Classical Mechanics with Mathematica®

Classical Mechanics with Mathematica®

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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.a€‹ 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 fielda€”from Newton to Lagrangea€”while also painting a clear picture of the most modern developments. Throughout, it makes heavy use of the powerful tools offered by Mathematicaa€‹. 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, Hamiltona€“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.In some cases, polynomial Lyapunov functions can be easily found (see exercises at end of chapter). ... be useful.5 More precisely, since f.0/ D 0, (10.1) can be written as follows: PxDAxCE†.x/; (10.11) where A D .rf/xD0 is an n n constant matrix and E†.x/ D o.k x k/ when x ! ... In this section, we search for approximate solutions of (10.1). It should be possible to search for such a solution as a Taylor expansion.

Title:Classical Mechanics with Mathematica®
Author: Antonio Romano
Publisher:Springer Science & Business Media - 2012-09-26

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