New Foundations for Classical Mechanics

New Foundations for Classical Mechanics

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(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.This shows explicitly that the gauge transformation adds a radial component to the angular velocity. We can solve ... In other words, the gauge can be choosen freely at one time, but its value for all other times is then fixed by the subsidiary condition. ... The Spinor Equation of Motion The spinor acceleration corresponding to the acceleration vector in position space is most easily found by differentiating (4.22). ... These are general kinematic results, enabling us to transform any problemanbsp;...

Title:New Foundations for Classical Mechanics
Author:David Hestenes
Publisher:Springer Science & Business Media - 2006-04-11


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