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