Classical Mechanics

Preface1 Conversational Basic 1.1 Getting Started 1.2 Elegant Output 1.3 Sometimes More is Really Less 1.4 Into the Wild Blue2 One-Dimensional Motion 2.1 Kinematics in One Dimension 2.2 Dynamics in One Dimension 2.3 Constant Force 2.4 Force as a Function of Time 2.5 Force as a Function of Position 2.6 Force as a Function of Velocity3 The Harmonic Oscillator 3.1 Introduction 3.2 Simple Harmonic Oscillator 3.3 Power Series Representation of an Arbitrary Function 3.4 Damped Harmonic Oscillator 3.5 Forced Harmonic Oscillator 3.6 Application to AC Circuits 3.7 Simple Pendulum 3.8 Physical Pendulum4 Vectors 4.1 Introduction 4.2 Vector Algebra 4.3 Vector Multiplication 4.4 Coordinate Systems 4.5 Vector Calculus 4.6 Vector Differential Operators5 Motion in Three Dimensions 5.1 Introduction 5.2 Separable Forces 5.3 Three-Dimensional Harmonic Oscillator 5.4 Potential Energy Function 5.5 Motion in Electromagnetic Fields6 Coordinate Systems 6.1 Introduction 6.2 Plane Polar Coordinates 6.3 Cylindrical Polar Coordinates 6.4 Spherical Polar Coordinates 6.5 Moving Coordinate Systems 6.6 Rotating Coordinate Systems 6.7 Motion Observed on the Rotating Earth 6.8 Foucault Pendulum7 Central Forces 7.1 Introduction 7.2 Potential Energy and Central Forces 7.3 Angular Momentum and Central Forces 7.4 Inverse-Square Force 7.5 Kepler's Laws 7.6 Orbital Transfers and "Gravitational Boosts" 7.7 Radial Oscillations about a Circular Orbit 7.8 Gravity 7.9 Rutherford Scattering8 Systems of Particles 8.1 N Particles, the General Case 8.2 Momentum 8.3 Motion with a Variable Mass—Rockets 8.4 Motion with a Variable Mass—Conveyor Belts 8.5 Collisions 8.6 Center of Mass Frame9 Rigid Bodies 9.1 Center of Mass 9.2 Angular Momentum 9.3 Rotation about an Axis 9.4 Moment of Inertia Theorems 9.5 The Inertia Tensor 9.6 Principal Axes 9.7 Kinetic Energy 9.8 Euler's Equations10 Lagrangian Mechanics 10.1 Introduction 10.2 Generalized Coordinates 10.3 Generalized Forces 10.4 Lagrange's Equations 10.5 Elementary Examples 10.6 Systems with Constraints 10.7 Applications 10.8 Ignorable Coordinates 10.9 Lagrangian Mechanics and a Rotating Top 10.10 Hamilton's Equations 10.11 Hamilton's Principle11 Statics 11.1 Introduction 11.2 Plane Trusses 11.3 Method of Joints 11.4 Method of Sections 11.5 Cables under Distributed Loads 11.6 Parabolic Cables 11.7 Catenary Cables 11.8 Cables with Concentrated Loads12 Fluid Mechanics 12.1 Introduction 12.2 Hydrostatics: Fluids at Rest 12.3 Moving with the Flow 12.4 Hydrodynamics13 Special Relativity 13.1 Introduction 13.2 Galilean Relativity 13.3 Historical Background 13.4 Einsteinean Relativity/Spacetime Coordinates 13.5 Simultaneity 13.6 Lorentz Transformations 13.7 Application of the Lorentz Transformations 13.8 Minkowski Diagrams 13.9 Velocity Transformation 13.10 Doppler Effect 13.11 Momentum and Mass-Energy 13.12 Relativistic MassAppendices A Conversational Pascal B Calculus Review C Multiple Integrals D Matrix MultiplicationIndex