Quaternions and Rotation Sequences

Author: Jack B. Kuipers
Publisher: Princeton University Press
ISBN: 9780691102986
Format: PDF, Docs
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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.

Quaternions and Rotation Sequences

Author: Jack B. Kuipers
Publisher:
ISBN: 9780691058726
Format: PDF
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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.

Visualizing Quaternions

Author: Andrew J. Hanson
Publisher: Elsevier
ISBN: 0080474772
Format: PDF, ePub, Docs
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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.

Quaternions for Computer Graphics

Author: John Vince
Publisher: Springer Science & Business Media
ISBN: 9780857297600
Format: PDF, Mobi
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Sir William Rowan Hamilton was a genius, and will be remembered for his significant contributions to physics and mathematics. The Hamiltonian, which is used in quantum physics to describe the total energy of a system, would have been a major achievement for anyone, but Hamilton also invented quaternions, which paved the way for modern vector analysis. Quaternions are one of the most documented inventions in the history of mathematics, and this book is about their invention, and how they are used to rotate vectors about an arbitrary axis. Apart from introducing the reader to the features of quaternions and their associated algebra, the book provides valuable historical facts that bring the subject alive. Quaternions for Computer Graphics introduces the reader to quaternion algebra by describing concepts of sets, groups, fields and rings. It also includes chapters on imaginary quantities, complex numbers and the complex plane, which are essential to understanding quaternions. The book contains many illustrations and worked examples, which make it essential reading for students, academics, researchers and professional practitioners.

Curves and Surfaces for Computer Graphics

Author: David Salomon
Publisher: Springer Science & Business Media
ISBN: 0387284524
Format: PDF, Kindle
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Requires only a basic knowledge of mathematics and is geared toward the general educated specialists. Includes a gallery of color images and Mathematica code listings.

From Natural Numbers to Quaternions

Author: Jürg Kramer
Publisher: Springer
ISBN: 3319694294
Format: PDF, ePub, Mobi
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This textbook offers an invitation to modern algebra through number systems of increasing complexity, beginning with the natural numbers and culminating with Hamilton's quaternions. Along the way, the authors carefully develop the necessary concepts and methods from abstract algebra: monoids, groups, rings, fields, and skew fields. Each chapter ends with an appendix discussing related topics from algebra and number theory, including recent developments reflecting the relevance of the material to current research. The present volume is intended for undergraduate courses in abstract algebra or elementary number theory. The inclusion of exercises with solutions also makes it suitable for self-study and accessible to anyone with an interest in modern algebra and number theory.

Rigid Body Dynamics for Beginners

Author: Phil Kim
Publisher: CreateSpace
ISBN: 9781493598205
Format: PDF, ePub, Mobi
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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.

A Tribble s Guide to Space

Author: Alan C. Tribble
Publisher: Princeton University Press
ISBN: 9780691027630
Format: PDF, Kindle
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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.

Dave Baum s Definitive Guide to LEGO MINDSTORMS

Author: Dave Baum
Publisher: Apress
ISBN: 1430253746
Format: PDF, ePub, Mobi
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Introduced in the fall of 1998, LEGO (R) MINDSTORMS (TM) quickly became LEGOs'best-selling kit of all time - with the average age of buyers turning out to be 23! Given the toys capabilities, its not surprising that a whole generation of adults interested in robotics or programming is rediscovering LEGO (R) through MINDSTORMS (TM). Although the Mindstorms (TM) kit includes basic instructions and sample robots, these are not comprehensive and do not adequately teach the principals of robotics. Without direction, inventing a robot from the ground-up can be a challenge. This book includes a wide variety of new robots, in-depth explanations for readers, and important theory behind the practice of building robots. In short, it provides all the information necessary to become a robotics expert using Mindstorms (TM). Dave Baum is considered to be the premiere expert on Lego (R) Mindstorms (TM), since he has even developed NQC ("Not Quite C") that has become the language of choice for performing sophisticated programming with these robots.