Bivectors and Waves in Mechanics and Optics

Softcover Nachdruck of the original 1. Auflage 1993
ISBN: 978-0-412-46460-7
Verlag: Taylor & Francis

Buch, Englisch, 281 Seiten, PB, Format (B × H): 145 mm x 222 mm, Gewicht: 551 g

Reihe: Applied Mathematics

Bivectors occur naturally in the description of elliptically polarized homogeneous and inhomogeneous plane waves. The description of a homogeneous plane wave generally involves a vector (the unit vector along the propagation direction) and a bivbector (the complex amplitude of the wave). Inhomogeneous plane waves are described in terms of two bivectors - the complex amplitude and the complex slowness. The use of bivectors and their associated ellipses is essential for the presentation of the 'directional ellipse' method given in this book, in deriving all possible inhomogeneous plane wave solutions in a given context.

The purpose of this book is to give an extensive treatment of the properties of bivectors and to show how these may be applied to the theory of homogeneous and inhomogeneous plane waves. For each chapter there are exercises with answers, many of which present further useful properties which are referred to afterwards. The material in this book is suitable for senior undergraduate and first year graduate students. It will also prove useful for researchers interested in homogeneous and inhomogeneous plane waves.

Zielgruppe

Research

Autoren/Hrsg.

Boulanger, P.

Boulanger, Philippe

Hayes, M. A.

Fachgebiete

• Naturwissenschaften Physik Mechanik Akustik, Schwingungsanalyse
• Naturwissenschaften Physik Elektromagnetismus Optik
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Angewandte Optik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau

Inhaltsverzeichnis

Preface 1 The ellipse 2 Bivectors 3 Complex symmetric matrices 4 Complex orthogonal matrices and complex skew-symmetric matrices 5 Ellipsoids 6 Homogeneous and inhomogeneous plane waves 7 Description of elliptical polarization 8 Energy flux 9 Electromagnetic plane waves 10 Plane waves in linearized elasticity theory 11 Plane waves in viscous fluids

Über Autor(innen)

Ph. Boulanger, Department de Mathematique, Universite Libre de Bruxelles, Belgium. M.A. Hayes, Mathematical Physics Department, University College Dublin, Ireland.