Hamiltonian Dynamics

By: Gaetano Vilasi

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Hardcover | 12 March 2001

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458 Pages

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22.86 x 15.24 x 2.54

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This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems.

As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity.

As a monograph, the book deals with the advanced research topic of completely integrable dynamics, with both finitely and infinitely many degrees of freedom, including geometrical structures of solitonic wave equations.

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Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Science Physics Classical Mathematics Topology Analytic Topology Geometry Differential & Riemannian Geometry Science in General

Maths for Scientists Mathematical Physics Applied Mathematics Chaos Theory Booktopia Publisher Services World Scientific Publishing

Preface
Introduction
Analytical Mechanics	p. 1
The Lagrangian Coordinates	p. 5
Hamiltonian Systems	p. 39
Transformation Theory	p. 65
The Integration Methods	p. 81
Basic Ideas of Differential Geometry	p. 125
Manifolds and Tangent Spaces	p. 129
Differential Forms	p. 159
Integration Theory	p. 195
Lie Groups and Lie Algebras	p. 211
Geometry and Physics	p. 227
Symplectic Manifolds and Hamiltonian Systems	p. 231
The Orbits Method	p. 271
Classical Electrodynamics	p. 295
Integrable Field Theories	p. 307
KdV Equation	p. 311
General Structures	p. 337
Meaning and Existence of Recursion Operators	p. 359
Miscellanea	p. 369
Integrability of Fermionic Dynamics	p. 389
Lagrange: A Short Biography	p. 401
Concerning the Lie Derivative	p. 404
Concerning the Kepler Action Variables	p. 406
Concerning the Reduced Phase Space	p. 409
On the Canonical Differential 1-Form	p. 410
Concerning Rigid Body Equations	p. 413
The Gelfand-Levitan-Marchenko Equation	p. 414
Bibliography	p. 427
Index	p. 437
Table of Contents provided by Blackwell. All Rights Reserved.

Hamiltonian Dynamics

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Hardcover

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