Quaternions: Theory and Applications

Sandra Griffin (Editor)

Series: Mathematics Research Developments
BISAC: MAT040000

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This book focuses on the theory and applications of quaternions. Chapter One collects some old problems on lattice orders and directed partial orders on complex numbers and quaternions, and summarizes recent development in answering those questions. Chapter Two discusses spin 1 particles with anomalous magnetic moments in the external uniform electric field. Chapter Three examines techniques of projective operators used to construct solutions for a spin 1 particle with anomalous magnetic moment in the external uniform magnetic field. Chapter Four analyzes the implementation of a cheap Micro AHRS (Attitude and Heading Reference System) using low-cost inertial sensors. Chapter Five reviews the basic concepts of quaternion and reduced biquaternions algebra. It introduces the 2D Hermite-Gaussian functions (2D-HGF) as the eigenfunction of discrete quaternion Fourier transform (DQFT) and discrete reduced biquaternion Fourier transform (DRBQFT), and the eigenvalues of two dimensional Hermite-Gaussian functions for three types of DQFT and two types of DRBQFT. Chapter Six investigates a leader-follower formation control problem of quadrotors. Chapter Seven considers determinantal representations the Drazin and weighted Drazin inverses over the quaternion skew field.
(Imprint: Novinka)

Preface

Chapter 1. Directed Partial Orders on Quaternions – A Brief Summary
Jingjing Ma (Department of Mathematics and Statistics, University of Houston Clear Lake, Houston, TX, USA)

Chapter 2. Spin 1 Particle with Anomalous Magnetic Moment in the External Uniform Electric Field
E.M. Ovsiyuk, Ya.A. Voynova, V.V. Kisel, V. Balan, and V.M. Red’kov (Mozyr State Pedagogical University, Belarus, and others)

Chapter 3. Techniques of Projective Operators used to Construct Solutions for a Spin 1 Particle with Anomalous Magnetic Moment in the External Uniform Magnetic Field
V.V. Kisel, Ya.A. Voynova, E.M. Ovsiyuk, V. Balan, and V.M. Red’kov (BGUIR, Minsk, Belarus, and others)

Chapter 4. A Quaternion Approach in the Estimation of the Attitude of an Industrial Robot
Bernardino Benito Salmerón-Quiroz, Gerardo Villegas-Medina, José Fermi Guerrero-Castellanos, Elena O. Milhacea, and Rodolfo Villalobos-Martinez, Ph.D (Salmerón-Quiroz and Villegas-Medina are with the Instituto Politécnico Nacional (I.P.N.), SEPI ESIME Azcapotzalco, CDMX, México, and others)

Chapter 5. 2D Hermite-Gaussian and Gauss-Laguerre Circular Harmonic Eigenfunction of the Quaternion and Reduced Biquaternion Fourier Transform
Soo-Chang Pei and Yu-Zhe Hsiao (Graduate Institute of Communication Engineering, National Taiwan University, Taipei, Taiwan)

Chapter 6. The Quaternions with an Application of Quadrotors Team Formation
Wesam Jasim and Dongbing Gu (School of Computer Science and Electronic Engineering, University of Essex, Wivenhoe Park, Colchester, UK)

Chapter 7. Determinantal Representations of the Drazin and W-Weighted Drazin Inverses Over the Quaternion Skew Field with Applications
Ivan Kyrchei (Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Lviv, Ukraine)

Index

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