Lagrangian and Eulerian description

Summary

In continuum mechanics a field can be written as a function of the material point and time: this is the Lagrangian or material description. It can also be written as a function of the place in space and time: this is the Eulerian or spatial description. The two descriptions are linked by the motion of the body. Solid mechanics often prefers the Lagrangian form, fluid mechanics the Eulerian form, and the change between them produces the material derivative.