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Classical Mechanics: Hamiltonian and Lagrangian Formalism
Author(s): Alexei Deriglazov (auth.)
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2010 Edition: 1
Language: English Pages
ISBN: 364214036X, 9783642140365
Size: 2 MB (2307305 bytes)
Formalism of classical mechanics underlies a number of powerful mathematical methods that are widely used in theoretical and mathematical physics. This book considers the basics facts of Lagrangian and Hamiltonian mechanics, as well as related topics, such as canonical transformations, integral invariants, potential motion in geometric setting, symmetries, the Noether theorem and systems with constraints. While in some cases the formalism is developed beyond the traditional level adopted in the standard textbooks on classical mechanics, only elementary mathematical methods are used in the exposition of the material. The mathematical constructions involved are explicitly described and explained, so the book can be a good starting point for the undergraduate student new to this field. At the same time and where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving the level of rigor that makes the book useful for the graduate students intending to work in one of the branches of the vast field of theoretical physics. To illustrate how classical-mechanics formalism works in other branches of theoretical physics, examples related to electrodynamics, as well as to relativistic and quantum mechanics, are included.
Table of contents :
Front Matter....Pages i-xii
Sketch of Lagrangian Formalism....Pages 1-75
Hamiltonian Formalism....Pages 77-118
Canonical Transformations of Two-Dimensional Phase Space....Pages 119-126
Properties of Canonical Transformations....Pages 127-153
Integral Invariants....Pages 155-166
Potential Motion in a Geometric Setting....Pages 167-202
Transformations, Symmetries and Noether Theorem....Pages 203-236
Hamiltonian Formalism for Singular Theories....Pages 237-302
Back Matter....Pages 303-308
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