D'Alembert-Euler condition
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- The correct title of this article is d'Alembert-Euler condition. The initial letter is shown capitalized due to technical restrictions.
In mathematics and physics, especially the study of mechanics and fluid dynamics, the d'Alembert-Euler condition is a requirement that the streaklines of a flow are irrotational. Let x=x(X,t) be the coordinates of the point x into which X is carried at time t by a (fluid) flow. Let 
be the second material derivative of x. Then the d'Alembert-Euler condition is:
.
The d'Alembert-Euler condition is named for Jean le Rond d'Alembert and Leonhard Euler who independently first described its use in the mid 1700's. It is not be confused with the Cauchy-Riemann conditions.
[edit] References
- Truesdell, Clifford A. (1954). The Kinematics of Vorticity. Bloomington, IN: Indiana University Press. See sections 45–48.
- d'Alembert–Euler conditions on the Springer Encyclopedia of Mathematics
