Classical Mechanics with Mathematica®

Valuable for its wide-ranging yet thorough approach to mechanics, this textbook succeeds in bridging the often daunting divide between classical analytical and modern differential geometries, and reflects the author's decades-long teaching experience.

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 fieldfrom Newton to Hamiltonwhile 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, HamiltonJacobi 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.

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

Auteur

Antonio Romano is Professor Emeritus at the Universitá degli Studi di Napoli Federico II in Naples, Italy.
Addolorata Morasco is a Researcher in mathematical physics at the Universitá degli Studi di Napoli Federico II in Naples, Italy.

Contenu
Part I: Introduction to Linear Algebra and Differential Geometry.- Vector Spaces 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.- Part II: Mechanics.- Kinematics of a Point Particle.- Kinematics of Rigid Bodies.- Principles of Dynamics.- Dynamics of a Material Point.- General Principles of Rigid Body Dynamics.- Dynamics of a Rigid Body.- Lagrangian Dynamics.- Hamiltonian Dynamics.- The Hamilton-Jacobi Theory.- Completely Integrable Systems.- Elements of Statistical Mechanics of Equilibrium.- Impulsive Dynamics.- Introduction to Fluid Mechanics.- An Introduction to Celestial Dynamics.- One-Dimensional Continuous Systems.- An Introduction to Special Relativity.- Variational Calculus with Applications.- Appendix A: First-Order PDEs.- Appendix B: Fourier Analysis.- Index.