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 {x1,,xn}.

Curl[f,x,chart]

gives the curl in the coordinates chart.

Details

  • Curl[f,x] can be input as xf. The character can be typed as del or \[Del], and the character can be typed as cross or \[Cross]. The list of variables x is entered as a subscript.
  • An empty template can be entered as delx, and 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 k<n, it must have dimensions {n,,n}, and the resulting curl is an array with depth n-k-1 of dimensions {n,,n}.
  • 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 {coordsys,metric,dim} 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.

Examples

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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 del to enter , for the list of subscripted variables, and cross to enter :

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

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Scope  (6)

Applications  (3)

Properties & Relations  (6)

Interactive Examples  (1)

See Also

Grad  Div  Laplacian  CoordinateChartData  Cross  HodgeDual  D  DSolve  NDSolve  NDEigensystem  NDEigenvalues

Tutorials

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