Quaternions

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Rotations Quaternions And Double Groups

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Author : Simon L. Altmann
language : en
Publisher: Courier Corporation
Release Date : 2013-04-09

Rotations Quaternions And Double Groups written by Simon L. Altmann and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Mathematics categories.

This self-contained text presents a consistent description of the geometric and quaternionic treatment of rotation operators, employing methods that lead to a rigorous formulation and offering complete solutions to many illustrative problems. Geared toward upper-level undergraduates and graduate students, the book begins with chapters covering the fundamentals of symmetries, matrices, and groups, and it presents a primer on rotations and rotation matrices. Subsequent chapters explore rotations and angular momentum, tensor bases, the bilinear transformation, projective representations, and the geometry, topology, and algebra of rotations. Some familiarity with the basics of group theory is assumed, but the text assists students in developing the requisite mathematical tools as necessary.

Quaternions And Rotation Sequences

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Author : J. B. Kuipers
language : en
Publisher: Princeton University Press
Release Date : 2020-03-31

Quaternions And Rotation Sequences written by J. B. Kuipers and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-31 with Mathematics categories.

Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth century--a feat he celebrated by carving the founding equations into a stone bridge--mathematicians and engineers have been fascinated by these mathematical objects. Today, they are used in applications as various as describing the geometry of spacetime, guiding the Space Shuttle, and developing computer applications in virtual reality. In this book, J. B. Kuipers introduces quaternions for scientists and engineers who have not encountered them before and shows how they can be used in a variety of practical situations. The book is primarily an exposition of the quaternion, a 4-tuple, and its primary application in a rotation operator. But Kuipers also presents the more conventional and familiar 3 x 3 (9-element) matrix rotation operator. These parallel presentations allow the reader to judge which approaches are preferable for specific applications. The volume is divided into three main parts. The opening chapters present introductory material and establish the book's terminology and notation. The next part presents the mathematical properties of quaternions, including quaternion algebra and geometry. It includes more advanced special topics in spherical trigonometry, along with an introduction to quaternion calculus and perturbation theory, required in many situations involving dynamics and kinematics. In the final section, Kuipers discusses state-of-the-art applications. He presents a six degree-of-freedom electromagnetic position and orientation transducer and concludes by discussing the computer graphics necessary for the development of applications in virtual reality.

Introduction To Quaternions With Numerous Examples

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Author : Philip Kelland
language : en
Publisher:
Release Date : 1873

Introduction To Quaternions With Numerous Examples written by Philip Kelland and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1873 with Quaternions categories.

Visualizing Quaternions

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Author : Andrew J. Hanson
language : en
Publisher: Elsevier
Release Date : 2006-02-06

Visualizing Quaternions written by Andrew J. Hanson and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-06 with Mathematics categories.

Introduced 160 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in modern computer graphics. They offer a powerful way to represent rotations and compared to rotation matrices they use less memory, compose faster, and are naturally suited for efficient interpolation of rotations. Despite this, many practitioners have avoided quaternions because of the mathematics used to understand them, hoping that some day a more intuitive description will be available. The wait is over. Andrew Hanson's new book is a fresh perspective on quaternions. The first part of the book focuses on visualizing quaternions to provide the intuition necessary to use them, and includes many illustrative examples to motivate why they are important—a beautiful introduction to those wanting to explore quaternions unencumbered by their mathematical aspects. The second part covers the all-important advanced applications, including quaternion curves, surfaces, and volumes. Finally, for those wanting the full story of the mathematics behind quaternions, there is a gentle introduction to their four-dimensional nature and to Clifford Algebras, the all-encompassing framework for vectors and quaternions. Richly illustrated introduction for the developer, scientist, engineer, or student in computer graphics, visualization, or entertainment computing. Covers both non-mathematical and mathematical approaches to quaternions.

The Outlines Of Quaternions

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Author : Henry William Lovett Hime
language : en
Publisher:
Release Date : 1894

The Outlines Of Quaternions written by Henry William Lovett Hime and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1894 with Quaternions categories.

Elements Of Quaternions

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Author : Arthur Sherburne Hardy
language : en
Publisher:
Release Date : 1881

Elements Of Quaternions written by Arthur Sherburne Hardy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1881 with Quaternions categories.

Quaternions

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Author : Dennis Morris
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2015-11-09

Quaternions written by Dennis Morris and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-09 with categories.

This book is about quaternions. The quaternions are derived from finite group theory. Non-commutative differentiation is included, as is non-commutative rotation. Quaternion trigonometry is included. Double cover rotation is included. The spinors of quantum physics are shown to be quaternions. Lie algebra and Clifford algebra are visited.

Quaternions And Cayley Numbers

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Author : J.P. Ward
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Quaternions And Cayley Numbers written by J.P. Ward and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

In essence, this text is written as a challenge to others, to discover significant uses for Cayley number algebra in physics. I freely admit that though the reading of some sections would benefit from previous experience of certain topics in physics - particularly relativity and electromagnetism - generally the mathematics is not sophisticated. In fact, the mathematically sophisticated reader, may well find that in many places, the rather deliberate progress too slow for their liking. This text had its origin in a 90-minute lecture on complex numbers given by the author to prospective university students in 1994. In my attempt to develop a novel approach to the subject matter I looked at complex numbers from an entirely geometric perspective and, no doubt in line with innumerable other mathematicians, re-traced steps first taken by Hamilton and others in the early years of the nineteenth century. I even enquired into the possibility of using an alternative multiplication rule for complex numbers (in which argzlz2 = argzl- argz2) other than the one which is normally accepted (argzlz2 = argzl + argz2). Of course, my alternative was rejected because it didn't lead to a 'product' which had properties that we now accept as fundamental (i. e.

A Manual Of Quaternions

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Author : Charles Jasper Joly
language : en
Publisher:
Release Date : 1905

A Manual Of Quaternions written by Charles Jasper Joly and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1905 with Quaternions categories.

Utility Of Quaternions In Physics

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Author : Alexander McAulay
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2017-06-18

Utility Of Quaternions In Physics written by Alexander McAulay and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-18 with categories.

In math, the quaternions are a number method that extends the complex numbers. They were originally described by the mathematician William Rowan Hamilton and applied to mechanics in space (3D). Quaternions characteristics are that multiplication of two quaternions is noncommutative. Hamilton defined a quaternion as the quotient of two lines in 3D (the quotient of two vectors). Quaternions find uses in theoretical and applied mathematics, in particular for calculations involving 3D rotations such as in computer graphics, computer vision, and crystallographic texture analysis. In useful applications, they find use alongside other methods, like Euler angles and rotation matrices, depending on the application. In contemporary mathematical language, quaternions form a 4D associative normed division algebra over the real numbers, and consequently also a domain. In fact, the quaternions were the elementary noncommutative division algebra to be discovered. According to the Frobenius theorem, it is one of only two finite-dimensional dividing rings containing the real numbers as a proper subring, and the other being the complex numbers. These rings are also Euclidean Hurwitz algebras, of whichever quaternions are the largest associative algebra.