Dynamics and Relativity

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ISBN: 9780470014592 | 0470014598
Cover: Hardcover
Copyright: 3/16/2009

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Dynamics and Relativity provides an essential introduction to classical mechanics and relativity. It places particular emphasis on the fundamentally different views of space and time held by Newton and Einstein reaching, in the final chapter, the idea of curved spacetime that lies at the heart of Einstein's General Theory of Relativity. The book develops the subject from first principles and assumes very little prior knowledge, other than some elementary calculus and trigonometry. It is divided into four parts: the first half is particularly suitable for students who are new to the subject. The second half introduces more advanced material and includes such topics as four-vectors and causality, gyroscopes and the relativistic corrections that underpin the workings of the GPS navigation system. Dynamics and Relativity includes material that is often not encountered in introductory courses but is nevertheless frequently required in more advanced courses.

Editors' Preface to the Manchester Physics Series	p. xi
Author's Preface	p. xiii
Introductory Dynamics	p. 1
Space, Time and Motion	p. 3
Defining Space and Time	p. 3
Space and the classical particle	p. 4
Unit vectors	p. 6
Addition and subtraction of vectors	p. 6
Multiplication of vectors	p. 7
Time	p. 8
Absolute space and space-time	p. 10
Vectors and Co-ordinate Systems	p. 11
Velocity and Acceleration	p. 14
Frames of reference	p. 16
Relative motion	p. 16
Uniform acceleration	p. 18
Velocity and acceleration in plane-polar co-ordinates: uniform circular motion	p. 20
Standards and Units	p. 21
Force, Momentum and Newton's Laws	p. 25
Force and Static Equilibrium	p. 25
Force and Motion	p. 31
Newton's Third Law	p. 35
Newton's bucket and Mach's principle	p. 39
Applications of Newton's Laws	p. 41
Free body diagrams	p. 41
Three worked examples	p. 42
Normal forces and friction	p. 46
Momentum conservation	p. 49
Impulse	p. 51
Motion in fluids	p. 51
Energy	p. 55
Work, Power and Kinetic Energy	p. 56
Potential Energy	p. 61
The stability of mechanical systems	p. 64
The harmonic oscillator	p. 65
Motion about a point of stable equilibrium	p. 67
Collisions	p. 68
Zero-momentum frames	p. 68
Elastic and inelastic collisions	p. 71
Energy Conservation in Complex Systems	p. 75
Angular Momentum	p. 81
Angular Momentum of a Particle	p. 81
Conservation of Angular Momentum in Systems of Particles	p. 83
Angular Momentum and Rotation About a Fixed Axis	p. 86
The parallel-axis theorem	p. 94
Sliding and Rolling	p. 95
Angular Impulse and the Centre of Percussion	p. 97
Kinetic Energy of Rotation	p. 99
Introductory Special Relativity	p. 103
The Need for a New Theory of Space and Time	p. 105
Space and Time Revisited	p. 105
Experimental Evidence	p. 108
The Michelson-Morley experiment	p. 108
Stellar aberration	p. 110
Einstein's Postulates	p. 113
Relativistic Kinematics	p. 115
Time Dilation, Length Contraction and Simultaneity	p. 115
Time dilation and the Doppler effect	p. 116
Length contraction	p. 121
Simultaneity	p. 123
Lorentz Transformations	p. 124
Velocity Transformations	p. 129
Addition of velocities	p. 129
Stellar aberration revisited	p. 130
Relativistic Energy and Momentum	p. 135
Momentum and Energy	p. 135
The equivalence of mass and energy	p. 142
The hint of an underlying symmetry	p. 144
Applications in Particle Physics	p. 145
When is relativity important?	p. 146
Two useful relations and massless particles	p. 149
Compton scattering	p. 152
Advanced Dynamics	p. 157
Non-Inertial Frames	p. 159
Linearly Accelerating Frames	p. 159
Rotating Frames	p. 161
Motion on the earth	p. 165
Gravitation	p. 173
Newton's Law of Gravity	p. 174
The Gravitational Potential	p. 177
Reduced Mass	p. 182
Motion in a Central Force	p. 184
Orbits	p. 186
Rigid Body Motion	p. 197
The Angular Momentum of a Rigid Body	p. 198
The Moment of Inertia Tensor	p. 200
Calculating the moment of inertia tensor	p. 203
Principal Axes	p. 207
Fixed-axis Rotation in the Lab Frame	p. 212
Euler's Equations	p. 214
The Free Rotation of a Symmetric Top	p. 216
The body-fixed frame	p. 216
The lab frame	p. 218
The wobbling earth	p. 223
The Stability of Free Rotation	p. 224
Gyroscopes	p. 226
Gyroscopic precession	p. 226
Nutation of a gyroscope	p. 232
Advanced Special Relativity	p. 237
The Symmetries of Space and Time	p. 239
Symmetry in Physics	p. 239
Rotations and translations	p. 240
Translational symmetry	p. 245
Galilean symmetry	p. 246
Lorentz Symmetry	p. 247
Four-Vectors and Lorentz Invariants	p. 253
The Velocity Four-vector	p. 254
The Wave Four-vector	p. 255
The Energy-momentum Four-vector	p. 258
Further examples in relativistic kinematics	p. 259
Electric and Magnetic Fields	p. 262
Space-Time Diagrams and Causality	p. 267
Relativity Preserves Causality	p. 270
An Alternative Approach	p. 272
Acceleration and General Relativity	p. 279
Acceleration in Special Relativity	p. 279
Twins paradox	p. 280
Accelerating frames of reference	p. 282
A Glimpse of General Relativity	p. 288
Gravitational fields	p. 290
Deriving the Geodesic Equation	p. 295
Solutions to Problems	p. 297
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Dynamics and Relativity

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