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The derivation of the equations of motion of an ideal fluid by Hamilton's principle

Published online by Cambridge University Press:  24 October 2008

J. W. Herivel
J. W. Herivel
Affiliation:
Queen's UniversityBelfast
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Abstract

A new formulation of Hamilton's principle for the case of an ideal fluid is proposed which is claimed to be the uniquely proper form for such a system. The resulting derivation of the equations of motion on varying with respect to the position of the fluid particles is free from the difficulties encountered in previous treatments based on incorrect forms of Hamilton's principle. The treatment also differs from previous treatments in transforming to the fixed (a, b, c) space before carrying out the variation, and in allowing for the equations of mass and entropy conservation by means of undetermined multipliers. The necessity for conservation of entropy, if Hamilton's principle is to be applied, is emphasized. Finally, the method, first used by Eckart, of deriving the equations of motion for an ideal fluid by means of a variational principle of the same form as Hamilton's, but varying with respect to the velocities of the fluid particles, is extended to the general case of rotational motion.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 2 , April 1955 , pp. 344 - 349
Copyright
Copyright © Cambridge Philosophical Society 1955

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References

REFERENCES

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(2)Lichtenstein, L.Grundlagen der Hydrodynamik (Berlin, 1929), chap. 9.Google Scholar
(3)Taub, A. H.Proc. Symp. appl. Math. 1 (1949), 148.CrossRefGoogle Scholar