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Geometric Mechanics: Toward a Unification of Classical Physics, 2nd, Revised and Enlarged Edition

Geometric Mechanics: Toward a Unification of Classical Physics, 2nd, Revised and Enlarged Edition

Richard Talman

ISBN: 978-3-527-61140-9

Jun 2007

605 pages


For physicists, mechanics is quite obviously geometric, yet the classical approach typically emphasizes abstract, mathematical formalism. Setting out to make mechanics both accessible and interesting for non-mathematicians, Richard Talman uses geometric methods to reveal qualitative aspects of the theory. He introduces concepts from differential geometry, differential forms, and tensor analysis, then applies them to areas of classical mechanics as well as other areas of physics, including optics, crystal diffraction, electromagnetism, relativity, and quantum mechanics. For easy reference, the author treats Lagrangian, Hamiltonian, and Newtonian mechanics separately -- exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively. Practical perturbative methods of approximation are also developed. This second, fully revised edition has been expanded to include new chapters on electromagnetic theory, general relativity, and string theory. 'Geometric Mechanics' features illustrative examples and assumes only basic knowledge of Lagrangian mechanics.

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1 Review of Classical Mechanics and String Field Theory
2 Geometry of Mechanics, I, Linear
3 Geometry of Mechanics, II, Curvilinear
4 Geometry of Mechanics, III, Multilinear
5 Lagrange-Poincaré Description of Mechanics
6 Newtonian/Gauge Invariant Mechanics
7 Hamiltonian Treatment of Geometric Optics
8 Hamilton-Jacobi Theory
9 Relativistic Mechanics
10 Conservation Laws and Symmetry
11 Electromagnetic Theory
12 Relativistic Strings
13 General Relativity
14 Analytic Bases for Approximation
15 Linear Hamiltonian Systems
16 Perturbation Theory
17 Symplectic Mechanics
* completely revised, updated and extended second edition, featuring new chapters on Electromagnetic Theory, General Relativity and String Theory
* chapter on Relativistic Mechanics (12) rewritten and expanded
* chapter on Linear Systems (15) shortened
* discussion of the topics which do not contribute to the new theme of the book reduced or eliminated (9.3 Tumblers, 12.10 Longitudinal Coordinate Transformation, 15.4 A Lagrangian Set of Solutions, 15.15.5 Periodic Solutions, 16.4 Multidimensional Perturbation Theory, etc.)