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9780470715741

Classical Mechanics From Newton to Einstein: A Modern Introduction

by
  • ISBN13:

    9780470715741

  • ISBN10:

    047071574X

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2010-10-11
  • Publisher: Wiley

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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
Table of Contents provided by Publisher. All Rights Reserved.

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