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Sabtu, 09 April 2011

Curl

Curl
In vector calculus, curl (or rotor) is a vector operator that describes a very small rotation of 3-dimensional vector field. . At every point in the field, represented by the vector curl .. This attribute vectors (length and direction) to characterize the rotation at that point.
. The direction of curl is the axis of rotation, as determined by the right-hand rule, and the amount of curl is the amount of rotation. If the vector field is the flow velocity of the moving fluid, the curl is the density of the fluid circulation .. A vector field is curl is zero is called rotating .. curl is a form of differentiation for vector field .. Forms related to the fundamental theorem of calculus is' theorem Stokes, relating to the surface an integral part of the curl of the vector field by a line integral of vector field around the boundary curve.
Alternative terminology rotor or the rotation and alternative notation rot F and ∇ × F is often used (the former especially in many European countries, which both use the del operator and cross product) to curl and curl F.

Unlike the gradient and divergence, curl does not generalize as only another dimension, some generalizations are possible, but only in three dimensions is geometrically defined the curl of another vector field vector field. This is the same phenomenon as in the 3-dimensional cross product, and the connection is reflected in the notation ∇ × to curl.
Name curl "curl" was first proposed by James Clerk Maxwell in 1871.
For equations in Cartesian coordinates, see Curl (mathematics) # usage.
Curl of the vector field F, denoted F curl or ∇ F ×, the point is defined in terms of projections to the various lines through the points. If n is any unit vector, the projection of curl F to n is defined as the value of a closed line integral limitation in the plane orthogonal to n. as path used in the integral becomes very, very close to the point, divided by the area covered.

            
Vortex (curl) of the vector field associated with rotation of the vector field tsb. Viewed from another perspective, the rotation can be used as a measure ketidakseragaman field, the less uniform the field, the greater the value pusarannya.

CURL PROPERTIES

             If A and B are vectors of differentiable and Φ is a differentiable scalar function, then:





                                                                                                           

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