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.
With a unique selection of topics and a large array of exercises to reinforce concepts, Classical Mechanics with Mathematica is an excellent resource for graduate students in physics. It can also serve as a reference for researchers wishing to gain a deeper understanding of both classical and modern mechanics.
- DOI https://doi.org/10.1007/978-0-8176-8352-8
- Copyright Information Springer Science+Business Media New York 2012
- Publisher Name Birkhäuser, Boston, MA
- eBook Packages Mathematics and Statistics
- Print ISBN 978-0-8176-8351-1
- Online ISBN 978-0-8176-8352-8
- Series Print ISSN 2164-3679
- Series Online ISSN 2164-3725
- About this book