Geometric Mechanics

Uses geometric methods to reveal qualitative aspects of the theory. This title 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.

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This title presents mechanics for the nonmathematician - a modern approach. 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 nonmathematicians, 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, Dr. Talman treats separately Lagrangian, Hamiltonian, and Newtonian mechanics - exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively.Practical perturbative methods of approximation are also developed. "Geometric Mechanics" features illustrative examples and assumes only basic knowledge of Lagrangian mechanics. Of related interest are: "Applied Dynamics: With Applications to Multibody and Mechatronic Systems", 1998 (0-471-13828-2), by Francis C.
Moon, offers a contemporary look at dynamics at an intermediate level, including nonlinear and chaotic dynamics; and, "Mathematical Physics: Applied Mathematics for Scientists and Engineers", 1998 (0-471-15431-8), by Bruce Kusse and Erik Westwig, offers a comprehensive treatment of the mathematical methods used to solve practical problems in physics and engineering.