Geometric mechanics

著者

書誌事項

Geometric mechanics

Richard Talman

（Physics textbook）

Wiley-VCH Verlag GmbH & Co. KGaA, 2004

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注記

Includes bibliographies and index

Originally published: New York : Wiley, c2000

内容説明・目次

内容説明

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 ...APPLIED DYNAMICS With Applications to Multibody and Mechatronic Systems Francis C. Moon A contemporary look at dynamics at an intermediate level, including nonlinear and chaotic dynamics. 1998 (0-471-13828-2) 504 pp. MATHEMATICAL PHYSICS Applied Mathematics for Scientists and Engineers Bruce Kusse and Erik Westwig A comprehensive treatment of the mathematical methods used to solve practical problems in physics and engineering. 1998 (0-471-15431-8) 680 pp.

目次

  • SOLVABLE SYSTEMS
  • Review of Solvable Systems
  • THE GEOMETRY OF MECHANICS
  • Geometry of Mechanics I: Linear
  • Geometry of Mechanics II: Curvilinear
  • Geometry of Mechanics III: Multilinear
  • LAGRANGIAN MECHANICS
  • Lagrange-Poincari Description of Mechanics
  • Simplifying the Poincari Equation With Group Theory
  • Conservation Laws and Symmetry
  • NEWTONIAN MECHANICS
  • Gauge-Invariant Mechanics
  • Geometric Phases
  • HAMILTONIAN MECHANICS
  • Hamiltonian Treatment of Geometric Optics
  • Hamilton-Jacobi Theory
  • Relativistic Mechanics
  • Symplectic Mechanics
  • APPROXIMATE METHODS
  • Analytic Basic for Approximation
  • Linear Systems
  • Perturbation Theory
  • Index.

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