TY - BOOK
AU - Antonio,Romano
ED - SpringerLink (Online service)
TI - Classical Mechanics with Mathematica®
T2 - Modeling and Simulation in Science, Engineering and Technology,
SN - 9780817683528
AV - QA641-670
U1 - 516.36 23
PY - 2012///
CY - Boston, MA
PB - Birkhäuser Boston, Imprint: Birkhäuser
KW - Mathematics
KW - Differential geometry
KW - Mathematical physics
KW - Physics
KW - Mechanics
KW - Fluids
KW - Continuum mechanics
KW - Differential Geometry
KW - Mathematical Physics
KW - Fluid- and Aerodynamics
KW - Continuum Mechanics and Mechanics of Materials
KW - Mathematical Methods in Physics
N1 - I Introduction to Linear Algebra and Differential Geometry.- 1 Vector Space and Linear Maps.- 2 Tensor Algebra.- 3 Skew-symmetric Tensors and Exterior Algebra.- 4 Euclidean and Symplectic Vector Spaces.- 5 Duality and Euclidean Tensors.- 6 Differentiable Manifolds.- 7 One-Parameter Groups of Diffeomorphisms.- 8 Exterior Derivative and Integration.- 9 Absolute Differential Calculus -- 10 An Overview of Dynamical Systems.- II Mechanics.- 11 Kinematics of a Point Particle.- 12 Kinematics of Rigid Bodies.- 13 Principles of Dynamics.- 14 Dynamics of a Material Point.- 15 General Principles of Rigid Body Dynamics.- 16 Dynamics of a Rigid Body.- 17 Lagrangian Dynamics.- 18 Hamiltonian Dynamics.- 19 Hamilton-Jacobi Theory.- 20 Completely Integrable Systems.- 21 Elements of Statistical Mechanics of Equilibrium.- 22 Impulsive Dynamics.- 23 Introduction to Fluid Mechanics -- A First-Order PDE.- B Fourier’s Series.- References.- Index
N2 - 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. With a unique selection of topics and a large array of exercises to reinforce concepts, Classical Mechanics with Mathematica is an excellent resource for graduate students in physics. It can also serve as a reference for researchers wishing to gain a deeper understanding of both classical and modern mechanics
UR - http://dx.doi.org/10.1007/978-0-8176-8352-8
ER -