Classical Mechanics: Hamiltonian and Lagrangian Formalism

ISBN-13: 9783642140365 / Angielski / Twarda / 2010 / 308 str.

Alexei Deriglazov

Opis

This account of the fundamentals of Hamiltonian mechanics also covers related topics such as integral invariants and the Noether theorem. With just the elementary mathematical methods used for exposition, the book is suitable for novices as well as graduates.

Recenzje

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)

Spis treści

Sketch of Lagrangian Formalism.- Hamiltonian Formalism.- Canonical Transformations of Two-Dimensional Phase Space.- Properties of Canonical Transformations.- Integral Invariants.- Potential Motion in a Geometric Setting.- Transformations, Symmetries and Noether Theorem.- Hamiltonian Formalism for Singular Theories.

Blurb

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.