Galilean Mechanics and Thermodynamics of Continua

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John Wiley & Sons, Feb 8, 2016 - Mathematics - 413 pages

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.

 

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Contents

Galileos Principle of Relativity
3
Statics
15
Dynamics of Particles
27
Statics of Arches Cables and Beams
57
Dynamics of Rigid Bodies
75
Calculus of Variations
105
Elementary Mathematical Tools
117
Statics of 3D Continua
143
Dynamics of Continua of Arbitrary Dimensions
215
More About Calculus of Variations
235
Thermodynamics of Continua
247
Mathematical Tools
281
Affine Structure on a Manifold
309
Galilean Bargmannian and Poincarean
321
Symplectic Structure on a Manifold
367
Advanced Mathematical Tools
399

Elasticity and Elementary Theory of Beams
157
Dynamics of 3D Continua and Elementary
187

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About the author (2016)

Géry de Saxcé is Professor at Lille 1 University - Science and Technology, France.

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