Overview
- Offers a unique and broad approach to mechanics, integrating linear algebra, analysis, and differential geometry
- Provides an illuminating historical perspective on the subject, including the models of Newton, Euler, Lagrange and Hamilton
- Gives a treatment of impulsive dynamics, rarely found elsewhere in the literatureIncludes over 200 carefully crafted excercises, frequently making use of Mathematica
- Suitable for both graduate and advanced undergraduate students?
- Includes supplementary material: sn.pub/extras
Part of the book series: Modeling and Simulation in Science, Engineering and Technology (MSSET)
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Table of contents (24 chapters)
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Front Matter
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Introduction to Linear Algebra and Differential Geometry
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Front Matter
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Keywords
About this book
This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject. Developed by the author from 35 years of teaching experience, the presentation is designed to give students an overview of the many different models used through the history of the field—from Newton to Lagrange—while also painting a clear picture of the most modern developments. Throughout, it makes heavy use of the powerful tools offered by Mathematica.
The volume is organized into two parts. The first focuses on developing the mathematical framework of linear algebra and differential geometry necessary for the remainder of the book. Topics covered include tensor algebra, Euclidean and symplectic vector spaces, differential manifolds, and absolute differential calculus. The second part of the book applies these topics to kinematics, rigid body dynamics, Lagrangian and Hamiltonian dynamics, Hamilton–Jacobi theory, completely integrable systems, statistical mechanics of equilibrium, and impulsive dynamics, among others.
Unique in its scope of coverage and method of approach, Classical Mechanics will be a very useful resource for graduate students and advanced undergraduates in applied mathematics and physics who hope to gain a deeper understanding of mechanics.
Reviews
From the reviews:
“By centering his presentation around the major aspects and omitting less important details, the author succeeds in providing a concise though lucid introduction into the mathematical areas … it in particular, can be recommended to students who wish to learn these mathematical concepts without indulging too much in formal and technical points. … The average graduate student … will be well served by Romano’s book. It enjoys many qualities that render this book a promising candidate for becoming a standard text in physics classrooms.” (H. Hogreve, Mathematical Reviews, October, 2013)
“The author presents a high-level textbook based mainly on differential geometry methods; at the same time, he tries to follow a historical process that leads to an easier understanding of the development of mechanics. … The book is written in a very clear and systematic manner; each chapter is followed by many exercises … . The volume represents a real contribution to the field, being useful not only to students but to all readers who wish to have a correct and well-written information, too.” (Petre P. Teodorescu, Zentralblatt MATH, Vol. 1263, 2013)Authors and Affiliations
About the author
Bibliographic Information
Book Title: Classical Mechanics with Mathematica®
Authors: Romano Antonio
Series Title: Modeling and Simulation in Science, Engineering and Technology
DOI: https://doi.org/10.1007/978-0-8176-8352-8
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2012
eBook ISBN: 978-0-8176-8352-8Published: 26 September 2012
Series ISSN: 2164-3679
Series E-ISSN: 2164-3725
Edition Number: 1
Number of Pages: XIV, 506
Number of Illustrations: 127 b/w illustrations
Topics: Differential Geometry, Classical Mechanics, Mathematical Physics, Fluid- and Aerodynamics, Solid Mechanics, Mathematical Methods in Physics