Quaternions And Rotation Sequences
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Quaternions And Rotation Sequences
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Author : J. B. Kuipers
language : en
Publisher: Princeton University Press
Release Date : 1999
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 1999 with Mathematics categories.
The book is 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 first part 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 last part, 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.
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.
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.
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.
A Tribble S Guide To Space
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Author : Alan C. Tribble
language : en
Publisher: Princeton University Press
Release Date : 2002
A Tribble S Guide To Space written by Alan C. Tribble 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 2002 with Science categories.
Space--the final frontier. It's as little as fifty miles away, and yet it is considered one of the most dangerous and remote of places. Popular television shows such as Star Trek and movies such as Apollo 13 and October Sky have fired the imaginations of would-be explorers. Alan Tribble has worked on the design and development of dozens of spacecraft, including the Space Shuttle and the International Space Station. A Tribble's Guide to Space is a how-to book that is firmly grounded in the realities of current state-of-the-art space engineering while tapping into the power of imagination that drives us to explore. Alan Tribble offers a delightful guide to the nuts and bolts of space exploration, from how to get there to how to phone home and how to survive the harsh environment of space. Using examples from famous space missions, both factual and fictional, Tribble tackles fascinating real-world problems encountered in space exploration. Why do submarine hatches open inward and spacecraft hatches open outward? What do curveballs and satellites have in common? Why did Scotty, the chief engineer of the fictional USS Enterprise, always "need more power?" Why did the fire that destroyed Apollo I on the launch pad burn so furiously that no one could react fast enough to save the lives of the crew? In answering these questions, Tribble examines getting to space, from the physics of motion to the practical implications of Einstein's theory of relativity. He explores the basics of spaceships and starships, from power usage to navigation--all from the viewpoint of a spacecraft designer. This book describes rocket science and more in a manner that captures the common excitement shared by anyone with an interest in space exploration. Armchair astronauts, engineers who work in a space company and anyone who has looked up at the sky and wondered how we will get there will find reading this book a wonderful and enlightening experience.
Understanding Quaternions
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Author : Peng Du
language : en
Publisher: Nova Science Publishers
Release Date : 2020
Understanding Quaternions written by Peng Du and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.
"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"--
Rigid Body Dynamics For Beginners
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Author : Phil Kim
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2013
Rigid Body Dynamics For Beginners written by Phil Kim 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 2013 with Dynamics, Rigid categories.
Has anyone experienced difficulty and confusion in understanding what the Euler angles, quaternions, and direction cosine matrices are, and furthermore, about the relationships among them? This book is for those who had struggled to figure out what all the aforementioned concepts are, and also provides a practical example that could be easily followed with MATLAB. In addition, some surface of linear motions will also be touched so that in the end, a set of equations of motion that describe the motion of a rigid body in three-dimensional space could be constructed. Following step by step, the reader will be gradually immersed into the joy of learning and applying basic attitude dynamics. The book will be good for those who are already familiar in the field by helping them reorganize the concepts and knowledge they have learned before.
On Quaternions And Octonions
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Author : John H. Conway
language : en
Publisher: CRC Press
Release Date : 2003-01-23
On Quaternions And Octonions written by John H. Conway and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-23 with Mathematics categories.
This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less f
Spacecraft Modeling Attitude Determination And Control
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Author : Yaguang Yang
language : en
Publisher: CRC Press
Release Date : 2019-02-06
Spacecraft Modeling Attitude Determination And Control written by Yaguang Yang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-06 with Science categories.
This book discusses all spacecraft attitude control-related topics: spacecraft (including attitude measurements, actuator, and disturbance torques), modeling, spacecraft attitude determination and estimation, and spacecraft attitude controls. Unlike other books addressing these topics, this book focuses on quaternion-based methods because of its many merits. The book lays a brief, but necessary background on rotation sequence representations and frequently used reference frames that form the foundation of spacecraft attitude description. It then discusses the fundamentals of attitude determination using vector measurements, various efficient (including very recently developed) attitude determination algorithms, and the instruments and methods of popular vector measurements. With available attitude measurements, attitude control designs for inertial point and nadir pointing are presented in terms of required torques which are independent of actuators in use. Given the required control torques, some actuators are not able to generate the accurate control torques, therefore, spacecraft attitude control design methods with achievable torques for these actuators (for example, magnetic torque bars and control moment gyros) are provided. Some rigorous controllability results are provided. The book also includes attitude control in some special maneuvers, such as orbital-raising, docking and rendezvous, that are normally not discussed in similar books. Almost all design methods are based on state-spaced modern control approaches, such as linear quadratic optimal control, robust pole assignment control, model predictive control, and gain scheduling control. Applications of these methods to spacecraft attitude control problems are provided. Appendices are provided for readers who are not familiar with these topics.
Geometry Through History
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Author : Meighan I. Dillon
language : en
Publisher: Springer
Release Date : 2018-03-21
Geometry Through History written by Meighan I. Dillon and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-21 with Mathematics categories.
Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the field.