New Foundations for Classical Mechanics

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Springer Science & Business Media, Sep 30, 1999 - Science - 706 pages
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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.
 

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Contents

Developments in Geometric Algebra
39
Mechanics of a Single Particle
120
Central Forces and TwoParticle Systems
195
5
252
16
270
20
281
30
313
11
319
Rigid Body Mechanics
419
73
473
Celestial Mechanics
512
Relativistic Mechanics
574
93 94 95 Relativistic Particle Dynamics EnergyMomentum Conservation Relativistic Rigid Body Mechanics 615 633 650
615
Appendix A Spherical Trigonometry B Elliptic Functions C Units Constants and Data Hints and Solutions for Selected Exercises References Index
661
334
695
96
696

ManyParticle Systems
334
39
342
64
349

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About the author (1999)

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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