A Transformation of the Hodograph Equation and the Determination of Certain Fluid Motions

A transformation is given of the hodograph equation of two-dimensional gas dynamics, from the usual variables q, 6t to q and a new variable (J). The transformation, which suits any gas for which pp~y = const, with y> 1, is so chosen that certain solutions, which in terms of q, 6 are multi valued,...

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Bibliographic Details
Published in:Philosophical Transactions of the Royal Society of London, Series A: Mathematical and Physical Sciences Series A: Mathematical and Physical Sciences, 1953-04, Vol.245 (904), p.583-624
Main Author: Cherry, Thomas Macfarland
Format: Article
Language:English
Subjects:
Approximation
Coefficients
Differential equations
Hodographs
Integers
Mathematical cusps
Mathematical transformations
Nozzles
Series convergence
Sine function
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Summary:A transformation is given of the hodograph equation of two-dimensional gas dynamics, from the usual variables q, 6t to q and a new variable (J). The transformation, which suits any gas for which pp~y = const, with y> 1, is so chosen that certain solutions, which in terms of q, 6 are multi valued, become single-valued functions of q,
ISSN:1364-503X
0080-4614
0962-8428
1471-2962
2054-0272
DOI:10.1098/rsta.1953.0007