de Saxcé / Vallee Galilean Mechanics and Thermodynamics of Continua

1. Auflage 2016
ISBN: 978-1-119-05803-8
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 448 Seiten, E-Book

This title proposes a unified approach to continuum mechanics which is consistent with Galilean relativity. Based on the notion of affine tensors, a simple generalization of the classical tensors, this approach allows gathering the usual mechanical entities -- mass, energy, force, moment, stresses, linear and angular momentum -- in a single tensor.
Starting with the basic subjects, and continuing through to the most advanced topics, the authors' presentation is progressive, inductive and bottom-up. They begin with the concept of an affine tensor, a natural extension of the classical tensors. The simplest types of affine tensors are the points of an affine space and the affine functions on this space, but there are more complex ones which are relevant for mechanics . torsors and momenta. The essential point is to derive the balance equations of a continuum from a unique principle which claims that these tensors are affine-divergence free.

Autoren/Hrsg.

de Saxcé, Géry

Vallee, Claude

Inhaltsverzeichnis

Chapter 1: Introduction
Chapter 2: Galileo's Principle of Relativity
Chapter 3: Statics
Chapter 4: Dynamics of particles
Chapter 5: Statics of arches, cables and beams
Chapter 6: Dynamics of rigid bodies
Chapter 7: Calculus of Variations
Chapter 8: Static of 3D continua
Chapter 9: Elasticity and elementary theory of beams
Chapter 10: Dynamics of 3D continua and elementary fluiddynamics
Chapter 11: Thermodynamics of reversible continua
Chapter 12: Thermodynamics of dissipative 3D continua
Chapter 13: Statics and Dynamics of shells
Chapter 14: Affine structure on a manifold
Chapter 15: Galilean and Bargmannian structures on amanifold
Chapter 16: Symplectic structure on a manifold