Del in cylindrical and spherical coordinates
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- This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and ϕ):
- The polar angle is denoted by θ: it is the angle between the z-axis and the radial vector connecting the origin to the point in question.
- The azimuthal angle is denoted by ϕ: it is the angle between the x-axis and the projection of the radial vector onto the xy-plane.
- The function atan2(y, x) can be used instead of the mathematical function arctan(y/x) owing to its domain and image. The classical arctan function has an image of (−π/2, +π/2), whereas atan2 is defined to have an image of (−π, π].
|Operation||Cartesian coordinates (x, y, z)||Cylindrical coordinates (ρ, ϕ, z)||Spherical coordinates (r, θ, ϕ)||Parabolic cylindrical coordinates (σ, τ, z)|
|A vector field|
|scalar field Gradient|
|Differential normal area|
|Non-trivial calculation rules:
- Orthogonal coordinates
- Curvilinear coordinates
- Vector fields in cylindrical and spherical coordinates
- Weisstein, Eric W. "Convective Operator". Mathworld. Retrieved 23 March 2011.
- Maxima Computer Algebra system scripts to generate some of these operators in cylindrical and spherical coordinates.