This volume of lectures, Classical Mechanics: Point Particles and Relativity, deals with the first and more elementary part of the important field of classical mechanics. We have tried to present the subject in a manner that is both interesting to the student and easily accessible. The main text is therefore accompanied by many exercises and examples that have been worked out in great detail. This should make the book useful also for students wishing to study the subject on their own.

Foreword

Preface

Ⅰ VECTOR CALCULUS

1 Introduction and Basic Definitions

2 The Scalar Product

3 Component Representation of a Vector

4 The Vector Product (Axial Vector)

5 The Triple Scalar Product

6 Application of Vector Calculus

Application in mathematics:

Application in physics:

7 Differentiation and Integration of Vectors

8 The Moving Trihedral (Accompanying Dreibein)--the Frenet

Formulas

Examples on Frenet's formulas:

9 Surfaces in Space

10 Coordinate Frames

11 Vector Differential Operations

The operations gradient, divergence, and curl (rotation)

Differential operators in arbitrary general (curvilinear) coordinates

12 Determination of Line Integrals

13 The Integral Laws of Gauss and Stokes

Gauss Law:

The Gauss theorem:

Geometric interpretation of the Gauss theorem:

Stokes law:

14 Calculation of Surface Integrals

15 Volume (Space) Integrals

Ⅱ NEWTONIAN MECHANICS

16 Newton's Axioms

17 Basic Concepts of Mechanics

Inertial systems

Measurement of masses

Work

Kinetic energy

Conservative forces

Potential

Energy law

Equivalence of impulse of force and momentum change

Angular momentum and torque

Conservation law of angular momentum

Law of conservation of the linear momentum

Summary

The law of areas

Conservation of orientation

18 The General Linear Motion

19 The Free Fall

Vertical throw

Inclined throw

20 Friction

Friction phenomena in a viscous medium

Motion in a viscous medium with Newtonian friction

Generalized ansatz for friction:

21 The Harmonic Oscillator

22 Mathematical Interlude--Series Expansion, Euler's Formulas

23 The Damped Harmonic Oscillator

24 The Pendulum

25 Mathematical Interlude: Differential Equations

26 Planetary Motions

27 Special Problems in Central Fields

The gravitational field of extended bodies

The attractive force of a spherical mass shell

The gravitational potential of a spherical shell covered with mass

Stability of circular orbits

28 The Earth and our Solar System

General notions of astronomy

Determination of astronomic quantities

Properties, position, and evolution of the solar system

World views

On the evolution of the universe

Dark Matter

What is the nature of the dark matter?

Ⅲ THEORY OF RELATIVITY

29 Relativity Principle and Michelson-Morley Experiment

The Michelson-Morley experiment

30 The Lorentz Transformation

Rotation of a three-dimensional coordinate frame

The Minkowski space

Group property of the Lorentz transformation

31 Properties of the Lorentz transformation

Time dilatation

Lorentz-Fitzgerald length contraction

Note on the invisibility of the Lorentz-Fitzgerald length contraction

The visible appearance of quickly moving bodies

Optical appearance of a quickly moving cube

Optical appearance of bodies moving with almost the speed of light

Light intensity distribution of a moving isotropic emitter

Doppler shift of quickly moving bodies

Relativistic space-time structure--space-time events

Relativistic past, present, future

The causality principle

The Lorentz transformation in the two-dimensional subspace of the Minkowski

space

32 Addition Theorem of the Velocities

Supervelocity of light, phase, and group velocity

33 The Basic Quantities of Mechanics in Minkowski Space

Lorentz scalars

Four-velocity in Minkowski space

Momentum in Minkowski space

Minkowski force (four-force)

Kinetic energy

The Tachyon hypothesis

Derivation of the energy law in the Minkowski space

The fourth momentum component

Conservation of momentum and energy for a free particle

Relativistic energy for free particles

Examples on the equivalence of mass and energy

34 Applications of the Special Theory of Relativity

The elastic collision

Compton scattering

The inelastic collision

Decay of an unstable particle

Index