Classical Mechanics with Mathematica®. 2nd ed. 2018

種類:

電子ブック

責任表示:

by Antonio Romano, Addolorata Marasco

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2018

著者名:

• Romano, Antonio.
• Marasco, Addolorata.
• SpringerLink (Online service)

シリーズ名:

Modeling and Simulation in Science, Engineering and Technology ;

ISBN:

9783319775951 [3319775952]    

注記:

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 -- Appen
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,

ローカル注記:

学内専用E-BOOKS (local access only)