Main Content

旋度

Curl of vector field

所有的页面崩溃

Syntax

旋度(V,X)
旋度(V)

Description

example

旋度(V,X)returns the旋度of the vector fieldVwith respect to the vectorX. The vector fieldVand the vectorXare both three-dimensional.

旋度(V)returns the curl of the vector fieldVwith respect to the vector of variables returned bysymvar(V,3).

Examples

collapse all

Compute the curl of this vector field with respect to vectorX= (x,y,z)in Cartesian coordinates.

syms x y z V = [x^3*y^2*z, y^3*z^2*x, z^3*x^2*y]; X = [x y z]; curl(V,X)
ans = x^2*z^3 - 2*x*y^3*z x^3*y^2 - 2*x*y*z^3 - 2*x^3*y*z + y^3*z^2

Compute the curl of the gradient of this scalar function. The curl of the gradient of any scalar function is the vector of 0s.

syms x y z f = x^2 + y^2 + z^2; vars = [x y z]; curl(gradient(f,vars),vars)
ans = 0 0 0

The vector Laplacian of a vector fieldVis defined as follows.

∇ 2 V = ∇ ( ∇ ⋅ V ) − ∇ × ( ∇ × V )

Compute the vector Laplacian of this vector field using the旋度,divergence, andgradientfunctions.

syms x y z V = [x^2*y, y^2*z, z^2*x]; vars = [x y z]; gradient(divergence(V,vars)) - curl(curl(V,vars),vars)
ans = 2*y 2*z 2*x

Input Arguments

collapse all

Input, specified as a three-dimensional vector of symbolic expressions or symbolic functions.

Variables, specified as a vector of three variables

More About

collapse all

Curl of a Vector Field

旋度的向量fieldV= (V1,V2,V3)with respect to the vectorX= (X1,X2,X3)in Cartesian coordinates is this vector.

c u r l ( V ) = ∇ × V = ( ∂ V 3 ∂ X 2 − ∂ V 2 ∂ X 3 ∂ V 1 ∂ X 3 − ∂ V 3 ∂ X 1 ∂ V 2 ∂ X 1 − ∂ V 1 ∂ X 2 )

Version History

Introduced in R2012a

See Also

|||||||