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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).
Wikipedia, Continuum mechanics
Gérard A Maugin, Continuum Mechanics Through the Twentieth Century: A Concise Historical Perspective, 2013
The axiomatization of continuum mechanics internal to toposes has led William Lawvere to the introduction of synthetic differential geometry
and to the notion of cohesion
William Lawvere, Some Thoughts on the Future of Category Theory in A. Carboni, M. Pedicchio, G. Rosolini, Category Theory , Proceedings of the International Conference held in Como, Lecture Notes in Mathematics 1488, Springer (1991)
William Lawvere, Axiomatic cohesion Theory and Applications of Categories, Vol. 19, No. 3, 2007, pp. 41–49. (pdf)
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.
Early precursor of continuum mechanics has been argued to be recognizable in Descartes‘s mechanism (Dusek 99, p.23).
Last revised on July 30, 2015 at 04:51:56. See the history of this page for a list of all contributions to it.