## Classical Mechanics: Point Particles and RelativityMore than a generation of German-speaking students around the world have worked their way to an understanding and appreciation of the power and beauty of modern theoretical physics—with mathematics, the most fundamental of sciences—using Walter Greiner’s textbooks as their guide. The idea of developing a coherent, complete presentation of an entire ?eld of science in a series of closely related textbooks is not a new one. Many older physicians remember with real pleasure their sense of adventure and discovery as they worked their ways through the classic series by Sommerfeld, by Planck, and by Landau and Lifshitz. From the students’ viewpoint, there are a great many obvious advantages to be gained through the use of consistent notation, logical ordering of topics, and coherence of presentation; beyond this, thecompletecoverageofthescienceprovidesauniqueopportunityfortheauthortoconvey his personal enthusiasm and love for his subject. These volumes on classical physics, ?nally available in English, complement Greiner’s textsonquantumphysics,mostofwhichhavebeenavailabletoEnglish-speakingaudiences for some time. The complete set of books will thus provide a coherent view of physics that includes, in classical physics, thermodynamics and statistical mechanics, classical dyn- ics, electromagnetism, and general relativity; and in quantum physics, quantum mechanics, symmetries, relativistic quantum mechanics, quantum electro- and chromodynamics, and the gauge theory of weak interactions. |

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### Contents

Introduction and Basic Definitions | 2 |

The Scalar Product | 5 |

Component Representation of a Vector | 9 |

The Vector Product Axial Vector | 13 |

The Triple Scalar Product | 25 |

Application of Vector Calculus | 27 |

Differentiation and Integration of Vectors | 39 |

The Moving Trihedral Accompanying Dreibein the Frenet Formulas | 49 |

Determination of astronomic quantities | 296 |

Properties position and evolution of the solar system | 308 |

World views | 315 |

On the evolution of the universe | 325 |

Dark Matter | 330 |

What is the nature of the dark matter? | 338 |

THEORY OF RELATIVITY | 361 |

Relativity Principle and MichelsonMorley Experiment | 362 |

Surfaces in Space | 64 |

Coordinate Frames | 68 |

Vector Differential Operations | 83 |

Differential operators in arbitrary general curvilinear coordinates | 96 |

Determination of Line Integrals | 109 |

The Integral Laws of Gauss and Stokes | 112 |

Calculation of Surface Integrals | 125 |

Volume Space Integrals | 130 |

NEWTONIAN MECHANICS | 133 |

Newtons Axioms | 134 |

Basic Concepts of Mechanics | 140 |

Measurement of masses | 141 |

Kinetic energy | 142 |

Potential | 143 |

Energy law | 144 |

Angular momentum and torque | 149 |

Conservation law of angular momentum | 150 |

The law of areas | 151 |

The General Linear Motion | 159 |

The Free Fall | 163 |

Vertical throw | 164 |

Inclined throw | 166 |

Friction | 172 |

Motion in a viscous medium with Newtonian friction | 177 |

The Harmonic Oscillator | 196 |

Mathematical Interlude Series Expansion Eulers Formulas | 210 |

The Damped Harmonic Oscillator | 214 |

The Pendulum | 229 |

Mathematical Interlude Differential Equations | 241 |

Planetary Motions | 246 |

Special Problems in Central Fields | 282 |

The attractive force of a spherical mass shell | 283 |

The gravitational potential of a spherical shell covered with mass | 285 |

Stability of circular orbits | 289 |

The Earth and our Solar System | 295 |

The MichelsonMorley experiment | 364 |

The Lorentz Transformation | 370 |

Rotation of a threedimensional coordinate frame | 372 |

The Minkowski space | 374 |

Group property of the Lorentz transformation | 383 |

Properties of the Lorentz transformation | 389 |

LorentzFitzgerald length contraction | 394 |

Note on the invisibility of the LorentzFitzgerald length contraction | 396 |

The visible appearance of quickly moving bodies | 398 |

Optical appearance of bodies moving with almost the speed of light | 400 |

Light intensity distribution of a moving isotropic emitter | 404 |

Doppler shift of quickly moving bodies | 407 |

Relativistic spacetime structure spacetime events | 412 |

Relativistic past present future | 413 |

The causality principle | 414 |

The Lorentz transformation in the twodimensional subspace of the Minkowski space | 415 |

Addition Theorem of the Velocities | 419 |

Supervelocity of light phase and group velocity | 421 |

The Basic Quantities of Mechanics in Minkowski Space | 425 |

Lorentz scalars | 426 |

Fourvelocity in Minkowski space | 427 |

Momentum in Minkowski space | 428 |

Kinetic energy | 433 |

The Tachyon hypothesis | 442 |

Derivation of the energy law in the Minkowski space | 444 |

The fourth momentum component | 445 |

Conservation of momentum and energy for a free particle | 446 |

Examples on the equivalence of mass and energy | 448 |

Applications of the Special Theory of Relativity | 461 |

Compton scattering | 465 |

The inelastic collision | 468 |

Decay of an unstable particle | 470 |

485 | |

### Common terms and phrases

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