Classical Mechanics with Mathematica®

Description

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. Front Matter....Pages i-xiv Front Matter....Pages 1-1 Vector Space and Linear Maps....Pages 3-15 Tensor Algebra....Pages 17-28 Skew-Symmetric Tensors and Exterior Algebra....Pages 29-40 Euclidean and Symplectic Vector Spaces....Pages 41-59 Duality and Euclidean Tensors....Pages 61-65 Differentiable Manifolds....Pages 67-93 One-Parameter Groups of Diffeomorphisms....Pages 95-103 Exterior Derivative and Integration....Pages 105-115 Absolute Differential Calculus....Pages 117-133 An Overview of Dynamical Systems....Pages 135-158 Front Matter....Pages 159-159 Kinematics of a Point Particle....Pages 161-176 Kinematics of Rigid Bodies....Pages 177-196 Principles of Dynamics....Pages 197-213 Dynamics of a Material Point....Pages 215-246 General Principles of Rigid Body Dynamics....Pages 247-260 Dynamics of a Rigid Body....Pages 261-286 Lagrangian Dynamics....Pages 287-335 Hamiltonian Dynamics....Pages 337-360 The Hamilton-Jacobi Theory....Pages 361-375 Completely Integrable Systems....Pages 377-402 Front Matter....Pages 159-159 Elements of Statistical Mechanics of Equilibrium....Pages 403-414 Impulsive Dynamics....Pages 415-426 Introduction to Fluid Mechanics....Pages 427-457 An Introduction to Special Relativity....Pages 459-485 Back Matter....Pages 487-506