Taylor J.R. Classical mechanics

University Science Books, 2005. - 808 pp., OCR.This book is intended for students of the physical sciences, especially physics, who have already studied some mechanics as part of an introductory physics course ("freshman physics" at a typical American university) and are now ready for a deeper look at the subject. The book grew out of the junior-level mechanics course which is offered by the Physics Department at Colorado and is taken mainly by physics majors, but also by some mathematicians, chemists, and engineers. Almost all of these students have taken a year of freshman physics, and so have at least a nodding acquaintance with Newton's laws, energy and momentum, simple harmonic motion, and so on. In this book I build on this nodding acquaintance to give a deeper understanding of these basic ideas, and then go on to develop more advanced topics, such as the Lagrangian and Hamiltonian formulations, the mechanics of noninertial frames, motion of rigid bodies, coupled oscillators, chaos theory, and a few more.
Mechanics is, of course, the study of how things move — how an electron moves down your TV tube, how a baseball flies through the air, how a comet moves round the sun. Classical mechanics is the form of mechanics developed by Galileo and Newton in the seventeenth century and reformulated by Lagrange and Hamilton in the eighteenth and nineteenth centuries. For more than two hundred years, it seemed that classical mechanics was the only form of mechanics, that it could explain the motion of all conceivable systems.Part one. EssentialsNewton's Laws of Motion
Classical Mechanics
Space and Time
Mass and Force
Newton's First and Second Laws; Inertial Frames
The Third Law and Conservation of the Momentum
Newton's Second Law in Cartesian Coordinates
Two-Dimensional Polar Coordinates
Problems for Chapter 1
Projectiles and Charged Particles
Air Resistance
Linear Air Resistance
Trajectory and Range in a Linear Motion
Quadratic Air Resistance
Motion of a Charge in a Uniform Magnetic Field
Complex Exponentials
Solution for the Charge in a B Field
Problems for Chapter 2
Momentum and Angular Momentum
Conservation of Momentum
Rockets
The Center of Mass
Angular Momentum for a Single Particle
Angular Momentum for Several Particles
Problems for Chapter 3
Energy
Kinetic Energy and Work
Potential Energy and Conservative Forces
Force as the Gradient of Potential Energy
The Second Condition that F be Conservative
Time-Dependent Potential Energy
Energy for Linear One-Dimensional Systems
Curvilinear One-Dimensional Systems
Central Forces
Energy of Interaction of Two Particles
The Energy of a Multiparticle System
Problems for Chapter 4
Oscillations
Hooke's Law
Simple Harmonic Motion
Two-Dimensional Oscillators
Damped Oscillators
Driven Damped Oscillations
Resonance
Fourier Series
Fourier Series Solution for the Driven Oscillator
The RMS Displacement; Parseval's Theorem
Problems for Chapter 5
Calculus of Variations
Two Examples
The Euler-Lagrange Equation
Applications of the Euler-Lagrange Equation
More than Two Variables
Problems for Chapter 6
Lagrange's Equations
Lagrange's Equations for Unconstrained Motion
Constrained Systems; an Example
Constrained Systems in General
Proof of Lagrange's Equations with Constraints
Examples of Lagrange's EquationsConservation Laws in Lagrangian Mechanics
Lagrange's Equations for Magnetic Forces
Lagrange Multipliers and Constraint Forces
Problems for Chapter 7
Two-Body Central Force Problems
The Problem
CM and Relative Coordinates; Reduced Mass
The Equations of Motion
The Equivalent One-Dimensional Problems
The Equation of the Orbit
The Kepler Orbits
The Unbonded Kepler Orbits
Changes of Orbit
Problems for Chapter 8
Mechanics in Noninertial Frames
Acceleration without Rotation
The Tides
The Angular Velocity Vector
Time Derivatives in a Rotating Frame
Newton's Second Law in a Rotating Frame
The Centrifugal Force
The Coriolis Force
Free Fall and The Coriolis Force
The Foucault Pendulum
Coriolis Force and Coriolis Acceleration
Problems for Chapter 9
Motion of Rigid Bodies
Properties of the Center of Mass
Rotation about a Fixed Axis
Rotation about Any Axis; the Inertia Tensor
Principal Axes of Inertia
Finding the Principal Axes; Eigenvalue Equations
Precession of a Top Due to a Weak Torque
Euler's Equations
Euler's Equations with Zero Torque
Euler Angles
Motion of a Spinning Top
Problems for Chapter 10
Coupled Oscillators and Normal Modes
Two Masses and Three Springs
Identical Springs and Equal Masses
Two Weakly Coupled Oscillators
Lagrangian Approach; the Double Pendulum
The General Case
Three Coupled Pendulums
Normal Coordinates
Problems for Chapter 11Part two. Further TopicsNonlinear Mechanics and Chaos
Linearity and Nonlinearity
The Driven Damped Pendulum or DDP
Some Expected Features of the DDP
The DDP; Approach to Chaos
Chaos and Sensitivity to Initial Conditions
Bifurcation Diagrams
State-Space Orbits
Poincare Sections
The Logistic Map
Problems for Chapter 12
Hamiltonian Mechanics
The Basic Variables
Hamilton's Equations for One-Dimensional Systems
Hamilton's Equations in Several Dimensions
Ignorable Coordinates
Lagrange's Equations vs. Hamilton's Equations
Phase-Space Orbits
Liouville's Theorem
Problems for Chapter 13
Collision Theory
The Scattering Angle and Impact Parameter
The Collision Cross Section
Generalizations of the Cross Section
The Differential Scattering Cross Section
Calculating the Differential Cross Section
Rutherford Scattering
Cross Sections in Various Frames
Relation of the CM and Lab Scattering Angles
Problems for Chapter 14
Special Relativity
Relativity
Galilean Relativity
The Postulates of Special Relativity
The Relativity of Time; Time Dilation
Length Contraction
The Lorentz Transformation
The Relativistic Velocity-Addition Formula
Four-Dimensional Space-Time; Four-Vectors
The Invariant Scalar Product
The Light Cone
The Quotient Rule and Doppler Effect
Mass, Four-Velocity, and Four-Momentum
Energy, the Fourth Component of Momentum
Collisions
Force in Relativity
Massless Particles; the Photon
Tensors
Electrodynamics and Relativity
Problems for Chapters 15
Continuum Mechanics
Transverse Motion of a Taut String
The Wave Equation
Boundary Conditions; Waves on a Finite String
The Three-Dimensional Wave Equation
Volume and Surface Forces
Stress and Strain: the Elastic Moduli
The Stress Tensor
The Strain Tensor for a Solid
Relation between Stress and Strain: Hooke's Law
The Equation of Motion for an Elastic Solid
Longitudinal and Transverse Waves in a Solid
Fluids: Description of the Motion
Waves in a Fluid
Problems for Chapter 16
Appendix: Diagonalizing Real Symmetric Matrices
Further Reading
Answers for Odd-Numbered Problems