Quaternions and Rotation Sequences

A Primer with Applications to Orbits, Aerospace, and Virtual Reality

Author: Jack B. Kuipers

Publisher: Princeton University Press

ISBN: 9780691102986

Category: Mathematics

Page: 371

View: 7334

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.

Von den natürlichen Zahlen zu den Quaternionen

Basiswissen Zahlbereiche und Algebra

Author: Jürg Kramer,Anna-Maria von Pippich

Publisher: Springer-Verlag

ISBN: 3658020555

Category: Mathematics

Page: 219

View: 1512

Dieses Buch richtet sich an Bachelor- und Lehramtsstudierende der ersten Semester und vermittelt einen fundierten Aufbau der Zahlbereiche. Ausgehend von den natürlichen Zahlen werden systematisch die ganzen, rationalen, reellen und komplexen Zahlen bis hin zu den Hamiltonschen Quaternionen konstruiert. Dazu werden jeweils die aus der Algebra benötigten Grundlagen bereitgestellt und motiviert. Für den Bachelor-Studiengang Mathematik bietet das Buch einen vielseitigen Aufbau der Zahlbereiche, für den in den Anfängervorlesungen oftmals die Zeit fehlt. Lehramtsstudierenden verhilft dieses Buch zu einem anschaulichen Verständnis der Zahlbereiche von einem mathematisch-fachwissenschaftlichen Standpunkt, welches für die mathematikdidaktische Ausbildung eine wesentliche Grundlage darstellt und für die mathematische Kompetenz im Lehrerberuf unabdingbar ist. Das Buch enthält zum besseren Verständnis zahlreiche Aufgaben und Lösungen.


Author: Jürgen Richter-Gebert,Thorsten Orendt

Publisher: Springer-Verlag

ISBN: 3642025307

Category: Mathematics

Page: 224

View: 3019

Wie kann man geometrische Objekte und Operationen so darstellen, dass sie durch möglichst einfache algebraische Manipulationen verarbeitet werden können? Dieser Leitfrage geht das Buch in insgesamt zwölf Kapiteln nach und schlägt damit eine Brücke vom Grundwissen in der Linearen Algebra zu modernen Ansätzen der Geometrie. Neben Übungsaufgaben und Abbildungen wird jedes Kapitel durch einen Exkurs zu Anwendungen und weiterführenden Themen ergänzt. Das Buch richtet sich an Studierende und Dozenten der Mathematik, Informatik und Physik (ab 3. Semester).

Multisensor Attitude Estimation

Fundamental Concepts and Applications

Author: Hassen Fourati,Djamel Eddine Chouaib Belkhiat

Publisher: CRC Press

ISBN: 1498745806

Category: Technology & Engineering

Page: 580

View: 4258

There has been an increasing interest in multi-disciplinary research on multisensor attitude estimation technology driven by its versatility and diverse areas of application, such as sensor networks, robotics, navigation, video, biomedicine, etc. Attitude estimation consists of the determination of rigid bodies’ orientation in 3D space. This research area is a multilevel, multifaceted process handling the automatic association, correlation, estimation, and combination of data and information from several sources. Data fusion for attitude estimation is motivated by several issues and problems, such as data imperfection, data multi-modality, data dimensionality, processing framework, etc. While many of these problems have been identified and heavily investigated, no single data fusion algorithm is capable of addressing all the aforementioned challenges. The variety of methods in the literature focus on a subset of these issues to solve, which would be determined based on the application in hand. Historically, the problem of attitude estimation has been introduced by Grace Wahba in 1965 within the estimate of satellite attitude and aerospace applications. This book intends to provide the reader with both a generic and comprehensive view of contemporary data fusion methodologies for attitude estimation, as well as the most recent researches and novel advances on multisensor attitude estimation task. It explores the design of algorithms and architectures, benefits, and challenging aspects, as well as a broad array of disciplines, including: navigation, robotics, biomedicine, motion analysis, etc. A number of issues that make data fusion for attitude estimation a challenging task, and which will be discussed through the different chapters of the book, are related to: 1) The nature of sensors and information sources (accelerometer, gyroscope, magnetometer, GPS, inclinometer, etc.); 2) The computational ability at the sensors; 3) The theoretical developments and convergence proofs; 4) The system architecture, computational resources, fusion level.

Clifford Analysis and Its Applications

Author: F. Brackx,J.S.R. Chisholm,V. Soucek

Publisher: Springer Science & Business Media

ISBN: 9401008620

Category: Mathematics

Page: 416

View: 3498

In its traditional form, Clifford analysis provides the function theory for solutions of the Dirac equation. From the beginning, however, the theory was used and applied to problems in other fields of mathematics, numerical analysis, and mathematical physics. recently, the theory has enlarged its scope considerably by incorporating geometrical methods from global analysis on manifolds and methods from representation theory. New, interesting branches of the theory are based on conformally invariant, first-order systems other than the Dirac equation, or systems that are invariant with respect to a group other than the conformal group. This book represents an up-to-date review of Clifford analysis in its present form, its applications, and directions for future research. Readership: Mathematicians and theoretical physicists interested in Clifford analysis itself, or in its applications to other fields.

3D User Interfaces

Theory and Practice, CourseSmart eTextbook

Author: Doug Bowman,Ernst Kruijff,Joseph J. LaViola Jr.,Ivan P. Poupyrev

Publisher: Addison-Wesley

ISBN: 013339056X

Category: Computers

Page: 507

View: 4238

Here’s what three pioneers in computer graphics and human-computer interaction have to say about this book: “What a tour de force—everything one would want—comprehensive, encyclopedic, and authoritative.” —Jim Foley “At last, a book on this important, emerging area. It will be an indispensable reference for the practitioner, researcher, and student interested in 3D user interfaces.” —Andy van Dam “Finally, the book we need to bridge the dream of 3D graphics with the user-centered reality of interface design. A thoughtful and practical guide for researchers and product developers. Thorough review, great examples.” —Ben Shneiderman As 3D technology becomes available for a wide range of applications, its successful deployment will require well-designed user interfaces (UIs). Specifically, software and hardware developers will need to understand the interaction principles and techniques peculiar to a 3D environment. This understanding, of course, builds on usability experience with 2D UIs. But it also involves new and unique challenges and opportunities. Discussing all relevant aspects of interaction, enhanced by instructive examples and guidelines, 3D User Interfaces comprises a single source for the latest theory and practice of 3D UIs. Many people already have seen 3D UIs in computer-aided design, radiation therapy, surgical simulation, data visualization, and virtual-reality entertainment. The next generation of computer games, mobile devices, and desktop applications also will feature 3D interaction. The authors of this book, each at the forefront of research and development in the young and dynamic field of 3D UIs, show how to produce usable 3D applications that deliver on their enormous promise. Coverage includes: The psychology and human factors of various 3D interaction tasks Different approaches for evaluating 3D UIs Results from empirical studies of 3D interaction techniques Principles for choosing appropriate input and output devices for 3D systems Details and tips on implementing common 3D interaction techniques Guidelines for selecting the most effective interaction techniques for common 3D tasks Case studies of 3D UIs in real-world applications To help you keep pace with this fast-evolving field, the book’s Web site, www.3dui.org, will offer information and links to the latest 3D UI research and applications.

3D programming for Windows

three-dimensional graphics programming for the Windows presentation foundation

Author: Charles Petzold

Publisher: Microsoft Pr


Category: Computers

Page: 430

View: 5829

Provides information on programming 3D graphics using Windows Presentation Foundation 3D API.


Author: N.A

Publisher: N.A

ISBN: 9780780384163

Category: Navigation (Aeronautics)

Page: 789

View: 8016



IEEE Position Location and Navigation Symposium : Monterey, California, April 26-29, 2004

Author: N.A

Publisher: IEEE Computer Society Press


Category: Electronics in navigation

Page: 789

View: 5689


Guidance and Control

Proceedings of the Annual Rocky Mountain Guidance and Control Conference Held ...

Author: William Frazier,Robert D. Culp

Publisher: N.A


Category: Space vehicles

Page: N.A

View: 5295


The F. Landis Markley Astronautics Symposium

Proceedings of the American Astronautical Society F. Landis Markley Astronautics Symposium Held June 29 to July 2, 2008, Cambridge, Maryland

Author: F. Landis Markley

Publisher: Univelt

ISBN: 9780877035480

Category: Technology & Engineering

Page: 936

View: 8114


Mechanics of Flight

Author: Warren F. Phillips

Publisher: Wiley


Category: Science

Page: 1152

View: 4462

Explains the principles of flight mechanics through worked examples and progressive problem solving With its unique balance of breadth and depth, coupled with a comprehensive presentation of theory and applications, Mechanics of Flight is rapidly becoming the textbook of choice to enable readers to master the science and mathematics of flight mechanics. By progressively building on the formulation and solution of simpler problems associated with aircraft performance, static stability, and control, the author guides readers from fundamental principles to the development of the general equations of motion and continues through dynamic stability, aircraft handling qualities, and flight simulation. In response to feedback from students, instructors, practicing engineers, and test pilots, this Second Edition features much new material, including new and updated coverage of: Effects of nonlinear aerodynamics on aircraft stability Effects of tail dihedral on longitudinal and lateral stability Lateral trim, engine failure, and minimum-control airspeed Dynamic stability constraints and center-of-gravity limits Flight simulation in geographic coordinates Throughout the text, many new worked examples demonstrate how to apply principles of flight mechanics to solve engineering problems. Moreover, the text offers an array of modern and classical techniques for solving a broad range of problems in flight mechanics. Unique features include presentations of the numerical lifting-line method for efficient and accurate evaluation of stability derivatives and the quaternion formulation for six-degree-of-freedom flight simulation. Moreover, the author provides the detail needed to enable readers to write their own code. Mechanics of Flight is designed as a textbook for a two-semester sequence of courses for students in mechanical and aerospace engineering. In addition, the text's self-contained chapters allow instructors to select individual topics for one-semester courses. The book is also a valuable reference for engineers working in the aerospace industry.

DS-RT 2001

Fifth IEEE International Workshop on Distributed Simulation and Real-Time Applications : Proceedings : 13-15 August, 2001, Cincinnati, Ohio

Author: J. Mark Pullen

Publisher: IEEE

ISBN: 9780769513485

Category: Computers

Page: 121

View: 8644