Fisica Para Informaticos

ESSENTIAL PHYSICS Part 1
RELATIVITY, PARTICLE DYNAMICS, GRAVITATION, AND WAVE MOTION FRANK W. K. FIRK Professor Emeritus of Physics Yale University

2000

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CONTENTS
PREFACE 1 MATHEMATICAL PRELIMINARIES 1.1 Invariants 1.2 Some geometrical invariants 1.3 Elements of differential geometry 1.4 Gaussian coordinates and the invariant line element 1.5 Geometry and groups 1.6 Vectors 1.7Quaternions 1.8 3-vector analysis 1.9 Linear algebra and n-vectors 1.10 The geometry of vectors 1.11 Linear operators and matrices 1.12 Rotation operators 1.13 Components of a vector under coordinate rotations 2 KINEMATICS: THE GEOMETRY OF MOTION 2.1 Velocity and acceleration 2.2 Differential equations of kinematics 2.3 Velocity in Cartesian and polar coordinates 2.4 Acceleration in Cartesian andpolar coordinates 3 CLASSICAL AND SPECIAL RELATIVITY 3.1 The Galilean transformation 3.2 Einstein’s space-time symmetry: the Lorentz transformation 3.3 The invariant interval: contravariant and covariant vectors 3.4 The group structure of Lorentz transformations 3.5 The rotation group 3.6 The relativity of simultaneity: time dilation and length contraction 3.7 The 4-velocity 4 NEWTONIAN DYNAMICS4.1 The law of inertia 75 56 58 61 63 66 68 71 42 45 49 50 11 12 15 17 20 23 24 26 28 31 34 36 38 7

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4.2 Newton’s laws of motion 4.3 Many interacting particles: conservation of linear and angular momentum 4.4 Work and energy in Newtonian dynamics 4.5 Potential energy 4.6 Particle interactions 4.7 The motion of rigid bodies 4.8 Angular velocity and the instantaneous center of rotation 4.9An application of the Newtonian method 5 INVARIANCE PRINCIPLES AND CONSERVATION LAWS 5.1 Invariance of the potential under translations: conservation of linear momentum 5.2 Invariance of the potential under rotations: conservation of angular momentum 6 EINSTEINIAN DYNAMICS 6.1 4-momentum and the energy-momentum invariant 6.2 The relativistic Doppler shift 6.3 Relativistic collisions and theconservation of 4- momentum 6.4 Relativistic inelastic collisions 6.5 The Mandelstam variables 6.6 Positron-electron annihilation-in-flight 7 NEWTONIAN GRAVITATION 7.1 Properties of motion along curved paths in the plane 7.2 An overview of Newtonian gravitation 7.3 Gravitation: an example of a central force 7.4 Motion under a central force: conservation of angular momentum 7.5 Kepler’s 2nd law explained7.6 Central orbits 7.7 Bound and unbound orbits 7.8 The concept of the gravitational field 7.9 The gravitational potential 8 EINSTEINIAN GRAVITATION: AN INTRODUCTION TO GENERAL RELATIVITY 8.1 The principle of equivalence 8.2 Time and length changes in a gravitational field 8.3 The Schwarzschild line element

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8.4 The metric in the presence of matter 8.5 The weak field approximation 8.6 The refractive index of space-time in the presence of mass 8.7 The deflection of light grazing the sun 9 AN INTRODUCTION TO THE CALCULUS OF VARIATIONS 9.1 The Euler equation 9.2 The Lagrange equations 9.3 The Hamilton equations 10 CONSERVATION LAWS, AGAIN 10.1 The conservation ofmechanical energy 10.2 The conservation of linear and angular momentum 11 CHAOS 11.1 The general motion of a damped, driven pendulum 11.2 The numerical solution of differential equations 12 WAVE MOTION 12.1 The basic form of a wave 12.2 The general wave equation 12.3 Lorentz invariant phase of a wave and the relativistic Doppler shift 12.4 Plane harmonic waves 12.5 Spherical waves 12.6 Thesuperposition of harmonic waves 12.7 Standing waves 13 ORTHOGONAL FUNCTIONS AND FOURIER SERIES 13.1 Definitions 13.2 Some trigonometric identities and their Fourier series 13.3 Determination of the Fourier coefficients of a function 13.4 The Fourier series of a periodic saw-tooth waveform APPENDIX A: SOLVING ORDINARY DIFFERENTIAL EQUATIONS BIBLIOGRAPHY

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