David Hestenes Boeken

This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applica tions matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics."

This small book initiated a significant revolution in mathematical physics, impacting many physicists and promising extensive future changes. Central to its approach is Clifford algebra, which unifies various mathematical languages, including spinors, quaternions, tensors, and differential forms. This unified framework offers an efficient ‘toolkit’ for addressing physical problems across quantum mechanics, classical mechanics, electromagnetism, and both special and general relativity. By learning just one mathematical system, users can engage with topics extending to current research in these fields. The techniques, known as ‘Geometric Algebra,’ are applicable in engineering, robotics, and computer science without modification, allowing physicists and engineers to bridge their disciplines effectively. Beyond mathematical utility, Geometric Algebra provides profound insights into physical problems, often revealing new aspects of physics itself. Examples of these insights are woven throughout the text, showcasing ideas that remain relevant for future research. The book serves not only as a mathematical guide but also as a source of inspiration for exploring the deeper connections between mathematics and physical phenomena.