nLab continuum mechanics

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).

Related concepts

• classical mechanics, quantum mechanics

  • kinematics, dynamics

  • rigid body dynamics

• Hamiltonian mechanics, Lagrangian mechanics

• cohesion, elasticity, solidity

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

• 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

• William Lawvere, Stephen Schanuel (eds.), Categories in Continuum Physics, Lectures given at a Workshop held at SUNY, Buffalo 1982, Lecture Notes in Mathematics 1174, 986

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)