Essential Dynamics and Relativity: 1st Edition (Paperback) book cover

Essential Dynamics and Relativity

1st Edition

By Peter J. O’Donnell

CRC Press

334 pages | 115 B/W Illus.

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Paperback: 9781466588394
pub: 2014-11-24

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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.


"… 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

Table of Contents


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



Resistive motion

Escape velocity


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


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


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


Special Relativity


Einstein’s postulates of special relativity

Lorentz transformations

Minkowski diagrams (space-time diagrams)

Relativistic kinematics


The light cone

Proper time

The four-component vector formalism

Relativistic Mechanics


Relativistic energy

Massless particles


Particle collisions

Appendix: Conic Sections



Exercises appear at the end of each chapter.

About the Author

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.

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Mathematical Physics
SCIENCE / Physics