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Table with the del operator in cartesian, cylindrical and spherical coordinates Operation Cartesian coordinates (x, y, z) Cylindrical coordinates (ρ, φ, z) Spherical coordinates (r, θ, φ), where θ is the polar angle and φ is the azimuthal angle α; Vector field A
A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis (axis L in the image opposite), the direction from the axis relative to a chosen reference direction (axis A), and the distance from a chosen reference plane perpendicular to the axis (plane ...
Del operator, represented by the nabla symbol. Del, or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by the nabla symbol ∇. When applied to a function defined on a one-dimensional domain, it denotes the standard derivative of the function as defined in calculus.
In other coordinate systems, such as cylindrical and spherical coordinates, the Laplacian also has a useful form. Informally, the Laplacian Δ f ( p ) of a function f at a point p measures by how much the average value of f over small spheres or balls centered at p deviates from f ( p ) .
Del in cylindrical and spherical coordinates – Mathematical gradient operator in certain coordinate systems; Differentiation rules – Rules for computing derivatives of functions; Exterior calculus identities; Exterior derivative – Operation on differential forms; List of limits
Vectors are defined in cylindrical coordinates by (ρ, φ, z), where ρ is the length of the vector projected onto the xy-plane, φ is the angle between the projection of the vector onto the xy-plane (i.e. ρ) and the positive x-axis (0 ≤ φ < 2π), z is the regular z-coordinate. (ρ, φ, z) is given in Cartesian coordinates by:
A Cartesian coordinate surface in this space is a coordinate plane; for example z = 0 defines the x-y plane. In the same space, the coordinate surface r = 1 in spherical coordinates is the surface of a unit sphere, which is curved. The formalism of curvilinear coordinates provides a unified and general description of the standard coordinate ...
Del in cylindrical and spherical coordinates – Mathematical gradient operator in certain coordinate systems; Double Fourier sphere method; Elevation (ballistics) – Angle in ballistics; Euler angles – Description of the orientation of a rigid body; Gimbal lock – Loss of one degree of freedom in a three-dimensional, three-gimbal mechanism