# d'Alembert–Euler condition

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 ${\displaystyle {\ddot {\mathbf {x} }}={\frac {D^{2}\mathbf {x} }{Dt}}}$ be the second material derivative of x. Then the d'Alembert-Euler condition is:
${\displaystyle \mathrm {curl} \ \mathbf {x} =\mathbf {0} .\,}$