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:
alembert, euler, condition, mathematics, physics, especially, study, mechanics, fluid, dynamics, alembert, euler, condition, requirement, that, streaklines, flow, irrotational, coordinates, point, into, which, carried, time, fluid, flow, displaystyle, ddot, ma. 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 x D 2 x D t displaystyle ddot mathbf x frac D 2 mathbf x Dt be the second material derivative of x Then the d Alembert Euler condition is c u r l x 0 displaystyle mathrm curl mathbf x mathbf 0 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 18th century It is not to be confused with the Cauchy Riemann conditions References EditTruesdell 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 This mathematics related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title D 27Alembert Euler condition amp oldid 1116657021, wikipedia, wiki, book, books, library,