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.
Vector Space and Linear Maps | Tensor Algebra | Skew-symmetric Tensors and Exterior Algebra | Euclidean and Symplectic Vector Spaces | Duality and Euclidean Tensors | Differentiable Manifolds | One-Parameter Groups of Diffeomorphisms | Exterior Derivative and Integration | Absolute Differential Calculus | An Overview of Dynamical Systems | Kinematics of a Point Particle | Kinematics of Rigid Bodies | Principles of Dynamics | Dynamics of a Material