Classical mechanics with Mathematica® / by Antonio Romano, Addolorata Marasco.
Romano, Antonio, 1941- author.; Marasco, Addolorata. author.
2018
QC19.2-20.85
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Title Classical mechanics with Mathematica® / by Antonio Romano, Addolorata Marasco.
Author Romano, Antonio, 1941- author.
Edition Second edition.
ISBN 9783319775951
3319775952
9783319775944
3319775944
DOI https://doi.org/10.1007/978-3-319-77595-1
Published Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
Language English
Description 1 online resource (xvi, 644 pages) : illustrations.
Item Number 10.1007/978-3-319-77595-1 doi
Call Number QC19.2-20.85
Dewey Decimal Classification 530.15
Summary 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® 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. Reviews of the First Edition: "The volume represents a real contribution to the field, being useful not only to students but to all readers who wish to have correct and well-written information." - Petre P. Teodorescu, zbMATH, Vol. 1263, 2013 "By centering his presentation around the major aspects and omitting less important details, the author succeeds in providing a concise though lucid introduction into the mathematical areas. It enjoys many qualities that render this book a promising candidate for becoming a standard text in physics classrooms." - H. Hogreve, Mathematical Reviews, October 2013.
Access Note Access limited to authorized users.
Digital File Characteristics text file PDF
Added Author Marasco, Addolorata. author.
Series Modeling and simulation in science, engineering & technology.
Available in Other Form Print version: 9783319775944
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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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