Motion and Relativity (eBook)

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