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9780387955865

Classical Mechanics

by ;
  • ISBN13:

    9780387955865

  • ISBN10:

    0387955860

  • Format: Paperback
  • Copyright: 2003-12-01
  • Publisher: Springer Verlag
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Summary

The series of texts on Classical Theoretical Physics is based on the highly successful series of courses given by Walter Greiner at the Johann Wolfgang Goethe University in Frankfurt am Main, Germany. Intended for advanced undergraduates and beginning graduate students, the volumes in the series provide not only a complete survey of classical theoretical physics 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 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

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