Classical mechanics with Mathematica
著者
書誌事項
Classical mechanics with Mathematica
（Modeling and simulation in science, engineering & technology）
Birkhäuser , Springer, c2018
2nd ed
- : Softcover
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注記
On t.p. the registered trademark symbol "R" is superscript following "Mathematica" in the title
Includes bibliographical references (p. 633-635) and index
"Softcover re-print of the Hardcover 2nd edition 2018" -- T.p. verso
内容説明・目次
内容説明
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 field-from Newton to Hamilton-while 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, Hamilton-Jacobi 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 (R) 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 (R) will be useful resource for graduate students and advanced undergraduates in applied mathematics and physics who hope to gain a deeper understanding of mechanics.
目次
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.
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