## Real Quaternionic Calculus Handbook

Author: João Pedro Morais,Svetlin Georgiev,Wolfgang Sprößig
Publisher: Springer Science & Business Media
ISBN: 3034806221
Category: Mathematics
Page: 216
View: 2946
Real quaternion analysis is a multi-faceted subject. Created to describe phenomena in special relativity, electrodynamics, spin etc., it has developed into a body of material that interacts with many branches of mathematics, such as complex analysis, harmonic analysis, differential geometry, and differential equations. It is also a ubiquitous factor in the description and elucidation of problems in mathematical physics. In the meantime real quaternion analysis has become a well established branch in mathematics and has been greatly successful in many different directions. This book is based on concrete examples and exercises rather than general theorems, thus making it suitable for an introductory one- or two-semester undergraduate course on some of the major aspects of real quaternion analysis in exercises. Alternatively, it may be used for beginning graduate level courses and as a reference work. With exercises at the end of each chapter and its straightforward writing style the book addresses readers who have no prior knowledge on this subject but have a basic background in graduate mathematics courses, such as real and complex analysis, ordinary differential equations, partial differential equations, and theory of distributions.

## Real Quaternionic Calculus Handbook

Author: Qing Jun Hou
Publisher: N.A
ISBN: 9781681175676
Category:
Page: 274
View: 4838
A quaternion is a four-element vector that can be used to encode any rotation in a 3D coordinate system. Technically, a quaternion is composed of one real element and three complex elements, and it can be used for much more than rotations. Quaternions provide an alternative measurement technique that does not suffer from gimbal lock. Quaternions are less intuitive than Euler Angles and the math can be a little more complicated. Quaternions find uses in both theoretical and applied mathematics, in particular for calculations involving threedimensional rotations such as in three-dimensional computer graphics, computer vision and crystallographic texture analysis. In practical applications, they can be used alongside other methods, such as Euler angles and rotation matrices, or as an alternative to them, depending on the application. In modern mathematical language, quaternions form a four-dimensional associative normed division algebra over the real numbers, and therefore also a domain. Real Quaternionic Calculus Handbook is a comprehensive guide aims to describe phenomena in special relativity, electrodynamics, spin etc., it has developed into a body of material that relates with many branches of mathematics, such as complex analysis, harmonic analysis, differential geometry, and differential equations.

## Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications

Author: Ruben Vera-Rodriguez
Publisher: Springer
ISBN: 3030134695
Category:
Page: N.A
View: 7962

## Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications

22nd Iberoamerican Congress, CIARP 2017, Valparaíso, Chile, November 7–10, 2017, Proceedings
Author: Marcelo Mendoza,Sergio Velastín
Publisher: Springer
ISBN: 331975193X
Category: Computers
Page: 730
View: 505
This book constitutes the refereed post-conference proceedings of the 22nd Iberoamerican Congress on Pattern Recognition, CIARP 2017, held in Valparaíso, Chile, in November 2017. The 87 papers presented were carefully reviewed and selected from 156 submissions. The papers feature research results in the areas of pattern recognition, image processing, computer vision, multimedia and related fields.

## A Mathematical Perspective on Flight Dynamics and Control

Author: Andrea L'Afflitto
Publisher: Springer
ISBN: 3319474677
Category: Technology & Engineering
Page: 122
View: 1782
This brief presents several aspects of flight dynamics, which are usually omitted or briefly mentioned in textbooks, in a concise, self-contained, and rigorous manner. The kinematic and dynamic equations of an aircraft are derived starting from the notion of the derivative of a vector and then thoroughly analysed, interpreting their deep meaning from a mathematical standpoint and without relying on physical intuition. Moreover, some classic and advanced control design techniques are presented and illustrated with meaningful examples. Distinguishing features that characterize this brief include a definition of angular velocity, which leaves no room for ambiguities, an improvement on traditional definitions based on infinitesimal variations. Quaternion algebra, Euler parameters, and their role in capturing the dynamics of an aircraft are discussed in great detail. After having analyzed the longitudinal- and lateral-directional modes of an aircraft, the linear-quadratic regulator, the linear-quadratic Gaussian regulator, a state-feedback H-infinity optimal control scheme, and model reference adaptive control law are applied to aircraft control problems. To complete the brief, an appendix provides a compendium of the mathematical tools needed to comprehend the material presented in this brief and presents several advanced topics, such as the notion of semistability, the Smith–McMillan form of a transfer function, and the differentiation of complex functions: advanced control-theoretic ideas helpful in the analysis presented in the body of the brief. A Mathematical Perspective on Flight Dynamics and Control will give researchers and graduate students in aerospace control an alternative, mathematically rigorous means of approaching their subject.

## Advances in Sensors: Reviews, Vol. 5

Author: Sergey Yurish
Publisher: Lulu.com
ISBN: 8409030284
Category:
Page: 560
View: 6747
The Vol. 5 of this Book Series contains 22 chapters written by 79 contributors-experts from universities, research centres and industry from 15 countries: Australia, Canada, China, France, Germany, Italy, Malaysia, Mexico, Poland, Portugal, Russia, Slovenia, Spain, Ukraine and USA. This volume contains information at the cutting edge of sensor research and related topics from the following three areas: Physical Sensors, Sensor Networks and Remote Sensing. Coverage includes current developments in various sensors, sensor instrumentation and applications. In order to offer a fast and easy reading of each topic, every chapter in this volume is independent and self-contained.With the unique combination of information in this volume, the 'Advances in Sensors: Reviews' Book Series will be of value for scientists and engineers in industry and at universities, to sensors developers, distributors, and end users.

## Алгебра

Author: Н. Бурбаки
Publisher: Рипол Классик
ISBN: 5458267788
Category: Mathematics
Page: 304
View: 9782
Группа французских математиков, объединённая под псевдонимом "Бурбаки", поставила перед собой цель - написать под общим заглавием "Элементы математики" полный трактат по современной математике. Многие выпуски этого трактата уже вышли во Франции, вызвав большой интерес математиков всего мира.

## 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: 1776
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.

## Трансцендентные и алгебраические числа

Author: А.О. Гельфонд
Publisher: Рипол Классик
ISBN: 5458267915
Category: Mathematics
Page: 228
View: 4173
Теория трансцендентных чисел сформировалась как теории, имеющая свои специфические методы и достаточное количество уже решенных проблем, только в XX веке. Отдельные постановки проблем этой теории существовали давно, и первая из них, насколько нам известно, принадлежит Л. Эйлеру. Проблема приближения алгебраических чисел рациональными дробями или, более общо, алгебраическими же числами также может быть отнесена к теории трансцендентных чисел, несмотря на то, что изучение приближения алгебраических чисел рациональными дробями стимулировалось проблемами теории диофантовых уравнений. Целью настоящей монографии является не только показать современное состояние теории трансцендентных чисел и изложить основные методы этой теории, но и дать представление об историческом ходе развития ее методов и о тех связях, которые существуют между этой теорией и другими проблемами теории чисел.

## Сборник задач по курсу математического анализа

Author: Г.Н. Берман
Publisher: Рипол Классик
ISBN: 5458287916
Category:
Page: 528
View: 6314
Сборник содержит систематически подобранные задачи и упражнения к основным разделам курса математического анализа. Большинство параграфов для удобства использования подразделено на части. Группам задач с однородным содержанием предшествует общее указание. Перед задачами физического содержания даются нужные справки по физике.Для студентов высших учебных заведений.

## Курс алгебры

Author: Эрнест Винберг
Publisher: Litres
ISBN: 5457718859
Category: Mathematics
Page: N.A
View: 5853
Книга представляет собой расширенный вариант курса алгебры, читаемого в течение трех семестров на математических факультетах. В нее включены такие дополнительные разделы, как элементы коммутативной алгебры (в связи с аффинной алгебраической геометрией), теории Галуа, теории конечномерных ассоциативных алгебр и теории групп Ли. Это позволяет использовать книгу не только как учебник по общему курсу алгебры, но и как пособие для тех, кто желает углубить свои познания в алгебре. Изложение иллюстрируется большим количеством примеров и сопровождается задачами, часто содержащими дополнительный материал.Книга предназначена для математиков и физиков – студентов, аспирантов, преподавателей и научных работников.

## Исчисление песчинок (Псаммит)

Author: Архимед
Publisher: Рипол Классик
ISBN: 545850500X
Category: Mathematics
Page: 110
View: 3599
Серия "Классики естествознания". Работа древнегреческого ученого Архимеда, в которой он пытается определить верхнюю грань числа песчинок, которые занимает в своём объёме Вселенная. С этой целью он пробует вычислить размер Вселенной, основываясь на астрономических представлениях того времени, а также изобретает способ наименования очень больших чисел. Работа была написана в виде письма тирану Сиракуз Гелону.

## Выпуклые многогранники

Author: А. Д. Александров
Publisher: Рипол Классик
ISBN: 545825712X
Category: Mathematics
Page: 434
View: 8884
Книга посвящена в основном вопросу о том, какие данные и в какой степени могут определять выпуклый многогранник.

## Вещественная алгебраическая геометрия

Author: Владимир Арнольд
Publisher: Litres
ISBN: 5457717879
Category: Mathematics
Page: N.A
View: 4148
Эта брошюра, написанная выдающимся современным математиком академиком РАН В.И.Арнольдом, основана на прочитанных автором популярных лекциях для старшеклассников. В живой и увлекательной форме излагаются основы теории алгебраических кривых в самых разных аспектах: от свойств конических сечений и до шестнадцатой проблемы Гильберта и понятия рода комплексной кривой.Рекомендуется всем интересующимся математикой, начиная со старшеклассников и студентов младших курсов.

## Обыкновенные дифференциальные уравнения

Author: Владимир Арнольд
Publisher: Litres
ISBN: 5457717887
Category: Mathematics
Page: N.A
View: 7644