Curl of vector field
Compute Curl of Vector Field
Compute the curl of this vector field with respect to vector X = (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
Show Curl of Gradient of Scalar Function is Zero
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
Compute Vector Laplacian of Vector Field
The vector Laplacian of a vector field V is defined as follows.
Compute the vector Laplacian of this vector field using the
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
V — Input
three-dimensional symbolic vector
Input, specified as a three-dimensional vector of symbolic expressions or symbolic functions.
X — Variables
vector of three variables
Variables, specified as a vector of three variables
Curl of a Vector Field
The curl of the vector field V = (V1, V2, V3) with respect to the vector X = (X1, X2, X3) in Cartesian coordinates is this vector.