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On the difference between a bounding surface and a material surface

  • E. B. Dussan V (a1)

Abstract

The ideas of Lagrange, Poisson, Kelvin and Truesdell are reviewed. It is shown that in order for a bounding surface not to be a material surface either u. n = c must fail or more than one deformation can be associated with the velocity field. Examples are given.

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References

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Birkhoff, G. & Rota, G. 1969 Ordinary Differential Equations, 2nd edn. Waltham, Mass.: Xerox Corp.
DUSSAN V. E. B. & DAVIS, S. H. 1974 On the motion of a fluid-fluid interface along a solid surface J. Fluid Mech. 65, 71.
Ince, E. L. 1956 Ordinary Differential Equations. Dover.
Kelvin, Lord 1848 Notes on hydrodynamics (2). On the equation of the bounding surface. [From Camb. Dublin Math. J. Feb. 1848.] In Math. Phys. Papers of Sir William Thomson, vol. 1, 82.
Lagrange, J. L. 1779 Mémoire sur différentes questions d'analyse relatives à la théorie des intégrales particulières. Nouveaux Mémoires de l'Académie Royale des Sciences et Belles-Lettres de Berlin.
Lagrange, J. L. 1781 Mémoire sur la théorie du mouvement des fluides. Nouveaux Mémoires de l'Académie Royale des Sciences et Belle-Lettres de Berlin.
Lamb, H. 1932 Hydrodynamics, 6th edn. Dover.
Poisson, S. D. 1842 Traité de Mécanique, p. 681.
Truesdell, C. A. 1951 On the equation of the bounding surface Bull. Tech. Univ. Istanbul, 3, 71.
Truesdell, C. A. & Toupin, R. 1960 Principles of Classical Mechanics and Field Theory. Handbuch der Physik, vol. III/1. Springer.
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On the difference between a bounding surface and a material surface

  • E. B. Dussan V (a1)

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