© 2018

An Introduction to Hamiltonian Mechanics


  • 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 R-separable 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 self-study students


Part of the Birkhäuser Advanced Texts Basler Lehrbücher book series (BAT)

Table of contents

  1. Front Matter
    Pages i-x
  2. Gerardo F. Torres del Castillo
    Pages 1-41
  3. Gerardo F. Torres del Castillo
    Pages 43-80
  4. Gerardo F. Torres del Castillo
    Pages 81-101
  5. Gerardo F. Torres del Castillo
    Pages 103-141
  6. Gerardo F. Torres del Castillo
    Pages 143-228
  7. Gerardo F. Torres del Castillo
    Pages 229-279
  8. Back Matter
    Pages 281-366

About this book


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 worked-out examples and well-chosen 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 self-study, this book includes detailed examples and exercises with complete solutions, although it can also serve as a class text.


inertia tensor Poisson bracket Hamiltonian mechanics canonical transformations rigid bodies Liouville Theorem Hamilton–Jacobi formalism canonoid transformations Lagrangian formalism Hamilton–Jacobi equation

Authors and affiliations

  1. 1.Instituto de Ciencias, BUAPPueblaMexico

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; 3-D Spinors, Spin-Weighted Functions and their Applications; and Spinors in Four-Dimensional Spaces.

Bibliographic information

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“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 self-study. The book does a very nice job of shepherding the reader from Newtonian mechanics to Lagrangian mechanics … . This book is a must-have library book for any mathematics or physics library.” (Steven Deckelman, MAA Reviews, May 20, 2019)