Classical Mechanics From Newton to Einstein: A Modern Introduction

by McCall, Martin W.

• ISBN13: 9780470715741
• ISBN10: 047071574X
• Edition: 2nd
• Format: Hardcover
• Copyright: 2010-10-11
• Publisher: Wiley
• More Book Details

Summary

Classical Mechanics provides a clear introduction to the subject, combining a user-friendly style with an authoritative approach, whilst requiring minimal prerequisite mathematics - only elementary calculus and simple vectors are presumed. The text starts with a careful look at Newton's Laws, before applying them in one dimension to oscillations and collisions. More advanced applications - including gravitational orbits, rigid body dynamics and mechanics in rotating frames are deferred until after the limitations of Newton's inertial frames have been highlighted through an exposition of Einstein's Special Relativity. Comprehensive yet concise introduction to classical mechanics and relativity. Emphasize real life examples. Includes many interesting problems and a key revision notes chapter. Presented in a style that assumes a minimum of mathematical knowledge. Contains new chapter on computational dynamics. Unique mixture of classical mechanics with relativity. Supplementary web link and solutions manual.

Author Biography

Dr. Martin McCallis based at Imperial College London (UK) in the Photonics Group of the Physics Department. He began his research career at GEC Hirst Research Centre working on Photorefractives for real-time image processing. After completing his PhD he moved back to academia as a postdoc at the University of Bath (UK) where he worked on nonlinear dynamics in optoelectronic systems. Dr. McCall returned to Imperial College as a faculty member in Physics where he focusses mainly on complexity within linear optics, looking at how light diffracts in periodic and quasi-periodic structures. His particular specialism is using coupled wave techniques for simplifying problems that are otherwise very complicated. Aside from electromagnetics, he has interests in classical mechanics, relativity, chess and ceroc dancing. In addition to his book on Classical Mechanics: a Modern Introduction (2000), Dr. McCall has published over 75 refereed journal papers and conference presentations. He is joint holder of five patents.

Table of Contents

Preface to Second Edition

Preface to First Edition

Newton'sLaws

What is Mechanics?

Mechanics as a Scientific Theory

Newtonian vs. Einsteinian Mechanics

Newton's Laws

A Deeper Look at Newton's Laws

Inertial Frames

Newton's Laws in Noninertial Frames

Switching Off Gravity

Finale - Laws, Postulates or Definitions?

Summary

Problems

One-dimensional Motion

Rationale for One-dimensional Analysis

The Concept of a Particle

Motion with a Constant Force

Work and Energy

Impulse and Power

Motion with a Position-dependent Force

The Nature of Energy

Potential Functions

Equilibria

Motion Close to a Stable Equilibrium

The Stability of the Universe

Trajectory of a Body Falling a Large Distance Under Gravity

Motion with a Velocity-dependent Force

Summary

Problems

Oscillatory Motion

Introduction

Prototype Harmonic Oscillator

Differential Equations

General Solution for Simple Harmonic Motion

Energy in Simple Harmonic Motion

Damped Oscillations

Light Damping - the Q Factor

Heavy Damping and Critical Damping

Forced Oscillations

Complex Number Method

Electrical Analogue

Power in Forced Oscillations

Coupled Oscillations

Summary

Problems

Two-body Dynamics

Rationale

Centre of Mass

Internal Motion: Reduced Mass

Collisions

Elastic Collisions

Inelastic Collisions

Centre-of-mass Frame

Rocket Motion

Launch Vehicles

Summary

Problems

Relativity 1: Space and Time

Why Relativity?

Galilean Relativity

The Fundamental Postulates of Relativity

Inertial Observers in Relativity

Comparing Transverse Distances Between Frames

Lessons from a Light Clock: Time Dilation

Proper Time

Interval Invariance

The Relativity of Simultaneity

The Relativity of Length: Length Contraction

The Lorentz Transformations

Velocity Addition

Particles Moving Faster than Light: Tachyons

Summary

Problems

Relativity 2: Energy and Momentum

Energy and Momentum

The Meaning of Rest Energy

Relativistic Collisions and Decays

Photons

Units in High-energy Physics

Energy/Momentum Transformations Between Frames

Relativistic Doppler Effect

Summary

Problems

Gravitational Orbits

Introduction

Work in Three Dimensions

Torque and Angular Momentum

Central Forces

Gravitational Orbits

Kepler's Laws

Comments

Summary

Problems

Rigid Body Dynamics

Introduction

Torque and Angular Momentum for Systems of Particles

Centre of Mass of Systems of Particles and Rigid Bodies

Angular Momentum of Rigid Bodies

Kinetic Energy of Rigid Bodies

Bats, Cats, Pendula and Gyroscopes

General Rotation About a Fixed Axis

Principal Axes

Examples of Principal Axes and Principal Moments of Inertia

Kinetic Energy of a Body Rotating About a Fixed Axis

Summary

Problems

Rotating Frames

Introduction

Experiments on Roundabouts

General Prescription for Rotating Frames

The Centrifugal Term

The Coriolis Term

The Foucault Pendulum

Free Rotation of a Rigid Body - Tennis Rackets and Matchboxes

Final Thoughts

Summary

Problems

Vectors, Matrices and Eigenvalues

The Scalar (Dot) Product

The Vector (Cross) Product

The Vector Triple Product

Multiplying a Vector by a Matrix

Calculating the Determinant of a 3 × 3 Matrix

Eigenvectors and Eigenvalues

Diagonalising Symmetric Matrices

Answers to Problems

Bibliography

Index

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