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| {{lowercase|d'Alembert-Euler condition}}
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| In [[mathematics]] and [[physics]], especially the study of [[mechanics]] and [[fluid dynamics]], the '''d'Alembert-Euler condition''' is a requirement that the [[Streamlines, streaklines and pathlines|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 <math>\ddot{\mathbf{x}}=\frac{D^2\mathbf{x}}{Dt}</math> be the second [[material derivative]] of '''x'''. Then the d'Alembert-Euler condition is:
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| :<math>\mathrm{curl}\ \mathbf{x}=\mathbf{0}. \, </math>
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| 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 equations|Cauchy-Riemann conditions]].
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| ==References==
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| *{{cite book |last=Truesdell |first=Clifford A. |authorlink=Clifford Truesdell |title=The Kinematics of Vorticity |year=1954 |publisher=Indiana University Press |location=Bloomington, IN}} See sections 45–48.
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| *[http://eom.springer.de/c/c020970.htm d'Alembert–Euler conditions] on the Springer Encyclopedia of Mathematics
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| {{DEFAULTSORT:D'alembert-Euler Condition}}
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| [[Category:Fluid mechanics]]
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| [[Category:Mechanical engineering]]
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| [[Category:Vector calculus]]
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Revision as of 16:46, 2 March 2014
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