New Foundations for Classical Mechanics

by David Hestenes

(revised) 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 applications 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.

Genres: Physics, Mathematics, Science

720 pages, Paperback

First published August 1, 1986

Reviews

[SalahDin Ahmed Salh Rezk · Rating 4 out of 5]

A great detailed textbook for physics on the undergraduate level from a geometric perspective. However, it is not very suitable for self-studying. Its writing style is good and clear, yet it does not take the extra steps to clarify things up and leave a lot to the reader and assume many points are given. The focus is more on the practical application in classical physics rather than the relation between the mathematical abstraction and physical models in general.