Details

Geometric Mechanics


Geometric Mechanics

Toward a Unification of Classical Physics
2nd Revised and Enlarged Edition

von: Richard Talman

223,99 €

Verlag: Wiley-VCH
Format: PDF
Veröffentl.: 24.09.2007
ISBN/EAN: 9783527611416
Sprache: englisch
Anzahl Seiten: 605

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Beschreibungen

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.
1 Review of Classical Mechanics and String Field Theory<br> 2 Geometry of Mechanics, I, Linear<br> 3 Geometry of Mechanics, II, Curvilinear<br> 4 Geometry of Mechanics, III, Multilinear<br> 5 Lagrange-Poincare Description of Mechanics<br> 6 Newtonian/Gauge Invariant Mechanics<br> 7 Hamiltonian Treatment of Geometric Optics<br> 8 Hamilton-Jacobi Theory<br> 9 Relativistic Mechanics<br> 10 Conservation Laws and Symmetry<br> 11 Electromagnetic Theory<br> 12 Relativistic Strings<br> 13 General Relativity<br> 14 Analytic Bases for Approximation<br> 15 Linear Hamiltonian Systems<br> 16 Perturbation Theory<br> 17 Symplectic Mechanics
Richard M. Talman is Professor of Physics at Cornell University, Ithaca, New York. He studied physics at the University of Western Ontario and received his Ph.D. at the California Institute of Technology in 1963. After accepting a full professorship for Physics at Cornell in 1971, he spent time as Visiting Scientist in Stanford, CERN, Berkeley, and the S.S.C. in Dallas and Saskatchewan. In addition, he has delivered lecture series at several institutions including Rice and Yale Universities. Professor Talman has been engaged in the design and construction of a series of accelerators, with special emphasis on x-rays.
Mechanics is quite obviously geometric, yet the traditional approach to the subject is based mainly on differential equations. Setting out to make mechanics both accessible and interesting for non-mathematicians, Richard Talman augments this approach with geometric methods such as differential geometry, differential forms, and tensor analysis to reveal qualitative aspects of the theory. <br> 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.<br> This second, fully revised edition has been expanded to further emphasize the importance of the geometric approach. Starting from Hamilton's principle, the author shows, from a geometric perspective, how "all" of classical physics can be subsumed within classical mechanics. Having developed the formalism in the context of classical mechanics, the subjects of electrodynamics, relativistic strings and general relativity are treated<br> as examples of classical mechanics. This modest unification of classical physics is intended to provide a background for the far more ambitious "grand unification" program of quantum field theory.<br> The final chapters develop approximate methods for the analysis of mechanical systems. Here the emphasis is more on practical perturbative methods than on the canonical transformation formalism. "Geometric Mechanics" features numerous illustrative examples and assumes only basic knowledge of Lagrangian mechanics.

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