Curl (redirected from Rot (mathematics))

curl

In mathematics, a differential operator that can be applied to a vector-valued function (or vector field) in order to measure its degree of local spinning. It consists of a combination of the function's first partial derivatives. One of the more common forms for expressing it is: in which v is the vector field (v₁, v₂, v₃), and v₁, v₂, v₃ are functions of the variables x, y, and z, and i, j, and k are unit vectors in the positive x, y, and z directions, respectively. In fluid mechanics, the curl of the fluid velocity field (i.e., vector velocity field of the fluid itself) is called the vorticity or the rotation because it measures the field's degree of rotation around a given point.

---

Curl

(1) A programming environment for developing rich Internet applications (RIAs) from Curl, Inc., Cambridge, MA (www.curl.com). Conceived at MIT, Curl combines HTML markup with an object-oriented programming language. The user's machine requires the Curl runtime engine and browser plug-in for execution. The first Curl implementation was released in 2002. See RIA.

(2) (cURL) A command line utility for executing functions with URL-oriented protocols such as FTP and HTTP. Pronounced "C-URL," there are versions for Unix, Linux, Windows, Mac and other operating systems. For more information, visit http://curl.haxx.se.

---

curl

Maths a vector quantity associated with a vector field that is the vector product of the operator ∇ and a vector function A, where ∇ = i∂/∂x + j∂/∂by + k∂/∂z, i, j, and k being unit vectors. Usually written curl A, rot A

---

curl [kərl]

(forestry)

A block of timber cut from a crotch for cutting into veneers.

(materials)

A defect of paper caused by unequal alteration in the dimensions of the top and underside of the sheet.

(mathematics)

The curl of a vector function is a vector which is formally the cross product of the del operator and the vector. Also known as rotation (rot).

---

curl

A winding, swirling, or circling in the grain of wood, usually obtained from the crotch or fork of a tree; also see fiddleback.

---

Curl 

of a vector field A, the vector characteristic of a “rotating component” of field A. The curl is represented by the symbol rot A. It can be interpreted in the following manner: Let A be the velocity field of a fluid flow. At a given point of the flow we place a small wheel with blades and orient its axis in the direction of rot A at that point. Then the angular velocity of the wheel’s rotation from the action of the current will be maximum, and its value will equal (| rot A |)/2. If the field A has the coordinates P(x, y, z), Q(x, y, z), and R(x, y, z), then the curl has the coordinates

E. G. POZNIAK