 Presents a precise definition and examples of the symmetries of a Hamiltonian, including transformations that depend explicitly on the time
 Contains the definition and examples of Rseparable solutions of the Hamilton–Jacobi equation
 Illustrates a complete and simplified proof for the Liouville Theorem and examples of its application
 Includes a complete list of detailed solutions for selfstudy students
Buy this book
 About this Textbook

This textbook examines the Hamiltonian formulation in classical mechanics with the basic mathematical tools of multivariate calculus. It explores topics like variational symmetries, canonoid transformations, and geometrical optics that are usually omitted from an introductory classical mechanics course. For students with only a basic knowledge of mathematics and physics, this book makes those results accessible through workedout examples and wellchosen exercises.
For readers not familiar with Lagrange equations, the first chapters are devoted to the Lagrangian formalism and its applications. Later sections discuss canonical transformations, the Hamilton–Jacobi equation, and the Liouville Theorem on solutions of the Hamilton–Jacobi equation.
Graduate and advanced undergraduate students in physics or mathematics who are interested in mechanics and applied math will benefit from this treatment of analytical mechanics. The text assumes the basics of classical mechanics, as well as linear algebra, differential calculus, elementary differential equations and analytic geometry. Designed for selfstudy, this book includes detailed examples and exercises with complete solutions, although it can also serve as a class text.  About the authors

Gerardo F. Torres del Castillo is a professor of physics and mathematics at the Universidad Autónoma de Puebla, where he has taught since 1979. He is the author or coauthor of more than 30 papers on classical mechanics. His other published books are Differentiable Manifolds; 3D Spinors, SpinWeighted Functions and their Applications; and Spinors in FourDimensional Spaces.
 Reviews

“This book is primarily intended for advanced undergraduate and graduate students in physics and applied mathematics. … in my opinion this book may be regarded as a valuable addition to the existing literature in the field.” (Frans Cantrijn, Mathematical Reviews, July, 2019)
“‘This book is intended for advanced undergraduate or graduate students in physics or applied mathematics and for researchers working in related subjects.’” (Cristian Lăzureanu, zbMATH 1422.70001, 2019)
“A book for beginning students of analytical mechanics, whether they be advanced undergraduates, graduate students or others wishing to learn more about mechanics through selfstudy. The book does a very nice job of shepherding the reader from Newtonian mechanics to Lagrangian mechanics … . This book is a musthave library book for any mathematics or physics library.” (Steven Deckelman, MAA Reviews, May 20, 2019)
 Table of contents (6 chapters)


The Lagrangian Formalism
Pages 141

Some Applications of the Lagrangian Formalism
Pages 4380

Rigid Bodies
Pages 81101

The Hamiltonian Formalism
Pages 103141

Canonical Transformations
Pages 143228

Table of contents (6 chapters)
Buy this book
Services for this Book
Recommended for you
Bibliographic Information
 Bibliographic Information

 Book Title
 An Introduction to Hamiltonian Mechanics
 Authors

 Gerardo Torres del Castillo
 Series Title
 Birkhäuser Advanced Texts Basler Lehrbücher
 Copyright
 2018
 Publisher
 Birkhäuser Basel
 Copyright Holder
 Springer Nature Switzerland AG
 eBook ISBN
 9783319952253
 DOI
 10.1007/9783319952253
 Hardcover ISBN
 9783319952246
 Softcover ISBN
 9783030069971
 Series ISSN
 10196242
 Edition Number
 1
 Number of Pages
 X, 366
 Number of Illustrations
 42 b/w illustrations
 Topics