Geometric Mechanics
1. Auflage November 1999
XXVIII, 554 Seiten, Softcover
Lehrbuch
Kurzbeschreibung
Ein moderner Ansatz zur Behandlung der klassischen Mechanik! Dieses Lehrbuch für fortgeschrittene Studenten unterscheidet sich von Werken zur gleichen Thematik in zweierlei Hinsicht: Zum einen argumentiert der Autor überwiegend physikalisch, das bedeutet, mathematische Formelgebäude treten etwas in den Hintergrund. Zum anderen enthält der Band Material zur relativistischen Physik, Chaostheorie und nichtlinearen Dynamik, das man in ähnlichen Lehrbüchern in der Regel nicht findet. Kenntnisse des Lagrange-, nicht jedoch des Hamilton-Formalismus werden vorausgesetzt. (08/99)
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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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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.
