New Foundations for Classical Mechanics

1. Front Matter

   Pages i-xi

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2. Origins of Geometric Algebra

   • David Hestenes

   Pages 1-38

3. Developments in Geometric Algebra

   • David Hestenes

   Pages 39-119

4. Mechanics of a Single Particle

   • David Hestenes

   Pages 120-194

5. Central Forces and Two-Particle Systems

   • David Hestenes

   Pages 195-251

6. Operators and Transformations

   • David Hestenes

   Pages 252-333

7. Many-Particle Systems

   • David Hestenes

   Pages 334-418

8. Rigid Body Mechanics

   • David Hestenes

   Pages 419-511

9. Celestial Mechanics

   • David Hestenes

   Pages 512-573

10. Foundations of Mechanics

    • David Hestenes

    Pages 574-602

11. Back Matter

    Pages 603-644

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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.

• classical mechanics
• mechanics

• Department of Physics, Arizona State University, Tempe, USA

  David Hestenes

David Hesteness is awarded the Oersted Medal for 2002.
The Oersted Award recognizes notable contributions to the teaching of physics. It is the most prestigious award conferred by the American Association of Physics Teachers.

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