New Foundations for Classical Mechanics

2. 1999 Auflage 1999
ISBN: 978-0-7923-5302-7
Verlag: Springer

Buch, Englisch, Band 99, 706 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 1184 g

Reihe: Fundamental Theories of Physics

(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.

Zielgruppe

Research

Autoren/Hrsg.

Hestenes, D.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Naturwissenschaften Physik Mechanik Klassische Mechanik, Newtonsche Mechanik
• Naturwissenschaften Astronomie Astronomie: Allgemeines

Inhaltsverzeichnis

Origins of Geometric Algebra.- Developments in Geometric Algebra.- Mechanics of a Single Particle.- Central Forces and Two-Particle Systems.- Operators and Transformations.- Many-Particle Systems.- Rigid Body Mechanics.- Celestical Mechanics.- Relativistic Mechanics.

Über Autor(innen)

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.