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Tables of Contents for Elastic Waves in Solids 1
Chapter/Section Title
Page #
Page Count
The Foundation of Classical Mechanics
1
26
Principia
1
1
Prerequisites for Newton
1
4
The Masterpiece
5
16
The Acceleration of Gravity
11
1
Circular Motion
12
1
Communication Satellite
13
1
Horizontal Throw
14
3
The Gravitational Constant
17
1
String Force
18
1
Forces and Tension
19
1
Dimensional Analysis
20
1
Concluding Remarks
21
1
Problems
22
5
Newton's Five Laws
27
46
Newton's Laws of Motion
27
4
Integration of the Equation of Motion
31
31
Constant Force
31
2
The Harmonic Oscillator
33
3
Mass on a Spring in the Gravitational Field of Earth
36
2
Sphere Falling Through a Liquid
38
2
Solid Against Solid
40
1
The Atwood Machine
41
1
Force in Harmonic Motion
42
2
Charged Particle in a Uniform Magnetic Field
44
4
Thomson's Experiment
48
3
Work and Energy in Linear Motion of a Particle
51
2
Free Fall Towards the Sun from a Great Distance
53
1
Momentum Conservation
54
2
Inelastic Collisions
56
1
Rocket Propulsion
57
2
Some Qualitative Remarks on Rocket Propulsion
59
2
Ball Against a Wall
61
1
Problems
62
11
Gravitational and Inertial Mass
73
10
Gravitational Mass
73
1
Inertial Mass
74
1
Proportionality Between Inertial and Gravitational Mass
75
1
Newton's Experiment
76
4
The Satellite
78
1
An Elevator in Free Fall
79
1
Three Balls
80
1
Problem
80
3
The Galilei Transformation
83
12
The Galilei Transformation
84
6
Galileo Speaks
90
3
Velocity Transformation
91
2
Problems
93
2
The Motion of the Earth
95
6
Examples
95
4
Vectors and the Rotation of a Rigid Body
95
2
Angular Velocities in the Solar System
97
2
Problems
99
2
Motion in Accelerated Reference Frames
101
52
Newton's 2nd Law Within Accelerated Reference Frames
101
7
The Equivalence Principle of Mechanics
108
3
The Einstein Box
111
5
Balloon in Accelerated Frame
114
1
Mass on an Oscillating Plate
115
1
Pendulum in an Elevator
115
1
The Centrifugal Force
116
5
Earth's Orbit Around the Sun
117
1
Grass on a Rotating Disk
117
1
The Variation of g with Latitude
118
3
Tidal Fields
121
7
The Roche Limit
126
2
The Coriolis Force
128
7
Coriolis Force on a Train
133
1
Particle on a Frictionless Disc
133
1
The Vertical Throw
134
1
Tidal Forces and Local Inertial Frames
135
2
Global and Local Inertial Frames
137
1
The Foucault Pendulum
137
5
Newton's Bucket
142
3
Review: Fictitious Forces
145
1
Problems
146
7
The Problem of Motion
153
14
Kinematic and Dynamic Views of the Problem of Motion
153
2
Einstein Speaks
155
2
Symmetry
157
1
The Symmetry (Invariance) of Newton's 2nd Law
157
2
Limited Absolute Space
159
1
The Asymmetry (Variance) of Newton's 2nd Law
159
3
Critique of the Newtonian View
162
1
Concluding Remarks
163
4
Energy
167
26
Work and Kinetic Energy
167
2
Conservative Force Fields
169
1
Central Force Fields
170
1
Potential Energy and Conservation of Energy
171
3
Calculation of Potential Energy
174
2
Constant Gravitational Field
175
1
Spring Force
175
1
Gravity Outside a Homogeneous Sphere
175
1
The Gravitational Field Around a Homogeneous Sphere
176
5
The Field Around a Spherical Shell
176
3
A Solid Sphere
179
2
Examples
181
7
Particle on a Frictionless Curve
181
1
String Force in the Pendulum
182
1
The Gravitational Potential Outside the Earth
183
1
Potential Energy Due to Electric Forces
183
1
A Tunnel Through the Earth
184
2
The Asymmetry of Nature
186
2
Review: Conservative Forces and Potential Energy
188
1
Problems
189
4
The Center-of-Mass Theorem
193
26
The Center of Mass
193
4
The Center-of-Mass Frame
197
2
Examples
199
13
Two Masses Connected with a Spring
199
3
Inelastic Collisions
202
2
The Collision Approximation
204
3
Freely Falling Spring
207
2
The Wedge
209
3
Review: Center of Mass and Center-of-Mass Theorems
212
1
Comments on the Conservation Theorems
212
1
Problems
213
6
The Angular Momentum Theorem
219
18
The Angular Momentum Theorem for a Particle
219
2
Conservation of Angular Momentum
221
2
Torque and Angular Momentum Around an Axis
223
1
The Angular Momentum Theorem for a System of Particles
224
3
Center of Gravity
227
1
Angular Momentum Around the Center of Mass
228
2
Review: Equations of Motion for a System of Particles
230
1
Examples of Conservation of Angular Momentum
230
7
Particle in Circular Motion
230
1
Rotation of Galaxies, Solar Systems, etc
231
6
Rotation of a Rigid Body
237
42
Equations of Motion
237
1
The Rotation Vector
238
1
Kinetic Energy
239
4
The Parallel Axis Theorem
240
2
The Perpendicular Axis Theorem
242
1
An Arbitrary Rigid Body in Rotation Around a Fixed Axis
243
2
The Parallel Axis Theorem in General Form
244
1
Calculation of the Moment of Inertia for Simple Bodies
245
5
Homogenous Thin Rod
245
1
Circular Disk
246
1
Thin Spherical Shell
247
1
Homogenous (Solid) Sphere, Mass M and Radius R
248
1
Rectangular Plate
249
1
Equation of Motion for a Rigid Body Rotating Around a Fixed Axis
250
4
Conservation of Angular Momentum
253
1
Work and Power in the Rotation of a Rigid Body Around a Fixed Axis
254
2
Torsion Pendulum
255
1
The Angular Momentum Theorem Referred to Various Points
256
2
Examples
258
8
Rotating Cylinder
258
2
Falling Cylinder
260
2
The Atwood Machine
262
1
The Physical Pendulum
263
1
The Rod
264
2
Review: Linear Motion and Rotation About a Fixed Axis
266
1
Problems
267
12
The Laws of Motion
279
34
Review: Classical Mechanics
279
1
Remarks on the Three Conservation Theorems
280
1
Examples
280
20
Conservation of Angular Momentum
280
4
Rotating Rod
284
2
Man on Disk
286
1
The Sprinkler
287
2
Rolling
289
6
Yo-Yo on the Floor
295
2
Rolling Over an Edge
297
2
Determinism and Predictability
299
1
Problems
300
13
The General Motion of a Rigid Body
313
32
Inertia in Rotational Motion
313
8
The Dumbbell
314
2
Flywheel on an Axis
316
2
Precession of a Gyroscope
318
3
The Inertia Tensor
321
5
The Dumbbell Revisited
324
2
Euler's Equations
326
4
Derivation of Euler's Equations
328
2
Kinetic Energy
330
1
Determination of the Principal Coordinate System
331
11
Rotating Dumbbell
333
1
Flywheel
334
1
The Gyroscope
335
5
Gyroscope Supported at the Center of Mass
340
1
The Earth as a Gyroscope
341
1
Problems
342
3
The Motion of the Planets
345
40
Tycho Brahe
345
1
Kepler and the Orbit of Mars
346
6
The Length of a Martian Year
347
2
The Orbit of the Planet Mars
349
2
Determination of Absolute Distance in the Solar System
351
1
Conic Sections
352
3
Newton's Law of Gravity Derived from Kepler's Laws
355
4
The Kepler Problem
359
7
Derivation of Kepler's 3rd Law from Newton's Law of Gravity
364
2
The Effective Potential
366
1
The Two-Body Problem
367
3
The Two-Body Problem and Kepler's 3rd Law
370
1
Double Stars: The Motion of the Heliocentric Reference Frame
370
2
Review: Kepler Motion
372
1
Examples
373
8
Planetary Orbits and Initial Conditions
373
1
Shape and Size of Planetary Orbits
374
2
Motion Near the Surface of the Earth
376
1
Velocities in an Elliptical Orbit
377
1
Hohman Orbit to Mars
378
3
Problems
381
4
Harmonic Oscillators
385
22
Small Oscillations
385
1
Energy in Harmonic Oscillators
386
2
Free Damped Oscillations
388
3
Weakly Damped Oscillations
389
1
Strongly Damped Oscillations
390
1
Critical Damping
390
1
Energy in Free, Weakly Damped Oscillations
391
1
Forced Oscillations
392
2
The Forced Damped Harmonic Oscillator
394
2
Frequency Characteristics
396
2
&ohgr; ≪ &ohgr;0: A Low Driving Frequency
396
1
&ohgr; ≫ &ohgr;0: A High Driving Frequency
397
1
&ohgr; ≅ &ohgr;0: Resonance
397
1
Power Absorption
398
The Q-Value of a Weakly Damped Harmonic Oscillator
299
102
The Lorentz Curve
401
1
Complex Numbers
402
2
Problems
404
3
Remarks on Nonlinearity and Chaos
407
22
Determinism vs Predictability
407
1
Linear and Nonlinear Differential Equations
408
2
Superposition
409
1
Phase Space
410
10
The Simple Harmonic Oscillator
411
1
Phase Space of the Pendulum
412
5
Bifurcation in a Nonlinear Model
417
3
A Forced, Damped Nonlinear Oscillator
420
3
Liapunov Exponents
423
2
Chaos in the Solar System
425
2
Problems
427
2
Appendix. Vectors and Vector Calculus
429
6
Selected References
435
2
Answers to Problems
437
8
Index
445