Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality

by J.B. Kuipers

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.

Genres: Mathematics

394 pages, Paperback

First published August 19, 2002

Reviews

[Ilumi_do3 · Rating 3 out of 5]

Me pareció bastante útil para aprender sobre los cuaterniones y las matrices de rotación, pero hay secciones enteras que ahondan en aplicaciones que, tal vez, no sean del interés de uno. Aunque tranquilamente se pueden saltear. Igual lo recomiendo.

[Blux · Rating 4 out of 5]

Great detailed exposition on quaternion algebra. The author starts out with an overview of traditional matrix algebra applied to 2D and 3D rotations, and then manages to show how quaternions, as an extension of complex numbers to represent rotations in 2D, are a useful tool for representing rotations in 3D.

The book contains various interesting practical applications for quaternions taken from the aerospace industry, and shows how quaternions are superior to traditional matrix algebra for representing rotations in 3D.

For everyone who likes to truly understand how quaternions work instead of just copy-pasting some formula's from a random textbook.

The following quote shows the author's motives are first and foremost to educate the reader, instead of displaying his mathematical intellect, from page 186:

No doubt some constraints on the matrix M will emerge, but the process seems overly difficult and tedious. Only the most masochistic reader will want to pursue these details.

Great stuff.