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Essential Dynamics and Relativity





ISBN 9781466588394
Published November 24, 2014 by CRC Press
334 Pages 115 B/W Illustrations

 
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Book Description

Essential Dynamics & Relativity provides students with an introduction to the core aspects of dynamics and special relativity. The author reiterates important ideas and terms throughout and covers concepts that are often missing from other textbooks at this level. He also places each topic within the wider constructs of the theory, without jumping from topic to topic to illustrate a point.

The first section of the book focuses on dynamics, discussing the basic aspects of single particle motion and analyzing the motion of multi-particle systems. The book also explains the dynamical behavior of both composite bodies (rigid bodies) and objects in non-inertial frames of reference (rotating reference frames).

The second section concentrates on relativity. The author describes the ideas leading to the inception of special relativity. He also formulates fundamental aspects, such as time dilation, length contraction, Lorentz transformations, and the visual aids of Minkowski diagrams, necessary to develop more sophisticated ideas. He then develops the concepts within the context of relativistic mechanics.

With many examples throughout and exercises at the end of each chapter, this text makes the often daunting and confusing ideas of dynamics and special relativity accessible to undergraduate students studying the subjects for the first time.

Table of Contents

DYNAMICS
The Galileo–Newton Formulation of Dynamics
Galilean relativity
Newton’s dynamical laws
Gravitational and inertial mass

Particle Dynamics in One Dimension
Motion of a particle under a force
Potential energy diagrams
Tension
Friction
Resistive motion
Escape velocity

Oscillations
Hooke’s law
Simple harmonic motion
Period of small oscillations
Damped simple harmonic motion
Damped simple harmonic motion with a forcing term
The LCR circuit

Particle Dynamics in Two and Three Dimensions
Projectiles
Energy and force
Charged particles in an electromagnetic field

Central Forces and Orbits
Central forces and angular momentum
Circular motion
Orbital motion
The inverse square law
The orbital equation
Perturbed orbits
Kepler’s laws of planetary motion
The perihelion precession of Mercury
Rutherford scattering

Multi-Particle Systems
Conservation of linear momentum
Conservation of angular momentum
The centre of mass frame
The two-body problem
Collisions
Inelastic collisions
Variable mass problems

Rigid Bodies
Rotation of a rigid body about a fixed axis
Planar motion of a rigid body

Rotating Reference Frames
Rates of change in a rotating frame
Newton’s second law in a rotating frame
The centrifugal force
The Coriolis force

RELATIVITY
Special Relativity
Inception
Einstein’s postulates of special relativity
Lorentz transformations
Minkowski diagrams (space-time diagrams)
Relativistic kinematics

Space-Time
The light cone
Proper time
The four-component vector formalism

Relativistic Mechanics
4-momentum
Relativistic energy
Massless particles
Aberration
Particle collisions

Appendix: Conic Sections

Solutions

Index

Exercises appear at the end of each chapter.

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Author(s)

Biography

Peter J. O’Donnell is a Lecturer in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge, where he is also a Fellow of St. Edmund’s College. Dr. O’Donnell’s current research focuses on Lanczos potential theory, black holes, and quantum gravity.

Reviews

"… an introduction to the central concepts of dynamics and special relativity … . Having a dual exploration of the two under one cover offers the rare opportunity for entry-level college physics students to understand their relationships, with mathematics backing the examples and exercises paired to better understand the concepts. The result is an approach more accessible to newcomers than most, and important for anyone studying dynamics and relativity."
Midwest Book Review, April 2015

"This book consists of two parts: one on classical Newtonian dynamics and one on Einstein’s special relativity theory. It is a refreshingly well-written book composed in a nice style but with due attention paid to precision. … [the] first part constitutes an excellent introduction to classical mechanics. The second part of the book is equally good and consists of three chapters on special relativity. … Throughout the book, many examples are given and many exercises are set (and solutions supplied at the end of the book). At several places, interesting historical remarks are made and which I believe are important for a full understanding of the ideas involved. This book is a welcome addition to the literature on this subject. It is well written in a most readable style and is a comprehensive introduction to classical and relativistic mechanics."
—Professor Graham Hall FRSE FRAS, Institute of Mathematics, University of Aberdeen