Curl

Curl[{f1,f2},{x1,x2}]
gives the curl .

Curl[{f1,f2,f3},{x1,x2,x3}]
gives the curl .

Curl[f,{x1,,xn}]
gives the curl of the ××× array f with respect to the -dimensional vector .

Curl[f,x,chart]
gives the curl in the coordinates chart.

DetailsDetails

  • Curl[f,x] can be input as . The character can be typed as EscdelEsc or \[Del], and the character can be typed as EsccrossEsc or \[Cross]. The list of variables is entered as a subscript.
  • An empty template can be entered as EscdelxEsc, and Tab moves the cursor from the subscript to the main body.
  • All quantities that do not explicitly depend on the variables given are taken to have zero partial derivative.
  • In Curl[f,{x1,,xn}], if f is an array with depth , it must have dimensions , and the resulting curl is an array with depth of dimensions .
  • If f is a scalar, Curl[f,{x1,,xn},chart] returns an array of depth n-1 in the orthonormal basis associated with chart.
  • In Curl[f,{x1,,xn},chart], if f is an array, the components of f are interpreted as being in the orthonormal basis associated with chart.
  • Coordinate charts in the third argument of Curl can be specified as triples in the same way as in the first argument of CoordinateChartData. The short form in which dim is omitted may be used.
  • Curl works with SparseArray and StructuredArray objects.

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

Curl of a vector field in Cartesian coordinates:

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Curl of a vector field in cylindrical coordinates:

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Rotational in two dimensions:

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Use EscdelEsc to enter , Ctrl+- for the list of subscripted variables, and EsccrossEsc to enter :

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Use EscdelxEsc to enter the template , fill in the variables, press Tab, and fill in the function:

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Introduced in 2012
(9.0)
| Updated in 2014
(10.0)