEWTONIAN APPEOXIMATION;104
9.4;4. THE CONSERVATION LAWS FOR A SYSTEM OF PARTICLES;115
10;CHAPTER IV. THE VABIATIONAL PRINCIPLE AND THE EQUATIONS OF MOTION OF THE THIRD KIND;119
10.1;1. FORMULATION OF THE PROBLEM;119
10.2;2. THE LAGEANGIAN UP TO THE SIXTH ORDEE;125
10.3;3. GENERALIZATION;130
10.4;4. A FOKKER-TYPE LAGRANGIAN FOR ROTATING BODIES;131
11;CHAPTER V. THE ONE AND TWO PARTICLE PEOBLEMS;137
11.1;1. ON THE QUESTION OF MEASUREMENT;137
11.2;2. ON THE MOTION OF A TEST PARTICLE IN THE FIELD OF A HEAVY PARTICLE;145
11.3;3. THE TWO-BODY PROBLEM;150
11.4;4. THE MOTION OF ROTATING BODIES;156
12;CHAPTER VI. MOTION AND RADIATION;161
12.1;1. A SIMPLE EXAMPLE;161
12.2;2. THE EQUATIONS OF MOTION IN THE FORM OF A SURFACE INTEGRAL;167
12.3;3. THE EQUATIONS OF MOTION IN THE FORM OF A SPACE INTEGRAL;170
12.4;4. THE EQUATIONS OF MOTION IN THE FORM OF SPACE AND SURFACE INTEGRALS;171
12.5;5. THE CONSEQUENCES OF THE DIFFERENT FORMS OF THE EQUATIONS OF MOTION;172
12.6;6. THE THREE LINEAR MOMENTA;175
12.7;7. THE EQUATION FOE GRAVITATIONAL RADIATION;177
12.8;8. ON THE INVARIANCE PROPERTIES OF Pa(G);182
12.9;9. GRAVITATIONAL RADIATION AND THE CHOICE OF A COORDINATE SYSTEM;183
12.10;10. ON THE GENERALIZATION OF THE COORDINATE SYSTEM;191
12.11;11. RADIATION AND THE APPROXIMATION METHOD;196
13;APPENDICES;203
13.1;1. THE d FUNCTION;203
13.2;2. THE FIELD VALUES ON THE WORLD-LINES;214
13.3;3. THE COVARIANT CHARACTER OP THE d's. TENSORS ON WORLD-LINES;218
14;BIBLIOGRAPHY;222
15;INDEX;228