Classical Mechanics: From Newton to Einstein: A Modern Introduction

ISBN-13: 9780470715727 / Angielski / Miękka / 2010 / 256 str.

Martin McCall;?Abar;?Abar

Opis

This new edition of Classical Mechanics, aimed at undergraduate physics and engineering students, presents ina user-friendly style an authoritative approach to the complementary subjects of classical mechanics and relativity. 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 and rigid body dynamics - are discussed after the limitations of Newton's inertial frames have been highlighted through an exposition of Einstein's Special Relativity. Examples given throughout are often unusual for an elementary text, but are made accessible to the reader through discussion and diagrams. Updates and additions for this new edition include:

• New vector notation in Chapter 1
• An enhanced discussion of equilibria in Chapter 2
• A new section on a body falling a large distance towards a gravitational source in Chapter 2
• New sections in Chapter 8 on general rotation about a fixed principal axes, simple examples of principal axes and principal moments of inertia and kinetic energy of a body rotating about a fixed axis
• New sections in chapter 9: Foucault pendulum and free rotation of a rigid body; the latter including the famous tennis racquet theorem
• Enhanced chapter summaries at the end of each chapter
• Novel problems with numerical answers

A solutions manual is available at: www.wiley.com/go/mccall

Recenzje

"This book aimed at undergraduate physics and engineering students, presents in a user–friendly style an authoritative approach to the complementary subjects of classical mechanics and relativity." (Zentralblatt MATH, 2011)

"When McCall (Imperial College London) decided to produce a second edition of his introductory textbook, he was keen to keep it accessible to third–year undergraduates with minimal background in mathematics. So he has embellished the original material rather than expanding into more advanced areas. New discussions include a body free–falling a large distance under gravity, a demonstration that snooker balls always scatter at 90 degrees, the rotation of arbitrary bodies, and the tennis racket theorem." (Reference and Research Book News, February 2011)

Spis treści

Preface to Second Edition.

Preface to First Edition.

1 Newton′sLaws.

1.1 What is Mechanics?

1.2 Mechanics as a Scientific Theory.

1.3 Newtonian vs. Einsteinian Mechanics.

1.4 Newton′s Laws.

1.5 A Deeper Look at Newton′s Laws.

1.6 Inertial Frames.

1.7 Newton′s Laws in Noninertial Frames.

1.8 Switching Off Gravity.

1.9 Finale Laws, Postulates or Definitions?

1.10 Summary.

1.11 Problems.

2 One–dimensional Motion.

2.1 Rationale for One–dimensional Analysis.

2.2 The Concept of a Particle.

2.3 Motion with a Constant Force.

2.4 Work and Energy.

2.5 Impulse and Power.

2.6 Motion with a Position–dependent Force.

2.7 The Nature of Energy.

2.8 Potential Functions.

2.9 Equilibria.

2.10 Motion Close to a Stable Equilibrium.

2.11 The Stability of the Universe.

2.12 Trajectory of a Body Falling a Large Distance Under Gravity.

2.13 Motion with a Velocity–dependent Force.

2.14 Summary.

2.15 Problems.

3 Oscillatory Motion.

3.1 Introduction.

3.2 Prototype Harmonic Oscillator.

3.3 Differential Equations.

3.4 General Solution for Simple Harmonic Motion.

3.5 Energy in Simple Harmonic Motion.

3.6 Damped Oscillations.

3.7 Light Damping the Q Factor.

3.8 Heavy Damping and Critical Damping.

3.9 Forced Oscillations.

3.10 Complex Number Method.

3.11 Electrical Analogue.

3.12 Power in Forced Oscillations.

3.13 Coupled Oscillations.

3.14 Summary.

3.15 Problems.

4 Two–body Dynamics.

4.1 Rationale.

4.2 Centre of Mass.

4.3 Internal Motion: Reduced Mass.

4.4 Collisions.

4.5 Elastic Collisions.

4.6 Inelastic Collisions.

4.7 Centre–of–mass Frame.

4.8 Rocket Motion.

4.9 Launch Vehicles.

4.10 Summary.

4.11 Problems.

5 Relativity 1: Space and Time.

5.1 Why Relativity?

5.2 Galilean Relativity.

5.3 The Fundamental Postulates of Relativity.

5.4 Inertial Observers in Relativity.

5.5 Comparing Transverse Distances Between Frames.

5.6 Lessons from a Light Clock: Time Dilation.

5.7 Proper Time.

5.8 Interval Invariance.

5.9 The Relativity of Simultaneity.

5.10 The Relativity of Length: Length Contraction.

5.11 The Lorentz Transformations.

5.12 Velocity Addition.

5.13 Particles Moving Faster than Light: Tachyons.

5.14 Summary.

5.15 Problems.

6 Relativity 2: Energy and Momentum.

6.1 Energy and Momentum.

6.2 The Meaning of Rest Energy.

6.3 Relativistic Collisions and Decays.

6.4 Photons.

6.5 Units in High–energy Physics.

6.6 Energy/Momentum Transformations Between Frames.

6.7 Relativistic Doppler Effect.

6.8 Summary.

6.9 Problems.

7 Gravitational Orbits.

7.1 Introduction.

7.2 Work in Three Dimensions.

7.3 Torque and Angular Momentum.

7.4 Central Forces.

7.5 Gravitational Orbits.

7.6 Kepler′s Laws.

7.7 Comments.

7.8 Summary.

7.9 Problems.

8 Rigid Body Dynamics.

8.1 Introduction.

8.2 Torque and Angular Momentum for Systems of Particles.

8.3 Centre of Mass of Systems of Particles and Rigid Bodies.

8.4 Angular Momentum of Rigid Bodies.

8.5 Kinetic Energy of Rigid Bodies.

8.6 Bats, Cats, Pendula and Gyroscopes.

8.7 General Rotation About a Fixed Axis.

8.8 Principal Axes.

8.9 Examples of Principal Axes and Principal Moments of Inertia.

8.10 Kinetic Energy of a Body Rotating About a Fixed Axis.

8.11 Summary.

8.12 Problems.

9 Rotating Frames.

9.1 Introduction.

9.2 Experiments on Roundabouts.

9.3 General Prescription for Rotating Frames.

9.4 The Centrifugal Term.

9.5 The Coriolis Term.

9.6 The Foucault Pendulum.

9.7 Free Rotation of a Rigid Body Tennis Rackets and Matchboxes.

9.8 Final Thoughts.

9.9 Summary.

9.10 Problems.

Appendix 1: Vectors, Matrices and Eigenvalues.

A.1 The Scalar (Dot) Product.

A.2 The Vector (Cross) Product.

A.3 The Vector Triple Product.

A.4 Multiplying a Vector by a Matrix.

A.5 Calculating the Determinant of a 3 × 3 Matrix.

A.6 Eigenvectors and Eigenvalues.

A.7 Diagonalising Symmetric Matrices.

Appendix 2: Answers to Problems.

Appendix 3: Bibliography.

Index.

O autorze

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.

Blurb

This new edition of Classical Mechanics, aimed at undergraduate physics and engineering students, presents in a user–friendly style an authoritative approach to the complementary subjects of classical mechanics and relativity.

The book 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 and rigid body dynamics,are discussed after the limitations of Newton′s inertial frames have been highlighted through an exposition of Einstein′s Special Relativity. Examples given throughout are often unusual for an elementary text, but are made accessible to the reader through discussion and diagrams.

Updates and additions for this new edition include:

• New vector notation in Chapter 1
• An enhanced discussion of equilibria in Chapter 2
• A new section on a body falling a large distance towards a gravitational source in Chapter 2
• New sections in Chapter 8 on general rotation about a fixed principal axes, simple examples of principal axes and principal moments of inertia and kinetic energy of a body rotating about a fixed axis
• New sections in chapter 9: Foucault pendulum and free rotation of a rigid body; the latter including the famous tennis racquet theorem
• Enhanced chapter summaries at the end of each chapter
• Novel problems with numerical answers

A solutions manual is available at: www.wiley.com/go/mccall