Bivectors and Waves in Mechanics and Optics
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...
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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.
Preface1The ellipse12Bivectors163Complex symmetric matrices414Complex orthogonal matrices and complex skew-symmetric matrices645Ellipsoids836Homogeneous and inhomogeneous plane waves1107Description of elliptical polarization1298Energy flux1559Electromagnetic plane waves16710Plane waves in linearized elasticity theory19111Plane waves in viscous fluids218Appendix. Spherical trigonometry231Answers to exercises235Bibliography271Index275
