Understanding Quaternions

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Bibliographic Details
Title:	Understanding Quaternions
Description:	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.
Authors:	Peng Du
Resource Type:	eBook.
Subjects:	Quaternions, Numbers, Complex
Categories:	MATHEMATICS / Geometry / General
Database:	eBook Academic Collection (EBSCOhost)

FullText	Links: – Type: ebook-pdf Text: Availability: 0
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Items	– Name: Title Label: Title Group: Ti Data: Understanding Quaternions – Name: Abstract Label: Description Group: Ab Data: 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. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Peng+Du%22">Peng Du</searchLink> – Name: TypePub Label: Resource Type Group: TypPub Data: eBook. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Quaternions%22">Quaternions</searchLink><br /><searchLink fieldCode="DE" term="%22Numbers%2C+Complex%22">Numbers, Complex</searchLink> – Name: SubjectBISAC Label: Categories Group: Su Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Geometry+%2F+General%22">MATHEMATICS / Geometry / General</searchLink>
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RecordInfo	BibRecord: BibEntity: Classifications: – Code: 512.5 Scheme: ddc Type: prePub Languages: – Code: eng Text: English Subjects: – SubjectFull: Quaternions Type: general – SubjectFull: Numbers, Complex Type: general Titles: – TitleFull: Understanding Quaternions Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Peng Du – PersonEntity: Name: NameFull: Peng Du IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2020 – D: 30 M: 10 Type: profile Y: 2020 Identifiers: – Type: isbn-print Value: 9781536183436 – Type: isbn-electronic Value: 9781536185539 Titles: – TitleFull: Understanding Quaternions Type: main
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