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Classical Mechanics - Hamiltonian and Lagrangian Formalism (Hardcover, 2nd ed. 2017)
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Classical Mechanics - Hamiltonian and Lagrangian Formalism (Hardcover, 2nd ed. 2017)
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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 is the 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.
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