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New Foundations for Classical Mechanics : Fundamental Theories of Physics - David Hestenes

New Foundations for Classical Mechanics

Fundamental Theories of Physics

Hardcover

Published: January 1999
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This book provides an introduction to geometric algebra as a unified language for physics and mathematics. It contains extensive applications to classical mechanics in a textbook format suitable for courses at an intermediate level. The text is supported by more than 200 diagrams to help develop geometrical and physical intuition. Besides covering the standard material for a course on the mechanics of particles and rigid bodies, the book introduces new, coordinate-free methods for rotational dynamics and orbital mechanics, developing these subjects to a level well beyond that of other textbooks. These methods have been widely applied in recent years to biomechanics and robotics, to computer vision and geometric design, to orbital mechanics in government and industrial space programs, as well as to other branches of physics. The book applies them to the major perturbations in the solar system, including the planetary perturbations of Mercury's perihelion. Geometric algebra integrates conventional vector algebra (along with its established notations) into a system with all the advantages of quaternions and spinors. Thus, it increases the power of the mathematical language of classical mechanics while bringing it closer to the language of quantum mechanics. This book systematically develops purely mathematical applications of geometric algebra useful in physics, including extensive applications to linear algebra and transformation groups. It contains sufficient material for a course on mathematical topics alone. The second edition has been expanded by nearly a hundred pages on relativistic mechanics. The treatment is unique in its exclusive use of geometric algebra and in its detailed treatment of spacetime maps, collisions, motion in uniform fields and relativistic precession. It conforms with Einstein's view that the Special Theory of Relativity is the culmination of developments in classical mechanics.

Preface
Origins of Geometric Algebrap. 1
Developments in Geometric Algebrap. 39
Mechanics of a Single Particlep. 120
Central Forces and Two-Particle Systemsp. 195
Operators and Transformationsp. 252
Many-Particle Systemsp. 334
Rigid Body Mechanicsp. 419
Celestial Mechanicsp. 512
Relativistic Mechanicsp. 574
Spherical Trigonometryp. 661
Elliptic Functionsp. 668
Units, Constants and Datap. 672
Hints and Solutions for Selected Exercisesp. 674
Referencesp. 690
Indexp. 694
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792353027
ISBN-10: 0792353021
Series: Fundamental Theories of Physics
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 706
Published: January 1999
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.5  x 4.45
Weight (kg): 1.18
Edition Number: 2
Edition Type: Revised