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In mathematics, the Euler-Tricomi equation is a linear partial differential equation useful in the study of transonic flow. It is named for Leonhard Euler and Francesco Giacomo Tricomi.
Additional recommended knowledge
It is hyperbolic in the half plane x > 0 and elliptic in the half plane x < 0. Its characteristics are xdx2 = dy2, which have the integral
where C is a constant of integration. The characteristics thus comprise two families of semicubical parabolas, with cusps on the line x = 0, the curves lying on the right hand side of the y-axis.
Particular solutions to the Euler-Tricomi equations include
where A,B,C,D are arbitrary constants.
The Euler-Tricomi equation is a limiting form of Chaplygin's equation.
|This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Euler-Tricomi_equation". A list of authors is available in Wikipedia.