| Description |
1 online resource (xv, 440 pages) |
| Contents |
Cover -- Contents -- Preface -- Introduction -- I Analytical Mechanics -- 1 The Lagrangian Coordinates -- 1.1 A Primer for Various Formulations of Dynamics -- 1.2 Constraints -- 1.3 Degrees of Freedom and Lagrangian Coordinates -- 1.4 The Calculus of Variations and the Lagrange Equations -- 1.5 Remarks on Lagrange's Equations -- 2 Hamiltonian Systems -- 2.1 The Legendre Transformation -- 2.2 The Hamilton Equations -- 2.3 The Poisson Bracket and the Jacobi-Poisson Theorem -- 2.4 A More Compact Form of The Hamiltonian Dynamics -- 2.5 The Variational Principle for the Hamilton Equations -- 3 Transformation Theory -- 3.1 Canonical, Completely Canonical and Symplectic Transformations -- 3.2 A New Characterization of Completely Canonical Transformations -- 3.3 New Characterization of Sympletic Transformations -- 4 The Integration Methods -- 4.1 Integrals Invariants of a Differential System -- 4.2 A Primer on the Lie Derivative -- 4.3 The Kepler Dynamics |
| Summary |
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 m |
| Bibliography |
Includes bibliographical references (pages 427-436) and index |
| Notes |
English |
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Print version record |
| Subject |
Hamiltonian systems.
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Geometry, Differential.
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Field theory (Physics)
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Mathematical physics.
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MATHEMATICS -- Topology.
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Geometry, Differential.
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Field theory (Physics)
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Mathematical physics.
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Systemes hamiltoniens.
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Geometrie differentielle.
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Champs, Theorie des (Physique)
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Physique mathematique.
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Hamiltonian systems.
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Field theory (Physics)
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Geometry, Differential
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Hamiltonian systems
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Mathematical physics
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| Form |
Electronic book
|
| LC no. |
98044390 |
| ISBN |
9812386319 |
|
9789812386311 |
|
1281869961 |
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9781281869968 |
|
9786611869960 |
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6611869964 |
|
