Overview
- 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 book series: Birkhäuser Advanced Texts Basler Lehrbücher (BAT)
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Table of contents (6 chapters)
Keywords
About this book
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 textassumes 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.
Reviews
“‘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)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: An Introduction to Hamiltonian Mechanics
Authors: Gerardo F. Torres del Castillo
Series Title: Birkhäuser Advanced Texts Basler Lehrbücher
DOI: https://doi.org/10.1007/978-3-319-95225-3
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-319-95224-6Published: 24 September 2018
Softcover ISBN: 978-3-030-06997-1Published: 03 January 2019
eBook ISBN: 978-3-319-95225-3Published: 08 September 2018
Series ISSN: 1019-6242
Series E-ISSN: 2296-4894
Edition Number: 1
Number of Pages: X, 366
Number of Illustrations: 42 b/w illustrations
Topics: Dynamical Systems and Ergodic Theory, Classical Mechanics, Mathematical Physics