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linalg(deprecated)

  

curl

  

curl of a vector

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

curl(f, v)

curl(f, v, co)

Parameters

f

-

list or vector of three expressions

v

-

list or vector of three variables

co

-

(optional), is either of type `=` or a list of three elements. This option is used to compute the curl in orthogonally curvilinear coordinate systems.

Description

• 

Important: The linalg package has been deprecated. Use the superseding command VectorCalculus[Curl], instead.

  

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

• 

curl(f, v) computes the curl of f with respect to v, where f is a three-dimensional function of the three variables v.  When the third argument is not given, the curl of f is computed in the Cartesian coordinate system.

• 

If the optional third argument co is of the form coords = coords_name or coords = coords_name([const]), curl will operate on commonly used orthogonally curvilinear coordinate systems. See ?coords for the list of the coordinate systems supported by Maple.

For orthogonally curvilinear coordinates v[1], v[2], v[3]

with unit vectors a[1], a[2], a[3], and scale factors

h[1], h[2], h[3]:

Let the rectangular coordinates x, y, z be defined in terms of the

specified orthogonally curvilinear coordinates. We have:

   h[n]^2 = [diff(x,v[n])^2 + diff(y,v[n])^2 + diff(z,v[n])^2], n=1,2,3.

The formula for the curl of f is:

   curl(f) = [1/(h[2]*h[3])*(diff(h[3]*f[3],v[2])-diff(h[2]*f[2],v[3])),

              1/(h[3]*h[1])*(diff(h[1]*f[1],v[3])-diff(h[3]*f[3],v[1])),

              1/(h[1]*h[2])*(diff(h[2]*f[2],v[1])-diff(h[1]*f[1],v[2]))];

  

If co is a list of three elements which specify the scale factors, curl will operate on orthogonally curvilinear coordinate systems.

• 

To compute the curl in other orthogonally curvilinear coordinate systems, use the addcoords routine.

• 

The command with(linalg,curl) allows the use of the abbreviated form of this command.

Examples

Important: The linalg package has been deprecated. Use the superseding command VectorCalculus[Curl], instead.

withlinalg:

fx2,xz,y2z:vx,y,z:

curlf,v

2yzx0z

(1)

gr,sinθ,z:vr,θ,z:

curlg,v,coords=cylindrical

00sinθr

(2)

define the scale factors in cylindrical coordinates

h1,r,1:

curlg,v,h

00sinθr

(3)

ir,sinθr,cosφr:vr,θ,φ:

curli,v,coords=spherical

cosθcosφsinθ2cosφ2sinθ

(4)

See Also

addcoords

coords

linalg(deprecated)[diverge]

linalg(deprecated)[grad]

linalg(deprecated)[laplacian]

LinearAlgebra

VectorCalculus[Curl]