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On some axisymmetrical two sphere potential problems

Published online by Cambridge University Press:  26 February 2010

R. Shail
R. Shail
Affiliation:
Department of Applied Mathematics, University of Liverpool.
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Extract

In this paper we shall consider some axisymmetrical problems involving the determination of a harmonic function which satisfies prescribed conditions on two given spherical surfaces. The latter may be exterior to one another or one inside the other. The classical problems which come under this heading are the electrostatic two sphere condenser and the motion of two spheres along the line of centres in an unbounded inviscid fluid. The early investigators of these problems used the well known method of images (Kelvin [1], Hicks [2]). In the electrostatic case (Dirichlet boundary conditions) the images are sets of point monopoles, and in the hydrodynamic case (Neumann boundary conditions) sets of dipole sources. Later Neumann [3] and Jeffery [4] gave solutions using a bipolar coordinate system.

Type
Research Article
Information
Mathematika , Volume 9 , Issue 1 , June 1962 , pp. 57 - 70
Copyright
Copyright © University College London 1962

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References

1. Kelvin, Lord, Papers on Electricity and Magnetism.Google Scholar
2. Hicks, W. M., Phil. Trans., 1880, p. 455.Google Scholar
3. Neumann, O., Hydrodynamische Untersuchungen (Leipzig, 1883).Google Scholar
4. Jeffery, G. B., Proc. Roy. Soc. (A), 87 (1912), 109.Google Scholar
5. Mitra, S. K., Bull. Calcutta Math. Soc, 36 (1944), 31.Google Scholar
6. Hermann, R. A., Quart. Journal, 22 (1887), 204.Google Scholar
7. Bassett, A. B., Proc. London Math. Soc., 28, 369.Google Scholar
8. Hobson, E. W., Spherical and ellipsoidal harmonics (Cambridge, 1931).Google Scholar
9. Schiffman, M. and Spencer, D. C., Quart. Appl. Math., 5 (1947–48), 270.CrossRefGoogle Scholar