Access this book
Tax calculation will be finalised at checkout
Other ways to access
About this book
Many different mathematical methods and concepts are used in classical mechanics: differential equations and phase ftows, smooth mappings and manifolds, Lie groups and Lie algebras, symplectic geometry and ergodic theory. Many modern mathematical theories arose from problems in mechanics and only later acquired that axiomatic-abstract form which makes them so hard to study. In this book we construct the mathematical apparatus of classical mechanics from the very beginning; thus, the reader is not assumed to have any previous knowledge beyond standard courses in analysis (differential and integral calculus, differential equations), geometry (vector spaces, vectors) and linear algebra (linear operators, quadratic forms). With the help of this apparatus, we examine all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the hamiltonian formalism. The author has tried to show the geometric, qualitative aspect of phenomena. In this respect the book is closer to courses in theoretical mechanics for theoretical physicists than to traditional courses in theoretical mechanics as taught by mathematicians.
Similar content being viewed by others
Table of contents (10 chapters)
-
Front Matter
-
Newtonian Mechanics
-
Front Matter
-
-
Lagrangian Mechanics
-
Front Matter
-
-
Hamiltonian Mechanics
-
Front Matter
-
-
Back Matter
Reviews
Second Edition
V.I. Arnol’d
Mathematical Methods of Classical Mechanics
"The book's goal is to provide an overview, pointing out highlights and unsolved problems, and putting individual results into a coherent context. It is full of historical nuggets, many of them surprising . . . The examples are especially helpful; if a particular topic seems difficult, a later example frequently tames it. The writing is refreshingly direct, never degenerating into a vocabulary lesson for its own sake. The book accomplishes the goals it has set for itself. While it is not an introduction to the field, it is an excellent overview."
—AMERICAN MATHEMATICAL MONTHLY
Authors and affiliations
Accessibility information
PDF accessibility summary
This PDF is Not accessible. It is based on scanned pages and does Not support features such as screen reader compatibility or descriptions for Non-text content (e.g., images and graphs). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may Not be able to use this content effectively. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility
Bibliographic information
Book title: Mathematical Methods of Classical Mechanics
Authors: V. I. Arnold
Series title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4757-1693-1
Publisher: Springer New York, NY
-
eBook packages: Springer Book Archive
Copyright information: Springer Science+Business Media New York 1978
eBook ISBN: 978-1-4757-1693-1Published: 11 November 2013
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition number: 1
Number of pages: X, 464
Additional information: Title of the original Russian edition: Matematiceskie metody klassiceskoj mechaniki
Topics: Mathematics, general