New Foundations for Classical Mechanics

New Foundations for Classical Mechanics
Title New Foundations for Classical Mechanics PDF eBook
Author D. Hestenes
Publisher Springer Science & Business Media
Pages 716
Release 2005-12-17
Genre Science
ISBN 0306471221

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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.

New Foundations for Classical Mechanics

New Foundations for Classical Mechanics
Title New Foundations for Classical Mechanics PDF eBook
Author David Hestenes
Publisher Springer Science & Business Media
Pages 716
Release 1999-09-30
Genre Science
ISBN 0792355148

Download New Foundations for Classical Mechanics Book in PDF, Epub and Kindle

(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.

New Foundations for Classical Mechanics

New Foundations for Classical Mechanics
Title New Foundations for Classical Mechanics PDF eBook
Author D. Hestenes
Publisher Springer Science & Business Media
Pages 655
Release 2012-12-06
Genre Science
ISBN 9400948026

Download New Foundations for Classical Mechanics Book in PDF, Epub and Kindle

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.

Foundations of Classical Mechanics

Foundations of Classical Mechanics
Title Foundations of Classical Mechanics PDF eBook
Author P. C. Deshmukh
Publisher Cambridge University Press
Pages 591
Release 2019-12-12
Genre Mathematics
ISBN 110848056X

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The book aims at speeding up undergraduates to attain interest in advanced concepts and methods in science and engineering.

Foundations Of Mechanics

Foundations Of Mechanics
Title Foundations Of Mechanics PDF eBook
Author Ralph Abraham
Publisher CRC Press
Pages 849
Release 2019-04-24
Genre Science
ISBN 0429689047

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Foundations of Mechanics is a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the two-body problem and three-body problem.

New Foundations for Classical Mechanics

New Foundations for Classical Mechanics
Title New Foundations for Classical Mechanics PDF eBook
Author David Hestenes
Publisher Springer Science & Business Media
Pages 703
Release 1999-09-30
Genre Language Arts & Disciplines
ISBN 9780792353027

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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.

Understanding Geometric Algebra for Electromagnetic Theory

Understanding Geometric Algebra for Electromagnetic Theory
Title Understanding Geometric Algebra for Electromagnetic Theory PDF eBook
Author John W. Arthur
Publisher John Wiley & Sons
Pages 320
Release 2011-09-13
Genre Science
ISBN 0470941634

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This book aims to disseminate geometric algebra as a straightforward mathematical tool set for working with and understanding classical electromagnetic theory. It's target readership is anyone who has some knowledge of electromagnetic theory, predominantly ordinary scientists and engineers who use it in the course of their work, or postgraduate students and senior undergraduates who are seeking to broaden their knowledge and increase their understanding of the subject. It is assumed that the reader is not a mathematical specialist and is neither familiar with geometric algebra or its application to electromagnetic theory. The modern approach, geometric algebra, is the mathematical tool set we should all have started out with and once the reader has a grasp of the subject, he or she cannot fail to realize that traditional vector analysis is really awkward and even misleading by comparison. Professors can request a solutions manual by email: [email protected]