Understanding Quaternions

Peng Du (Herausgeber)

Buch | Softcover

184 Seiten

2020
Nova Science Publishers Inc (Verlag)
978-1-5361-8343-6 (ISBN)

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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.

Preface; Mathematical Basics and Applications of Quaternions; Understanding Quaternions from Modern Algebra and Theoretical Physics; Solutions with Spherical Symmetry of the Equation for a Spin 3/2 Particle; Spinor Maxwell Equations in Riemannian Space-Time and Modeling Constitutive Relations; Understanding Quaternions: Applications for Rigid Body Motion Predictions with CFD; Applications for the Ballast-Flight; Applications for the Stability of Caisson-Type Breakwaters; Index.

Erscheinungsdatum	02.11.2020
Verlagsort	New York
Sprache	englisch
Maße	155 x 230 mm
Gewicht	294 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-5361-8343-1 / 1536183431
ISBN-13	978-1-5361-8343-6 / 9781536183436
Zustand	Neuware