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Geometric Mechanics

Geometric Mechanics

Richard Talman

ISBN: 978-3-527-61780-7

Dec 2007

582 pages

Select type: O-Book

Description

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.

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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-Poincaré Description of Mechanics.

Simplifying the Poincaré 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.