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 literature
- Includes almost 200 carefully crafted excercises, frequently making use of Mathematica
- Suitable for both graduate and advanced undergraduate students
Part of the book series: Modeling and Simulation in Science, Engineering and Technology (MSSET)
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Table of contents (27 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 authors from over 30 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 Hamilton—while also painting a clear picture of the most modern developments.
The text 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. This new edition has been completely revised and updated and now includes almost 200 exercises, as well as new chapters on celestial mechanics, one-dimensional continuous systems, and variational calculus with applications. Several Mathematica® notebooks are available to download that will further aid students in their understanding of some of the more difficult material.Unique in its scope of coverage and method of approach, Classical Mechanics with Mathematica® will be useful resource for graduate students and advanced undergraduates in applied mathematics and physics who hope to gain a deeper understanding of mechanics.
Authors and Affiliations
About the authors
Addolorata Morasco is a Researcher in mathematical physics at the Universitá degli Studi di Napoli Federico II in Naples, Italy.
Bibliographic Information
Book Title: Classical Mechanics with Mathematica®
Authors: Antonio Romano, Addolorata Marasco
Series Title: Modeling and Simulation in Science, Engineering and Technology
DOI: https://doi.org/10.1007/978-3-319-77595-1
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Hardcover ISBN: 978-3-319-77594-4Published: 11 June 2018
Softcover ISBN: 978-3-030-08489-9Published: 05 January 2019
eBook ISBN: 978-3-319-77595-1Published: 29 May 2018
Series ISSN: 2164-3679
Series E-ISSN: 2164-3725
Edition Number: 2
Number of Pages: XVI, 644
Number of Illustrations: 150 b/w illustrations
Topics: Mathematical Physics, Differential Geometry, Classical Mechanics, Mathematical Methods in Physics