Classical Mechanics : Point Particles and Relativity

Foreword v Preface vii 1 VECTOR CALCULUS 1(132) 1 Introduction and Basic Definitions 2(3) 2 The Scalar Product 5(4) 3 Component Representation of a Vector 9(4) 4 The Vector Product (Axial Vector) 13(12) 5 The Triple Scalar Product 25(2) 6 Application of Vector Calculus 27(12) Application in mathematics: 27(4) Application in physics: 31(8) 7 Differentiation and Integration of Vectors 39(10) 8 The Moving Trihedral (Accompanying Dreibein)-the Frenet Formulas 49(15) Examples on Frenet's formulas: 55(9) 9 Surfaces in Space 64(4) 10 Coordinate Frames 68(15) 11 Vector Differential Operations 83(26) The operations gradient, divergence, and curl (rotation) 83(13) Differential operators in arbitrary general (curvilinear) coordinates 96(13) 12 Determination of Line Integrals 109(3) 13 The Integral Laws of Gauss and Stokes 112(13) Gauss Law: 112(2) The Gauss theorem: 114(1) Geometric interpretation of the Gauss theorem: 115(2) Stokes law: 117(8) 14 Calculation of Surface Integrals 125(5) 15 Volume(Space)Integrals 130(3) II NEWTONIAN MECHANICS 133(228) 16 Newton's Axioms 134(6) 17 Basic Concepts of Mechanics 140(19) Inertial systems 140(1) Measurement of masses 141(1) Work 141(1) Kinetic energy 142(1) Conservative forces 142(1) Potential 143(1) Energy law 144(1) Equivalence of impulse of force and momentum change 144(5) Angular momentum and torque 149(1) Conservation law of angular momentum 150(1) Law of conservation of the linear momentum 150(1) Summary 150(1) The law of areas 151(1) Conservation of orientation 151(8) 18 The General Linear Motion 159(4) 19 The Free Fall 163(9) Vertical throw 164(2) Inclined throw 166(6) 20 Friction 172(24) Friction phenomena in a viscous medium 172(5) Motion in a viscous medium with Newtonian friction 177(2) Generalized ansate for friction: 179(17) 21 The Harmonic Oscillator 196(14) 22 Mathematical Interlude-Series Expansion, Euler's Formulas 210(4) 23 The Damped Harmonic Oscillator 214(15) 24 The Pendulum 229(12) 25 Mathematical Interlude: Differential Equations 241(5) 26 Planetary Motions 246(36) 27 Special Problems in Central Fields 282(13) The gravitational field of extended bodies 282(1) The attractive force of a spherical mass shell 283(2) The gravitational potential of a spherical shell covered with mass 285(4) Stability of circular orbits 289(6) 28 The Earth and our Solar System 295(66) General notions of astronomy 295(1) Determination of astronomic quantities 296(12) Properties, position, and evolution of the solar system 308(7) World views 315(10) On the evolution of the universe 325(5) Dark Matter 330(8) What is the nature of the dark matter? 338(23) III THEORY OF RELATIVITY 361(124) 29 Relativity Principle and Michelson-Morley Experiment 362(8) The Michelson-Morley experiment 364(6) 30 The Lorentz Transformation 370(19) Rotation of a three-dimensional coordinate frame 372(2) The Minkowski space 374(9) Group property of the Lorentz transformation 383(6) 31 Properties of the Lorentz transformation 389(30) Time dilatation 389(5) Lorentz-Fitzgerald length contraction 394(2) Note on the invisibility of the Lorentz-Fitzgerald length contraction 396(2) The visible appearance of quickly moving bodies 398(1) Optical appearance of a quickly moving cube 398(2) Optical appearance of bodies moving with almost the speed of light 400(4) Light intensity distribution of a moving isotropic emitter 404(3) Doppler shift of quickly moving bodies 407(5) Relativistic space-time structure-space-time events 412(1) Relativistic past, present, future 413(1) The causality principle 414(1) The Lorentz transformation in the two-dimensional subspace of the Minkowski space 415(4) 32 Addition Theorem of the Velocities 419(6) Supervelocity of light, phase, and group velocity 421(4) 33 The Basic Quantities of Mechanics in Minkowski Space 425(36) Lorentz scalars 426(1) Four-velocity in Minkowski space 427(1) Momentum in Minkowski space 428(1) Minkowski force (four-force) 428(5) Kinetic energy 433(9) The Tachyon hypothesis 442(2) Derivation of the energy law in the Minkowski space 444(1) The fourth momentum component 445(1) Conservation of momentum and energy for a free particle 446(1) Relativistic energy for free particles 446(2) Examples on the equivalence of mass and energy 448(13) 34 Applications of the Special Theory of Relativity 461(24) The elastic collision 461(4) Compton scattering 465(3) The inelastic collision 468(2) Decay of an unstable particle 470(15) Index 485