14.3 Spherical Coordinates
INTRODUCTION
In this section we continue our examination of boundary-value problems in different coordinate systems. This time we are going to consider problems involving the heat, wave, and Laplace’s equation in spherical coordinates.
Laplacian in Spherical Coordinates
As shown in FIGURE 14.3.1, a point in 3-space is described in terms of rectangular coordinates and in spherical coordinates. The rectangular coordinates x, y, and z of the point are related to its spherical coordinates r, θ, and ϕ through the equations
(1)
By using the equations in (1) it can be shown that the Laplacian ∇2u in the spherical coordinate ...
Get Advanced Engineering Mathematics, 7th Edition now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
