Conical coordinates
From Infogalactic: the planetary knowledge core
Conical coordinates are a three-dimensional orthogonal coordinate system consisting of concentric spheres (described by their radius ) and by two families of perpendicular cones, aligned along the z- and x-axes, respectively.
Basic definitions
The conical coordinates are defined by
with the following limitations on the coordinates
Surfaces of constant are spheres of that radius centered on the origin
whereas surfaces of constant and are mutually perpendicular cones
In this coordinate system, both Laplace's equation and the Helmholtz equation are separable.
Scale factors
The scale factor for the radius is one (), as in spherical coordinates. The scale factors for the two conical coordinates are
References
Bibliography
- Lua error in package.lua at line 80: module 'strict' not found.
- Lua error in package.lua at line 80: module 'strict' not found.
- Lua error in package.lua at line 80: module 'strict' not found.
- Lua error in package.lua at line 80: module 'strict' not found.
- Lua error in package.lua at line 80: module 'strict' not found.
- Lua error in package.lua at line 80: module 'strict' not found.