Classical Mechanics
Springer International Publishing (Verlag)
978-3-319-44146-7 (ISBN)
The revised edition of this advanced textbook provides the reader with a solid grounding in the formalism of classical mechanics, underlying a number of powerful mathematical methods that are widely used in modern theoretical and mathematical physics. It reviews the fundamentals of Lagrangian and Hamiltonian mechanics, and goes on to cover 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.
New material for the revised edition includes additional sections on the Euler-Lagrange equation, the Cartan two-form in Lagrangian theory, and Newtonian equations of motion in context of general relativity. Also new for this edition isthe inclusion of problem sets and solutions to aid in the understanding of the material presented.
The mathematical constructions involved are explicitly described and explained, so the book is a good starting point for the student new to this field. Where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving the level of rigor that makes the book useful for more advanced 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.
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.
Sketch of Lagrangian Formalism.- Hamiltonian Formalism.- Canonical Transformations of Two-Dimensional Phase Space.- Properties of Canonical Transformations.- Integral Invariants.- Some Mechanical Problems in a Geometric Setting.- Transformations, Symmetries and Noether Theorem.- Hamiltonian Formalism for Singular Theories.- Classical and Quantum Relativistic Mechanics of a Spinning Particle.- Index.
"In this book, the Hamiltonian and Lagrangian formulations in the frameworks of classical and quantum mechanics are presented. Most of the theoretical results are proved. The examples are interesting. ... This book can be used by undergraduate students in physics." (Cristian Lazureanu, zbMATH 1364.70001, 2017)
| Erscheinungsdatum | 26.10.2016 |
|---|---|
| Zusatzinfo | XVI, 445 p. 53 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Naturwissenschaften ► Physik / Astronomie ► Mechanik |
| Schlagworte | Applications of Mathematics • Appl.Mathematics/Computational Methods of Engineer • Canonical Transformation Mechanics • Continuum Mechanics and Mechanics of Materials • Hamiltonian Formalism Mechanics • Hamiltonian Methods Physics • Mechanics • Noether Theorem • Physics and Astronomy • Textbook Classical Mechanics • Textbook Hamiltonian formalism • Theoretical, Mathematical and Computational Physic |
| ISBN-10 | 3-319-44146-9 / 3319441469 |
| ISBN-13 | 978-3-319-44146-7 / 9783319441467 |
| Zustand | Neuware |
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