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.
Table of Contents
Introduction Notation Chapter I Gravitational Interaction and the General Theory of Motion 1. General Statement of the Physical Problem. Particles and the Gravitational Field 2. Newton's Theory of Gravitation 3. Interaction in G. R. T. The Equations of Motion of the First and Second Kind 4. The Einstein Field Equations 5. The Bianchi Identities 6. The Equations of Motion are a Consequence of the Field Equations 7. Forms for the Equations of Motion of the Second Kind 8. The Equations of Motion in Gravitational and Non-Gravitational Fields 9. Equations of Motion in Different Coordinate Systems 10. On the Method of Solution of the Field Equations with the Help of Dipole Procedure Chapter II The Approximation Method and the Equations of Motion 1. General Remarks on the Approximation Method 2. On the Development of the Metric Field 3. On the Three Levels of Our Reasoning 4. The Approximation Method and the Coordinate System 5. The Approximation Method and the Field Equations 6. On the Two Forms of the Equations of Motion and the Integrability Conditions Chapter III The Newtonian and Post-Newtonian Approximation 1. The Newtonian Approximation 2. The Gravitational Field for the Post-Newtonian Equations of Motion 3. The Equations of Motion in the Post-Newtonian Approximation 4. The Conservation Laws for a System of Particles Chapter IV The Variational Principle and the Equations of Motion of the Third Kind 1. Formulation of the Problem 2. The Lagrangian Up to the Sixth Order 3. Generalization 4. A Fokker-Type Lagrangian for Rotating Bodies Chapter V The One and Two Particle Problems 1. On the Question of Measurement 2. On the Motion of a Test Particle in the Field of a Heavy Particle 3. The Two-Body Problem 4. The Motion of Rotating Bodies Chapter VI Motion and Radiation 1. A Simple Example 2. The Equations of Motion in the Form of a Surface Integral 3. The Equations of Motion in the Form of a Space Integral 4. The Equations of Motion in the Form of Space and Surface Integrals 5. The Consequences of the Different Forms of the Equations of Motion 6. The Three Linear Momenta 7. The Equation for Gravitational Radiation 8. On the Invariance Properties of Pa(G) 9. Gravitational Radiation and the choice of a Coordinate System 10. On the Generalization of the Coordinate System 11. Radiation and the Approximation Method Appendices 1. The δ Function 2. The Field Values on the World-Lines 3. The Covariant Character of the δ's. Tensors on World-Lines Bibliography Index