グライナー・古典力学テキスト<br>Classical Mechanics : Point Particles and Relativity (Classical Theoretical Physics)

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グライナー・古典力学テキスト
Classical Mechanics : Point Particles and Relativity (Classical Theoretical Physics)

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  • Springer(2004発売)
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  • ポイント 845pt
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  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 505 p.
  • 商品コード 9780387955865

基本説明

Contents: Vector Calculus Introduction and Basic Definitions; The Scalar Product; Component Representation of a Vector.- Newtonian Mechanics Newton's Axioms; Basic Concepts of Mechanics; The General Linear Motion; and more.

Full Description

Intended for advanced undergraduates and beginning graduate students, this text is based on the highly successful course given by Walter Greiner at the University of Frankfurt, Germany. The two volumes on classical mechanics provide not only a complete survey of the topic but also an enormous number of worked examples and problems to show students clearly how to apply the abstract principles to realistic problems.

Table of Contents

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 49 (15)
Dreibein)-the Frenet Formulas
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 83 (13)
curl (rotation)
Differential operators in arbitrary 96 (13)
general (curvilinear) coordinates
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 115(2)
theorem:
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 144(5)
momentum change
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 177(2)
friction
Generalized ansate for friction: 179(17)
21 The Harmonic Oscillator 196(14)
22 Mathematical Interlude-Series Expansion, 210(4)
Euler's Formulas
23 The Damped Harmonic Oscillator 214(15)
24 The Pendulum 229(12)
25 Mathematical Interlude: Differential 241(5)
Equations
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 283(2)
shell
The gravitational potential of a 285(4)
spherical shell covered with mass
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 308(7)
the solar system
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 362(8)
Experiment
The Michelson-Morley experiment 364(6)
30 The Lorentz Transformation 370(19)
Rotation of a three-dimensional 372(2)
coordinate frame
The Minkowski space 374(9)
Group property of the Lorentz 383(6)
transformation
31 Properties of the Lorentz transformation 389(30)
Time dilatation 389(5)
Lorentz-Fitzgerald length contraction 394(2)
Note on the invisibility of the 396(2)
Lorentz-Fitzgerald length contraction
The visible appearance of quickly moving 398(1)
bodies
Optical appearance of a quickly moving 398(2)
cube
Optical appearance of bodies moving with 400(4)
almost the speed of light
Light intensity distribution of a moving 404(3)
isotropic emitter
Doppler shift of quickly moving bodies 407(5)
Relativistic space-time 412(1)
structure-space-time events
Relativistic past, present, future 413(1)
The causality principle 414(1)
The Lorentz transformation in the 415(4)
two-dimensional subspace of the Minkowski
space
32 Addition Theorem of the Velocities 419(6)
Supervelocity of light, phase, and group 421(4)
velocity
33 The Basic Quantities of Mechanics in 425(36)
Minkowski Space
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 444(1)
Minkowski space
The fourth momentum component 445(1)
Conservation of momentum and energy for a 446(1)
free particle
Relativistic energy for free particles 446(2)
Examples on the equivalence of mass and 448(13)
energy
34 Applications of the Special Theory of 461(24)
Relativity
The elastic collision 461(4)
Compton scattering 465(3)
The inelastic collision 468(2)
Decay of an unstable particle 470(15)
Index 485