Relativity and Engineering

1. Kinematics in Inertial Axes.- 1.1 The "Aether" in the Nineteenth Century.- 1.2 Some Experimental Evidence.- 1.3 Einstein's Relativity Postulates.- 1.4 Time and Length Standards. Synchronization.- 1.5 The "Simple" Lorentz Transformation.- 1.6 More General Lorentz Transformations.- 1.7 Time Dilatation and Proper Time.- 1.8 Length Measurements.- 1.9 Volume and Surface Elements.- 1.10 Visual Perception of Objects in Motion.- 1.11 Transformation of Velocities and Accelerations.- 1.12 Four-Vectors.- 1.13 Kinematics in Four Dimensions.- Problems.- 2. Dynamics in Inertial Axes.- 2.1 Equation of Motion of a Point Mass.- 2.2 Mass and Energy.- 2.3 A Few Simple Trajectories.- 2.4 Transformation Equations for Force, Energy, and Momentum.- 2.5 Four-Dimensional Dynamics.- 2.6 Systems of Points.- 2.7 Elastic Collisions.- 2.8 Motion of a Point with Variable Rest Mass.- 2.9 Rocket Acceleration.- 2.10 Inelastic Collisions.- 2.11 Incoherent Matter.- 2.12 The Kinetic Energy-Momentum Tensor.- 2.13 The Total Energy-Momentum Tensor.- Problems.- 3. Vacuum Electrodynamics in Inertial Axes.- 3.1 Transformation Formulas for the Sources.- 3.2 Transformation Equations for the Fields.- 3.3 Force on a Charged Particle.- 3.4 Four-Currents.- 3.5 The Electromagnetic Tensors.- 3.6 Potentials.- 3.7 Transformation of a Plane Wave: The Doppler Effect.- 3.8 The Lienard-Wiechert Fields.- 3.9 Fields of a Charge in Uniform Motion.- 3.10 Fields of a Static Dipole in Uniform Motion.- 3.11 Radiation from an Antenna in Uniform Motion.- 3.12 Radiation from a Moving Oscillation Dipole.- 3.13 Doppler Spectrum from a Moving Source.- Problems.- 4. Fields in Media in Uniform Translation.- 4.1 Polarization Densities.- 4.2 Constitutive Equations.- 4.3 Some Useful Forms of Maxwell's Equations.- 4.4 Point Charge Moving Uniformly in a Dielectric Medium.- 4.5 The Cerenkov Effect.- 4.6 Waves in a Moving Dielectric. The Fresnel Dragging Coefficient.- 4.7 Green's Dyadic for a Moving Dielectric.- 4.8 Electric Dipole Radiating in a Moving Dielectric.- Problems.- 5. Boundary-Value Problems for Media in Uniform Translation.- 5.1 Boundary Conditions.- 5.2 Dielectric Slab Moving in Time-Independent Fields.- 5.3 The Wilsons' Experiment.- 5.4 Sliding Contacts. A Simple Problem.- 5.5 Material Bodies Moving at Low Velocities.- 5.6 Conductors Moving in a Pre-Existing Static Magnetic Field.- 5.7 Circuit Equations.- 5.8 Motional E.M.F..- 5.9 Normal Incidence of a Time-Harmonic Plane Wave on a Moving Mirror.- 5.10 Arbitrary Time-Dependence of the Incident Plane Wave.- 5.11 Oblique Incidence of a Time-Harmonic Plane Wave on a Moving Mirror.- 5.12 A Time-Harmonic Plane Wave Incident on a Dielectric Medium.- 5.13 Reflection of a Plane Wave on a Moving Medium of Finite Conductivity.- 5.14 Revisiting the Boundary Conditions at a Moving Interface.- 5.15 Scattering by a Cylinder Moving Longitudinally.- 5.16 Scattering by a Cylinder Moving Transversely.- 5.17 Three-Dimensional Scattering by Moving Bodies.- 5.18 The Quasistationary Method.- Problems.- 6. Electromagnetic Forces and Energy.- 6.1 Surface and Volume Forces in Vacuum.- 6.2 Maxwell's Stress Tensor.- 6.3 A Few Simple Force Calculations.- 6.4 Radiation Pressure on a Moving Mirror.- 6.5 Radiation Force on a Dielectric Cylinder.- 6.6 Static Electric Force on a Dielectric Body.- 6.7 Magnetic Levitation.- 6.8 Levitation on a Line Current.- 6.9 Electromagnetic Energy in an Inertial System.- 6.10 Four-Dimensional Formulation in Vacuum.- 6.11 The Electromagnetic Energy-Momentum Tensor in Material Media.- Problems.- 7. Accelerated Systems of Reference.- 7.1 Coordinate Transformations.- 7.2 The Metric Tensor.- 7.3 Examples of Transformations.- 7.4 Coordinates and Measurements.- 7.5 Time and Length.- 7.6 Four-Vectors and Tensors.- 7.7 Three-Vectors.- 7.8 Velocities and Volume Densities.- 7.9 Covariant Derivative.- Problems.- 8. Gravitation.- 8.1 Inertial and Gravitational Masses.- 8.2 The Principle of Equivalence.- 8.3 Curvature.- 8.4 Einstein's Equations.- 8.5 The Small-Field Approximation.- 8.6 Gravitational Frequency Shift.- 8.7 Time Measurement Problems.- 8.8 Some Important Solutions of Einstein's Equations.- 8.9 Point Dynamics.- 8.10 Motion in the Schwarzschild Metric.- 8.11 Motion of a Photon in the Schwarzschild Metric.- 8.12 Strongly Concentrated Masses.- 8.13 Static Cosmological Metrics.- 8.14 Nonstatic Cosmological Metrics.- 8.15 Recent Cosmological Observations.- Problems.- 9. Maxwell's Equations in a Gravitational Field.- 9.1 Field Tensors and Maxwell's Equations.- 9.2 Maxwell's Equations in Rotating Coordinates.- 9.3 Transformation Equations for Fields and Sources.- 9.4 Constitutive Equations in Vacuum.- 9.5 Constitutive Equations in a Time-Orthogonal Metric.- 9.6 Constitutive Equations in Material Media.- 9.7 The Co-Moving Frame Assumption.- 9.8 Boundary Conditions.- Problems.- 10. Electromagnetism of Accelerated Bodies.- 10.1 Conducting Body of Revolution Rotating in a Static Magnetic Field.- 10.2 Conducting Sphere Rotating in a Uniform Magnetic Field.- 10.3 Motional E.M.F.- 10.4 Generators with Contact Electrodes.- 10.5 Dielectric Body of Revolution Rotating in a Static Field.- 10.6 Rotating Permanent Magnets.- 10.7 Scattering by a Rotating Circular Dielectric Cylinder.- 10.8 Scattering by a Rotating Circular Conducting Cylinder.- 10.9 Scattering by a Rotating Dielectric Body of Revolution.- 10.10 Scattering by a Rotating Sphere.- 10.11 Reflection from a Mirror in Arbitrary Linear Motion.- 10.12 Reflection from an Oscillating Mirror, at Normal Incidence.- 10.13 Reflection from an Oscillating Mirror, at Oblique Incidence.- 10.14 Scattering by Other Moving Surfaces.- Problems.- 11. Field Problems in a Gravitational Field.- 11.1 Fields Associated with Rotating Charges.- 11.2 Schiff's Paradox.- 11.3 Kennard's Experiment.- 11.4 Optical Rotation Sensors.- 11.5 Scattering by a Rotating Body of Arbitrary Shape.- 11.6 Transformation of an Incident Wave to Rotating Coordinates.- 11.7 Scattered Field in Rotating Coordinates.- 11.8 Two Examples.- 11.9 Low Frequency Scattering by Rotating Cylinders.- 11.10 Quasistationary and Relativistic Fields.- 11.11 Axes in Hyperbolic Motion.- 11.12 The Induction Law.- 11.13 Maxwell's Equations in a Schwarzschild Metric.- 11.14 Light Deflection in a Gravitational Field.- Problems.- Appendix A. Complements of Kinematics and Dynamics.- A.1 Transformation Matrix for the "Parallel" Transformation.- A.2 Transformation with Rotation.- A.3 Transformation of Velocities.- A.4 Relationship Between Force and Acceleration.- A.5 Equations of Motion in Cylindrical Coordinates (r,?,z).- A.6 Equations of Motion in Spherical Coordinates (R,?,?).- Appendix B. Dyadics.- B.1 The Dyadic Notation.- B.2 Operators on Dyadics.- B.3 Green's Dyadic.- Appendix C. Basis Vectors.- Appendix D. Moving Open Circuits.- List of Symbols.- Some Useful Numerical Constants.- References.