Classical Mechanics

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Imperial College Press, Jan 1, 2004 - Science - 478 pages
4 Reviews
This book.covers the fundamental principles and techniques of classical mechanics. It emphasizes the basic principles, and Lagrangian methods are introduced at a relatively early stage, to get students to appreciate their use in simple contexts. Later chapters use Lagrangian and Hamiltonian methods extensively. This edition retains all the main features of the fourth edition, including the two chapters on geometry of dynamical systems and on order and chaos, and the new appendices on conics and on dynamical systems near a critical point. The material has been somewhat expanded, in particular to contrast continuous and discrete behaviours.
  

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Review: Classical Mechanics (5th Edition)

User Review  - Ida - Goodreads

I did not feel "safe" with the book, as though I was constantly missing something and a great deal of it was just not satisfying. The first book of the sort I ever read which strongly discouraged ... Read full review

Contents

Introduction
1
11 Space and Time
2
12 Newtons Laws
5
13 The Concepts of Mass and Force
10
14 External Forces
13
Linear Motion
17
22 Motion near Equilibrium the Harmonic Oscillator
20
23 Complex Representation
24
97 Instantaneous Angular Velocity
216
98 Rotation about a Principal Axis
218
99 Eulers Angles
221
910 Summary
225
Lagrangian Mechanics
231
102 Lagranges Equations
233
103 Precession of a Symmetric Top
236
104 Pendulum Constrained to Rotate about an Axis
238

24 The Law of Conservation of Energy
25
25 The Damped Oscillator
27
26 Oscillator under Simple Periodic Force
30
27 General Periodic Force
34
28 Impulsive Forces the Greens Function Method
37
29 Collision Problems
39
210 Summary
42
Energy and Angular Momentum
49
32 Projectiles
51
33 Moments Angular Momentum
53
34 Central Forces Conservation of Angular Momentum
55
35 Polar Coordinates
57
36 The Calculus of Variations
59
37 Hamiltons Principle Lagranges Equations
62
38 Summary
66
Central Conservative Forces
73
42 The Conservation Laws
76
43 The Inverse Square Law
78
44 Orbits
84
45 Scattering Crosssections
90
46 Mean Free Path
94
47 Rutherford Scattering
96
48 Summary
98
Rotating Frames
105
52 Particle in a Uniform Magnetic Field
108
53 Acceleration Apparent Gravity
111
54 Coriolis Force
114
55 Larmor Effect
120
56 Angular Momentum and the Larmor Effect
121
57 Summary
124
Potential Theory
129
62 The Dipole and Quadrupole
131
63 Spherical Charge Distributions
134
64 Expansion of Potential at Large Distances
137
65 The Shape of the Earth
140
66 The Tides
144
67 The Field Equations
148
68 Summary
152
The TwoBody Problem
159
72 The Centreofmass Frame
162
73 Elastic Collisions
165
74 CM and Lab Crosssections
168
75 Summary
173
ManyBody Systems
177
82 Angular Momentum Central Internal Forces
181
83 The EarthMoon System
183
84 Energy Conservative Forces
188
85 Lagranges Equations
190
86 Summary
192
Rigid Bodies
197
92 Rotation about an Axis
198
93 Perpendicular Components of Angular Momentum
203
94 Principal Axes of Inertia
205
95 Calculation of Moments of Inertia
208
96 Effect of a Small Force on the Axis
211
105 Charged Particle in an Electromagnetic Field
241
106 The Stretched String
244
107 Summary
248
Small Oscillations and Normal Modes
253
112 Equations of Motion for Small Oscillations
256
113 Normal Modes
258
114 Coupled Oscillators
261
115 Oscillations of Particles on a String
266
116 Normal Modes of a Stretched String
269
117 Summary
272
Hamiltonian Mechanics
277
122 Conservation of Energy
280
123 Ignorable Coordinates
282
124 General Motion of the Symmetric Top
285
125 Liouvilles Theorem
289
126 Symmetries and Conservation Laws
291
127 Galilean Transformations
295
128 Summary
300
Dynamical Systems and Their Geometry
307
132 Firstorder Systems the Phase Line n 1
309
133 Secondorder Systems the Phase Plane n 2
312
134 PreyPredator Competingspecies Systems and War
318
135 Limit Cycles
324
136 Systems of Third and Higher Order
329
137 Sensitivity to Initial Conditions and Predictability
337
138 Summary
340
Order and Chaos in Hamiltonian Systems
347
142 Surfaces of Section
351
143 ActionAngle Variables
354
144 Some Hamiltonian Systems which Exhibit Chaos
359
145 Slow Change of Parameters Adiabatic Invariance
369
146 Nearintegrable Systems
372
147 Summary
374
Vectors
381
A2 The Scalar Product
384
A3 The Vector Product
385
A4 Differentiation and Integration of Vectors
388
A5 Gradient Divergence and Curl
390
A6 Integral Theorems
393
A7 Electromagnetic Potentials
397
A8 Curvilinear Coordinates
398
A9 Tensors
401
A10 Eigenvalues Diagonalization of a Symmetric Tensor
403
Conics
409
B2 Polar Form
412
Phase Plane Analysis near Critical Points
415
C2 Almost Linear Systems
421
C3 Systems of Third and Higher Order
423
Discrete Dynamical Systems Maps
425
D2 Twodimensional Maps
433
D3 Twist Maps and Torus Breakdown
437
Answers to Problems
445
Bibliography
463
Index
465
Copyright

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About the author (2004)

Tom Kibble is Senior Research Fellow and Emeritus Professor of Theoretical Physics at Imperial College London, and a Fellow of the Royal Society. He has published many articles on theoretical particle physics and cosmology.

Frank Berkshire is also at Imperial College London. He is Senior Lecturer and Director of Undergraduate Studies in the Department of Mathematics, and has published on dynamical systems, waves and fluids. He was elected as Imperial College Teaching Fellow in 1996.

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