Abstract
The problems presented by the motion of two solid spheres in a perfect fluid have been attacked by various writers. In each case the method has been that of approximation by successive images, and it appears that no general analytical method of solution has been developed as in the case of the analogous problems for the sphere, ellipsoid and anchor-ring. In this paper a general solution of Laplace's equation is obtained in a form suitable for problems in which the boundary conditions are given over any two spherical surfaces. A similar solution is obtained of the differential equation of Stokes’ current function. With the aid of these results it is theoretically possible to determine completely a potential function when its value is specified over any two spheres. The method is illustrated by an application to the electrostatic field of two charged conducting spheres. In this case the method leads to a simple expression for the capacity of either of the spheres. The co-ordinates employed are defined by rotating about the
z
axis the system of circles, in any plane, through two fixed points on the axis and the orthogonal system of circles. Thus, if
x, y, z
, are the Cartesian co-ordinates and ρ = √(
x
2
+
y
2
), and the distance between the fixed points is 2
a
, we have a system of orthogonal curvilinear co-ordinates
u, v, w
, where
u
+
iv
=log
ρ
+
i
(
z
+
a
)/
ρ
+
i
(
z
-
a
),
w
= tan
-1
y
/
x
.
Cited by
109 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献