Classical Mechanics: Hamiltonian and Lagrangian Formalism

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Springer, Oct 8, 2016 - Science - 445 pages
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.
 

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Contents

1 Sketch of Lagrangian Formalism
1
2 Hamiltonian Formalism
91
3 Canonical Transformations of TwoDimensional Phase Space
137
4 Properties of Canonical Transformations
147
5 Integral Invariants
175
6 Some Mechanical Problems in a Geometric Setting
189
7 Transformations Symmetries and Noether Theorem
235
8 Hamiltonian Formalism for Singular Theories
271
9 Classical and Quantum Relativistic Mechanics of a Spinning Particle
353
Bibliography
437
Index
441
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About the author (2016)

Prof. Dr. Alexei Anatolevich Deriglazov has studied physics at the Tomsk State University (Russia). He has more than 25 years of teaching experience at the Universities of Sao Paulo, Rio de Janeiro and Juiz de Fora (Brazil) in Mathematical Physics. His research interests are focused on Geometry and Topology, Mathematical Physics and Quantum Physics.


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