# Understanding Quaternions

\$95.00

Dong Ding (Editor)
Roberval Laboratory, University of Technology of Compiègne, France

Zhuoyue Li (Editor)
School of Marine Science and Technology, Northwestern Polytechnical University, China

Series: Mathematics Research Developments
BISAC: MAT012000

Quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton. They form an interesting algebra where each object contains 4 scalar variables, instead of Euler angles, which is useful to overcome the gimbal lock phenomenon when treating the rotation of objects.

This book is about the mathematical basics and applications of quaternions. The first four chapters mainly concerns the mathematical theories, while the latter three chapters are related with three application aspects. It is expected to provide useful clues for researchers and engineers in the related area. In detail, this book is organized as follows:
In Chapter 1, mathematical basics including the quaternion algebra and operations with quaternions, as well as the relationships of quaternions with other mathematical parameters and representations are demonstrated. In Chapter 2, how quaternions are formulated in Clifford Algebra, how it is used in explaining rotation group in symplectic vector space and parallel transformation in holonomic dynamics are presented. In Chapter 3, the wave equation for a spin 3/2 particle, described by 16-component vector-bispinor, is investigated in spherical coordinates.

In Chapter 4, hyperbolic Lobachevsky and spherical Riemann models, parameterized coordinates with spherical and cylindric symmetry are studied. In Chapter 5, ship hydrodynamics with allowance of trim and sinkage is investigated and validated with experiments. In Chapter 6, the ballast flying phenomenon based on Discrete Discontinuous Analysis is presented. In Chapter 7, a numerical study is proposed to analyze the effect of the caisson sliding subjected to a hydrodynamic loading in the stability of the rear side of the rubble mound breakwater.

ISBN: N/A

Preface

Chapter 1. Mathematical Basics and Applications of Quaternions
(Aram Baghiyan, Improvis LLC, Yerevan, Armenia)

Chapter 2. Understanding Quaternions from Modern Algebra and Theoretical Physics
(Sadataka Furui, Teikyo University, Graduate School of Science and Engineering, Utsunomiya, Tochigi, Japan)

Chapter 3. Solutions with Spherical Symmetry of the Equation for a Spin 3/2 Particle
(A.V. Ivashkevich, Institute of Physics, National Academy of Sciences of Belarus, Belarus)

Chapter 4. Spinor Maxwell Equations in Riemannian Space-Time and Modeling Constitutive Relations
(A. V. Ivashkevich, E. M. Ovsiyuk, V. V. Kisel and V. M. Red’kov, Researcher, B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, Belarus, and others)

Chapter 5. Understanding Quaternions – Applications for Rigid Body Motion Predictions with CFD
(P. Du, A. Ouahsine and Haibao Hu, School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an, Shaanxi, China, and others)

Chapter 6. Applications for the Ballast-Flight
(D. Ding, A. Ouahsine and P. Du, Laboratoire Roberval, UMR-CNRS 7337, UT Compiègne-Sorbonne Université, Centre de Recherches, Royallieu, Compiègne Cedex, France, and others)

Chapter 7. Applications for the Stability of Caisson-Type Breakwaters
(D. Ding, A. Ouahsine and P. Du, Laboratoire Roberval, UMR-CNRS 7337, UT Compiègne-Sorbonne Université, Centre de Recherches, Royallieu, Compiègne Cedex, France, and others)

Index