Understanding quaternions

著者

• Du, Peng
• Hu, Haibao
• Ding, Dong
• Li, Zhuoyue

書誌事項

Understanding quaternions

Peng Du, Haibao Hu, Dong Ding, and Zhouyue [i.e. Zhuoyue] Li, [editors]

（Mathematics research developments series）

Nova Science Publishers, c2020

• pbk.

注記

"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" -- Preface

Includes bibliographical references and index

内容説明・目次

内容説明

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.

目次

• 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.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BC02271506
• ISBN:
  • 9781536183436
• LCCN: 2020037161
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: New York
• ページ数/冊数: vi, 189 p.
• 大きさ: 23 cm
• 分類:
  • LCC : QA196
  • DC23 : 512/.5
• 件名:
  • LCSH : Quaternions
  • LCSH : Numbers, Complex
• 親書誌ID:
  • BA91354859