Del in cylindrical and spherical coordinates - Wikipedia, the free en... http://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coord...
Del in cylindrical and spherical coordinates
From Wikipedia, the free encyclopedia
T his is a list of some vector calculus formulae of general use in working with various coordinate systems.
Note
T his page uses standard physics notation. For spherical coordinates, θ is the angle between the z axis and the radius vector connecting the origin to the point in question. φ is the angle between the projection of the radius vector onto the x-y plane and the x axis. Some (American mathematics) sources reverse this definition. T he function atan2(y, x) is used instead of the mathematical function arctan(y/x) due to its domain and image. T he classical arctan(y/x) has an image of (-π/2, +π/2), whereas atan2(y, x) is defined to have an image of (-π, π]. (T he expressions for the Nabla in spherical coordinates may need to be corrected)
1 of 3 01/23/2009 10:15 AM Del in cylindrical and spherical coordinates - Wikipedia, the free en... http://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coord...
Table with the del operator in cylindrical, spherical and parabolic cylindrical coordinates
Cartesian Cylindrical coordinates Parabolic cylindrical coordinates Operation Spherical coordinates (r,θ,φ) coordinates (x,y,z) (ρ,φ,z) (σ,τ,z)
Definition of coordinates
Definition of unit vectors
Gradient
Divergence
Curl
Laplace operator
Vector Laplacian
2 of 3 01/23/2009 10:15 AM Del in cylindrical and spherical coordinates - Wikipedia, the free en... http://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coord...
Differential displacement
Differential normal area
Differential volume Non-trivial calculation rules:
1. (Laplacian) 2. 3. 4. (using Lagrange's formula for the cross product) 5.
See also
Orthogonal coordinates Curvilinear coordinates Vector fields in cylindrical and spherical coordinates
Retrieved from "http://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates" Categories: Vector calculus | Coordinate systems
T his page was last modified on 30 October 2008, at 14:34. All text is available under the terms of the GNU Free Documentation License. (See Copyrights for details.) Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a U.S. registered 501(c)(3) tax-deductible nonprofit charity.
3 of 3 01/23/2009 10:15 AM