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Author : Alexander McAulay
Publisher :
ISBN 13 :
Total Pages : 134 pages
Book Rating : 4.3/5 (555 download)
Download or read book Utility of Quaternions in Physics written by Alexander McAulay and published by . This book was released on 1893 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 121 pages
Book Rating : 4.:/5 (646 download)
Download or read book Utility of Quaternions in Physics written by and published by . This book was released on 1893 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alexander McAulay
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781548174828
Total Pages : 120 pages
Book Rating : 4.1/5 (748 download)
Download or read book Utility of Quaternions in Physics written by Alexander McAulay and published by Createspace Independent Publishing Platform. This book was released on 2017-06-18 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : A. McAulay
Publisher : Forgotten Books
ISBN 13 : 9780331922653
Total Pages : 122 pages
Book Rating : 4.9/5 (226 download)
Download or read book Utility of Quaternions in Physics (Classic Reprint) written by A. McAulay and published by Forgotten Books. This book was released on 2017-11-25 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Utility of Quaternions in Physics IT is a curious phenomenon in the History of Mathematics that the greatest work of the greatest Mathematician of the century which prides itself upon being the most enlightened the world has yet seen, has suffered the most chilling neglect. The cause of this is not at first sight obvious. We have here little to do with the benefit provided by Quaternions to Pure Mathematics. The reason for the neglect here may be that Hamilton himself has developed the Science to such an extent as to make successors an impossibility. One cannot however resist a strong suspicion that were the subject even studied we should hear more from Pure Mathematicians, of Hamilton's valuable results. This reason at any rate cannot be assigned for the neglect'of the Physical side of Quaternions. Hamilton has done but little in this field, and yet when we ask what Mathematical Physicists have been tempted by the bait to win easy laurels (to put the incentive on no higher grounds), the answer must be scarcely one. Prof. Tait is the grand exception to this. But well known Physicist though he be, his fellow-workers for the most part render themselves incapable of appreciating his valuable services by studying the subject if at all only as dilettanti. The number who read a small amount in Quaternions is by no means small, but those who get further than what is recommended by Maxwell as imperatively necessary are but a small percentage of the whole. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author : McAulay Alexander
Publisher : Legare Street Press
ISBN 13 : 9781017329803
Total Pages : 0 pages
Book Rating : 4.3/5 (298 download)
Download or read book Utility of Quaternions in Physics written by McAulay Alexander and published by Legare Street Press. This book was released on 2022-10-27 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author : A. McAulay
Publisher : Forgotten Books
ISBN 13 : 9781330308141
Total Pages : 123 pages
Book Rating : 4.3/5 (81 download)
Download or read book Utility of Quaternions in Physics written by A. McAulay and published by Forgotten Books. This book was released on 2015-06-15 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Utility of Quaternions in Physics The present publication is an essay that was sent in (December, 1887) to compete for the Smith's Prizes at Cambridge. To the onlooker it is always a mournful thing to see what he considers splendid abilities or opportunities wasted for lack of knowledge of some paltry common-place truth. Such is in the main my feeling when considering the neglect of the study of Quaternions by that wonderful corporation the University of Cambridge. To the alumnus she is apt to appear as the leader in all branches of Mathematics. To the outsider she appears rather as the leader in Applied Mathematics and as a ready welcomer of other branches. If Quaternions were simply a branch of Pure Mathematics we could understand why the study of them was almost confined to the University which gave birth to them, but as the truth is quite otherwise it is hard to shew good reason why they have not struck root also in Cambridge. The prophet on whom Hamilton's mantle has fallen is more than a mathematician and more than a natural philosopher - he is both, and it is to be noted also that he is a Cambridge man. He has preached in season and out of season (if that were possible) that Quaternions are especially useful in Physical applications. Why then has his Alma Mater turned a deaf ear? I cannot believe that she is in her dotage and has lost her hearing. The problem is beyond me and I give it up. But I wish to add my little efforts to Prof. Tait's powerful advocacy to bring about another state of affairs. Cambridge is the prepared ground on which if anywhere the study of the Physical applications of Quaternions ought to flourish. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author : Alexander McAulay
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.3/5 (91 download)
Download or read book Utility of Quaternions in Physics written by Alexander McAulay and published by . This book was released on 1893 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Patrick R. Girard
Publisher : Springer Science & Business Media
ISBN 13 : 3764377917
Total Pages : 180 pages
Book Rating : 4.7/5 (643 download)
Download or read book Quaternions, Clifford Algebras and Relativistic Physics written by Patrick R. Girard and published by Springer Science & Business Media. This book was released on 2007-06-25 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of Clifford algebras in mathematical physics and engineering has grown rapidly in recent years. Whereas other developments have privileged a geometric approach, this book uses an algebraic approach that can be introduced as a tensor product of quaternion algebras and provides a unified calculus for much of physics. It proposes a pedagogical introduction to this new calculus, based on quaternions, with applications mainly in special relativity, classical electromagnetism, and general relativity.
Author : A McAulay
Publisher :
ISBN 13 : 9781673858877
Total Pages : 120 pages
Book Rating : 4.8/5 (588 download)
Download or read book Utility of Quaternions in Physics written by A McAulay and published by . This book was released on 2019-12-10 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present publication is an essay that was sent in (December, 1887) to compete for the Smith's Prizes at Cambridge.To the onlooker it is always a mournful thing to see what he considers splendid abilities or opportunities wasted for lack of knowledge of some paltry commonplace truth. Such is in the main my feeling when considering the neglect of the study of Quaternions by that wonderful corporation the University of Cambridge. To the alumnus she is apt to appear as the leader in all branches of Mathematics. To the outsider she appears rather as the leader in Applied Mathematics and as a ready welcomer of other branches.
Author : Alexander McAulay
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781724710185
Total Pages : 130 pages
Book Rating : 4.7/5 (11 download)
Download or read book Utility of Quaternions in Physics written by Alexander McAulay and published by Createspace Independent Publishing Platform. This book was released on 2018-08-12 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Utility of Quaternions in Physics: Large Print By Alexander McAulay 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. We are delighted to publish this classic book as part of our extensive Classic Library collection. Many of the books in our collection have been out of print for decades, and therefore have not been accessible to the general public. The aim of our publishing program is to facilitate rapid access to this vast reservoir of literature, and our view is that this is a significant literary work, which deserves to be brought back into print after many decades. The contents of the vast majority of titles in the Classic Library have been scanned from the original works. To ensure a high quality product, each title has been meticulously hand curated by our staff. Our philosophy has been guided by a desire to provide the reader with a book that is as close as possible to ownership of the original work. We hope that you will enjoy this wonderful classic work, and that for you it becomes an enriching experience.
Author : A. McAULAY McAULAY
Publisher : Independently Published
ISBN 13 : 9781791393946
Total Pages : 119 pages
Book Rating : 4.3/5 (939 download)
Download or read book Utility of Quaternions in Physics written by A. McAULAY McAULAY and published by Independently Published. This book was released on 2018-12-10 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present publication is an essay that was sent in (December, 1887) to compete for the Smith's Prizes at Cambridge.To the onlooker it is always a mournful thing to see what he considers splendid abilities or opportunities wasted for lack of knowledge of some paltry commonplace truth. Such is in the main my feeling when considering the neglect of the study of Quaternions by that wonderful corporation the University of Cambridge. To the alumnus she is apt to appear as the leader in all branches of Mathematics. To the outsider she appears rather as the leader in Applied Mathematics and as a ready welcomer of other branches.
Author : A McAulay
Publisher :
ISBN 13 : 9781678503833
Total Pages : 120 pages
Book Rating : 4.5/5 (38 download)
Download or read book Utility of Quaternions in Physics written by A McAulay and published by . This book was released on 2019-12-20 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present publication is an essay that was sent in (December, 1887) to compete for the Smith's Prizes at Cambridge.To the onlooker it is always a mournful thing to see what he considers splendid abilities or opportunities wasted for lack of knowledge of some paltry commonplace truth. Such is in the main my feeling when considering the neglect of the study of Quaternions by that wonderful corporation the University of Cambridge. To the alumnus she is apt to appear as the leader in all branches of Mathematics. To the outsider she appears rather as the leader in Applied Mathematics and as a ready welcomer of other branches.
Author : Helge Kragh
Publisher : Cambridge University Press
ISBN 13 : 9780521380898
Total Pages : 404 pages
Book Rating : 4.3/5 (88 download)
Download or read book Dirac written by Helge Kragh and published by Cambridge University Press. This book was released on 1990-03-30 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first full length biography of Dirac, one of the most brilliant physicists of the twentieth century.
Author : John Vince
Publisher : Springer Nature
ISBN 13 : 1447175093
Total Pages : 188 pages
Book Rating : 4.4/5 (471 download)
Download or read book Quaternions for Computer Graphics written by John Vince and published by Springer Nature. This book was released on 2021-09-02 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: If you have ever wondered what quaternions are — then look no further, John Vince will show you how simple and useful they are. This 2nd edition has been completely revised and includes extra detail on the invention of quaternions, a complete review of the text and equations, all figures are in colour, extra worked examples, an expanded index, and a bibliography arranged for each chapter. Quaternions for Computer Graphics includes chapters on number sets and algebra, imaginary and complex numbers, the complex plane, rotation transforms, and a comprehensive description of quaternions in the context of rotation. The book will appeal to students of computer graphics, computer science and mathematics, as well as programmers, researchers, academics and professional practitioners interested in learning about quaternions. John Vince explains in an easy-to-understand language, with the aid of useful figures, how quaternions emerged, gave birth to modern vector analysis, disappeared, and reemerged to be adopted by the flight simulation industry and computer graphics. This book will give you the confidence to use quaternions within your every-day mathematics, and explore more advanced texts.
Author : J. B. Kuipers
Publisher : Princeton University Press
ISBN 13 : 0691211701
Total Pages : 396 pages
Book Rating : 4.6/5 (912 download)
Download or read book Quaternions and Rotation Sequences written by J. B. Kuipers and published by Princeton University Press. This book was released on 2020-03-31 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Jakob Schwichtenberg
Publisher : Springer
ISBN 13 : 3319666312
Total Pages : 287 pages
Book Rating : 4.3/5 (196 download)
Download or read book Physics from Symmetry written by Jakob Schwichtenberg and published by Springer. This book was released on 2017-12-01 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations. Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations.
Author : Simon L. Altmann
Publisher : Courier Corporation
ISBN 13 : 0486317730
Total Pages : 315 pages
Book Rating : 4.4/5 (863 download)
Download or read book Rotations, Quaternions, and Double Groups written by Simon L. Altmann and published by Courier Corporation. This book was released on 2013-04-09 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
