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Classical Mechanics

Hamiltonian and Lagrangian Formalism

  • Book
  • © 2010

Overview

Authors:
  1. Alexei Deriglazov

    1. Depto. Fisica, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil

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  • With worked examples, 55 end of chapter exercises and chapter summaries
  • The equivalence of various definitions of the canonical transformation is proved explicitly, in contrast to competing books
  • Discussion of (global) symmetries and the Noether theorem in the framework of classical mechanics gives a new approach not covered by most mechanics textbooks
  • Includes supplementary material: sn.pub/extras

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xii
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  2. Sketch of Lagrangian Formalism

    • Alexei Deriglazov
    Pages 1-75

  3. Hamiltonian Formalism

    • Alexei Deriglazov
    Pages 77-118

  4. Canonical Transformations of Two-Dimensional Phase Space

    • Alexei Deriglazov
    Pages 119-126

  5. Properties of Canonical Transformations

    • Alexei Deriglazov
    Pages 127-153

  6. Integral Invariants

    • Alexei Deriglazov
    Pages 155-166

  7. Potential Motion in a Geometric Setting

    • Alexei Deriglazov
    Pages 167-202

  8. Transformations, Symmetries and Noether Theorem

    • Alexei Deriglazov
    Pages 203-236

  9. Hamiltonian Formalism for Singular Theories

    • Alexei Deriglazov
    Pages 237-302

  10. Back Matter

    Pages 303-308
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Keywords

About this book

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.

Reviews

From the reviews:

“The aim of the author of this interesting book is to present the main ideas of Hamiltonian mechanics and allied topics, by using just elementary mathematical methods. … 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. This handbook is well addressed to undergraduate students in physics.” (Franco Cardin, Zentralblatt MATH, Vol. 1206, 2011)

Authors and Affiliations

  • Depto. Fisica, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil

    Alexei Deriglazov

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