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| Matrices, Vectors, and Vector Calculus | |
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| Introduction | |
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| Concept of a Scalar | |
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| Coordinate Transformations | |
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| Properties of Rotation Matrices | |
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| Matrix Operations | |
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| Further Definitions | |
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| Geometrical Significance of Transformation Matrices | |
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| Definitions of a Scalar and a Vector in Terms of Transformation Properties | |
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| Elementary Scalar and Vector Operations | |
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| Scalar Product of Two Vectors | |
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| Unit Vectors | |
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| Vector Product of Two Vectors | |
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| Differentiation of a Vector with Respect to a Scalar | |
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| Examples of Derivatives--Velocity and Acceleration | |
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| Angular Velocity | |
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| Gradient Operator | |
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| Integration of Vectors | |
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| Problems | |
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| Newtonian Mechanics--Single Particle | |
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| Introduction | |
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| Newton's Laws | |
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| Frames of Reference | |
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| The Equation of Motion for a Particle | |
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| Conservation Theorems | |
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| Energy | |
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| Limitations of Newtonian Mechanics | |
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| Problems | |
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| Oscillations | |
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| Introduction | |
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| Simple Harmonic Oscillator | |
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| Harmonic Oscillations in Two Dimensions | |
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| Phase Diagrams | |
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| Damped Oscillations | |
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| Sinusoidal Driving Forces | |
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| Physical Systems | |
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| Principle of Superposition--Fourier Series | |
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| The Response of Linear Oscillators to Impulsive Forcing Functions (Optional) | |
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| Problems | |
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| Nonlinear Oscillations and Chaos | |
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| Introduction | |
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| Nonlinear Oscillations | |
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| Phase Diagrams for Nonlinear Systems | |
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| Plane Pendulum | |
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| Jumps, Hysteresis, and Phase Lags | |
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| Chaos in a Pendulum | |
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| Mapping | |
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| Chaos Identification | |
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| Problems | |
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| Gravitation | |
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| Introduction | |
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| Gravitational Potential | |
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| Lines of Force and Equipotential Surfaces | |
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| When Is the Potential Concept Useful? | |
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| Ocean Tides | |
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| Problems | |
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| Some Methods in the Calculus of Variations | |
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| Introduction | |
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| Statement of the Problem | |
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| Euler's Equation | |
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| The "Second Form" of the Euler Equation | |
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| Functions with Several Dependent Variables | |
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| Euler Equations When Auxiliary Conditions Are Imposed | |
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| The [delta] Notation | |
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| Problems | |
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| Hamilton's Principle--Lagrangian and Hamiltonian Dynamics | |
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| Introduction | |
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| Hamilton's Principle | |
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| Generalized Coordinates | |
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| Lagrange's Equations of Motion in Generalized Coordinates | |
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| Lagrange's Equations with Undetermined Multipliers | |
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| Equivalence of Lagrange's and Newton's Equations | |
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| Essence of Lagrangian Dynamics | |
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| A Theorem Concerning the Kinetic Energy | |
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| Conservation Theorems Revisited | |
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| Canonical Equations of Motion--Hamiltonian Dynamics | |
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| Some Comments Regarding Dynamical Variables and Variational Calculations in Physics | |
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| Phase Space and Liouville's Theorem (Optional) | |
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| Virial Theorem (Optional) | |
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| Problems | |
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| Central-Force Motion | |
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| Introduction | |
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| Reduced Mass | |
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| Conservation Theorems--First Integrals of the Motion | |
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| Equations of Motion | |
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| Orbits in a Central Field | |
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| Centrifugal Energy and the Effective Potential | |
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| Planetary Motion--Kepler's Problem | |
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| Orbital Dynamics | |
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| Apsidal Angles and Precession (Optional) | |
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| Stability of Circular Orbits (Optional) | |
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| Problems | |
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| Dynamics of a System of Particles | |
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| Introduction | |
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| Center of Mass | |
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| Linear Momentum of the System | |
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| Angular Momentum of the System | |
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| Energy of the System | |
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| Elastic Collisions of Two Particles | |
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| Kinematics of Elastic Collisions | |
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| Inelastic Collisions | |
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| Scattering Cross Sections | |
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| Rutherford Scattering Formula | |
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| Rocket Motion | |
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| Problems | |
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| Motion in a Nonintertial Reference Frame | |
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| Introduction | |
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| Rotating Coordinate Systems | |
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| Centrifugal and Coriolis Forces | |
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| Motion Relative to the Earth | |
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| Problems | |
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| Dynamics of Rigid Bodies | |
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| Introduction | |
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| Simple Planar Motion | |
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| Inertia Tensor | |
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| Angular Momentum | |
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| Principal Axes of Inertia | |
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| Moments of Inertia for Different Body Coordinate Systems | |
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| Further Properties of the Inertia Tensor | |
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| Eulerian Angles | |
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| Euler's Equations for a Rigid Body | |
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| Force-Free Motion of a Symmetric Top | |
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| Motion of a Symmetric Top with One Point Fixed | |
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| Stability of Rigid-Body Rotations | |
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| Problems | |
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| Coupled Oscillations | |
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| Introduction | |
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| Two Coupled Harmonic Oscillators | |
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| Weak Coupling | |
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| General Problem of Coupled Oscillations | |
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| Orthogonality of the Eigenvectors (Optional) | |
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| Normal Coordinates | |
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| Molecular Vibrations | |
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| Three Linearly Coupled Plane Pendula--an Example of Degeneracy | |
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| The Loaded String | |
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| Problems | |
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| Continuous Systems; Waves | |
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| Introduction | |
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| Continuous String as a Limiting Case of the Loaded String | |
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| Energy of a Vibrating String | |
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| Wave Equation | |
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| Forced and Damped Motion | |
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| General Solutions of the Wave Equation | |
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| Separation of the Wave Equation | |
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| Phase Velocity, Dispersion, and Attenuation | |
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| Group Velocity and Wave Packets | |
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| Problems | |
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| Special Theory of Relativity | |
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| Introduction | |
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| Galilean Invariance | |
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| Lorentz Transformation | |
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| Experimental Verification of the Special Theory | |
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| Relativistic Doppler Effect | |
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| Twin Paradox | |
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| Relativistic Momentum | |
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| Energy | |
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| Spacetime and Four-Vectors | |
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| Lagrangian Function in Special Relativity | |
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| Relativistic Kinematics | |
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| Problems | |
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| Appendices | |
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| Taylor's Theorem | |
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| Problems | |
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| Elliptic Integrals | |
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| Elliptic Integrals of the First Kind | |
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| Elliptic Integrals of the Second Kind | |
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| Elliptic Integrals of the Third Kind | |
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| Problems | |
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| Ordinary Differential Equations of Second Order | |
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| Linear Homogeneous Equations | |
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| Linear Inhomogeneous Equations | |
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| Problems | |
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| Useful Formulas | |
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| Binomial Expansion | |
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| Trigonometric Relations | |
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| Trigonometric Series | |
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| Exponential and Logarithmic Series | |
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| Complex Quantities | |
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| Hyperbolic Functions | |
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| Problems | |
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| Useful Integrals | |
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| Algebraic Functions | |
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| Trigonometric Functions | |
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| Gamma Functions | |
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| Differential Relations in Different Coordinate Systems | |
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| Rectangular Coordinates | |
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| Cylindrical Coordinates | |
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| Spherical Coordinates | |
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| A "Proof" of the Relation [characters not reproducible] = [characters not reproducible] | |
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| Numerical Solution for Example 2.7 | |
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| Selected References | |
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| Bibliography | |
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| Answers to Even-Numbered Problems | |
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| Index | |