Preface Useful Constants and Units List of Symbols 1. Introduction 1.1 Space and Time 1.2 Newton's Laws 1.3 The Concepts of Mass and Force 1.4 External Forces 1.5 Summary 2. Linear Motion 2.1 Conservative Forces; Conservation of Energy 2.2 Motion near Equilibrium; the Harmonic Oscillator 2.3 Complex Representation 2.4 The Law of Conservation of Energy 2.5 The Damped Oscillator 2.6 Oscillator under Simple Periodic Force 2.7 General Periodic Force 2.8 Impulsive Forces; the Green's Function Method 2.9 Collision Problems 2.10 Summary 3. Energy and Angular Momentum 3.1 Energy; Conservative Forces 3.2 Projectiles 3.3 Moments; Angular Momentum 3.4 Central Forces; Conservation of Angular Momentum 3.5 Polar Co-ordinates 3.6 The Calculus of Variations 3.7 Hamilton's Principle; Lagrange's Equations 3.8 Summary 4. Central Conservative Forces 4.1 The Isotropic Harmonic Oscillator 4.2 The Conservation Laws 4.3 The Inverse Square Law 4.4 Orbits 4.5 Scattering Cross-sections 4.6 Mean Free Path 4.7 Rutherford Scattering 4.8 Summary 5. Rotating Frames 5.1 Angular Velocity; Rate of Change of a Vector 5.2 Particle in a Uniform Magnetic Field 5.3 Acceleration; Apparent Gravity 5.4 Coriolis Force 5.5 Larmor Effect 5.6 Angular Momentum and the Larmor Effect 5.7 Summary 6. Potential Theory 6.1 Gravitational and Electrostatic Potentials 6.2 The Dipole and Quadrupole 6.3 Spherical Charge Distributions
6.4 Expansion of Potential at Large Distances 6.5 The Shape of the Earth 6.6 The Tides 6.7 The Field Equations 6.8 Summary 7. The Two-Body Problem 7.1 Centre-of-mass and Relative Co-ordinates 7.2 The Centre-of-mass Frame 7.3 Elastic Collisions 7.4 CM and Lab Cross-sections 7.5 Summary 8. Many-Body Systems 8.1 Momentum; Centre-of-mass Motion 8.2 Angular Momentum; Central Internal Forces 8.3 The Earth-Moon System 8.4 Energy; Conservative Forces 8.5 Lagrange's Equations 8.6 Summary 9. Rigid Bodies 9.1 Basic Principles 9.2 Rotation about an Axis 9.3 Perpendicular Components of Angular Momentum 9.4 Principal Axes of Inertia 9.5 Calculation of Moments of Inertia 9.6 Effect of a Small Force on the Axis 9.7 Instantaneous Angular Velocity 9.8 Rotation about a Principal Axis 9.9 Euler's Angles 9.10 Summary 10. Lagrangian Mechanics 10.1 Generalized Co-ordinates; Holonomic Systems 10.2 Lagrange's Equations 10.3 Precession of a Symmetric Top 10.4 Pendulum Constrained to Rotate about an Axis 10.5 Charged Particle in an Electromagnetic Field 10.6 The Stretched String 10.7 Summary 11. Small Oscillations and Normal Modes 11.1 Orthogonal Co-ordinates 11.2 Equations of Motion for Small Oscillations 11.3 Normal Modes 11.4 Coupled Oscillators 11.5 Oscillations of Particles on a String 11.6 Normal Modes of a Stretched String 11.7 Summary 12. Hamiltonian Mechanics 12.1 Hamilton's Equations 12.2 Conservation of Energy 12.3 Ignorable Co-ordinates 12.4 General Motion of the Symmetric Top
12.5 Liouville's Theorem 12.6 Symmetries and Conservation Laws 12.7 Galilean Transformations 12.8 Summary 13. Dynamical Systems and Their Geometry 13.1 Phase Space and Phase Portraits 13.2 First-order Systems -- the Phase Line (n = 1) 13.3 Second-order Systems -- the Phase Plane (n -- 2) 13.4 Prey-Predator, Competing-species Systems and War 13.5 Limit Cycles 13.6 Systems of Third (and Higher) Order 13.7 Sensitivity to Initial Conditions and Predictability 13.8 Summary 14. Order and Chaos in Hamiltonian Systems 14.1 Integrability 14.2 Surfaces of Section 14.3 Action/Angle Variables 14.4 Some Hamiltonian Systems which Exhibit Chaos 14.5 Slow Change of Parameters -- Adiabatic Invariance 14.6 Near-integrable Systems 14.7 Summary Appendix A. Vectors A.1 Definitions and Elementary Properties A.2 The Scalar Product A.3 The Vector Product A.4 Differentiation and Integration of Vectors A.5 Gradient, Divergence and Curl A.6 Integral Theorems A.7 Electromagnetic Potentials A.8 Curvilinear Co-ordinates A.9 Tensors A.10 Eigenvalues; Diagonalization of a Symmetric Tensor Appendix B. Conics B.1 Cartesian Form B.2 Polar Form Appendix C. Phase Plane Analysis near Critical Points C.1 Linear Systems and their Classification C.2 Almost Linear Systems C.3 Systems of Third (and Higher) Order Appendix D. Discrete Dynamical Systems -- Maps D.1 One-dimensional Maps D.2 Two-dimensional Maps D.3 Twist Maps and Torus Breakdown Answers to Problems Bibliography Index
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