By J. B. Kuipers

ISBN-10: 0691058725

ISBN-13: 9780691058726

Ever because the Irish mathematician William Rowan Hamilton brought quaternions within the 19th century--a feat he celebrated through carving the founding equations right into a stone bridge--mathematicians and engineers were eager about those mathematical gadgets. this present day, they're utilized in purposes as quite a few as describing the geometry of spacetime, guiding the gap go back and forth, and constructing laptop functions in digital truth. during this e-book, J. B. Kuipers introduces quaternions for scientists and engineers who've no longer encountered them earlier than and indicates how they are often utilized in quite a few sensible events.

The publication is essentially an exposition of the quaternion, a 4-tuple, and its fundamental software in a rotation operator. yet Kuipers additionally provides the extra traditional and general three x three (9-element) matrix rotation operator. those parallel shows enable the reader to pass judgement on which ways are greatest for particular functions. the quantity is split into 3 major elements. the hole chapters current introductory fabric and determine the book's terminology and notation. the subsequent half offers the mathematical houses of quaternions, together with quaternion algebra and geometry. It comprises extra complicated certain themes in round trigonometry, in addition to an creation to quaternion calculus and perturbation idea, required in lots of events related to dynamics and kinematics. within the ultimate part, Kuipers discusses cutting-edge purposes. He provides a six degree-of-freedom electromagnetic place and orientation transducer and concludes through discussing the pc photos important for the advance of purposes in digital truth.