Dynamics and Relativity
by Forshaw, Jeffrey; Smith, GavinEdition: 1st
Format: Hardcover
Pub. Date: 2009-03-16
Publisher(s): Wiley
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Summary
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.
Author Biography
Dr Jeff Forshaw, Department of Physics & Astronomy, University of Manchester, Oxford Road, Manchester, UK.
Dr Gavin Smith, Department of Physics & Astronomy, University of Manchester, Oxford Road, Manchester, UK.
Table of Contents
| 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 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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