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.
Mục lục
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-Poincare 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
Giới thiệu về tác giả
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.
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