nLab
continuum mechanics

Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

Continuum mechanics refers to the physics/mechanics of continuous bodies such as notably fluids? but also solids (solid state physics). As opposed to the mechanics of point particles (to which it is of course related by various limiting processes).

References

General

  • Wikipedia, Continuum mechanics

  • Gérard A Maugin, Continuum Mechanics Through the Twentieth Century: A Concise Historical Perspective, 2013

Formalization

The axiomatization of continuum mechanics internal to toposes has led William Lawvere to the introduction of synthetic differential geometry

  • William Lawvere, Toposes of laws of motion , transcript of a talk in Montreal, Sept. 1997 (pdf)

and to the notion of cohesion

For more on this see also the collection

and

  • William Lawvere, Variable sets, topoi and etendu Notices Amer. Math. Soc. 22 (1975) A675.

  • W. Noll, The foundations of mechanics and thermodynamics Springer, 1974.

History

Early precursor of continuum mechanics has been argued to be recognizable in Descartes’s mechanism (Dusek 99, p.23).

  • V. Dusek, The Holistic Inspirations of Physics NewBrunswick: Rutgers University Press (1999) (review)

Revised on July 30, 2015 04:51:56 by Bas Spitters (192.38.33.16)