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A Direct Method of using the Hodograph Plane in Fluid Dynamics

Published online by Cambridge University Press:  20 January 2009

A. G. Mackie
Affiliation:
Mathematics Department, St Salvator's CollegeUniversity of St Andrews
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The application of the hodograph method in problems in fluid dynamics dates back to the time of Helmholtz and Kirchhoff. The underlying principle is simple. It is in effect to rewrite the governing differential equations with the roles of the original dependent and independent variables reversed. Such a procedure is not uncommon in problems depending upon ordinary differential equations. For example, if the velocity of a particle in rectilinear motion is prescribed as a function of distance from a fixed point, the problem of finding the relation between its position and the time t can be solved by one quadrature if t is regarded as the dependent variable.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1958

References

* Proc. Camb. Phil. Soc. (in the press).Google Scholar