O’Donnell Essential Dynamics and Relativity

1. Auflage 2014
ISBN: 978-1-4665-8840-0
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 334 Seiten

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.

Autoren/Hrsg.

O’Donnell, Peter J.

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

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.

Über Autor(innen)

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.