Classical Mechanics

Imperial College Press, Jan 1, 2004 - Science - 478 pages
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)

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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