In this section, we shall express the gradient, divergence and curl in terms of orthogonal curvilinear coordinates u1, u2, u3. Then, the Laplacian can be expressed as the divergence of a gradient by the chain rule, we have
In rectangular cartesian coordinates system,
Where f is a scaler function. In engineering problems this f is usually a potential link.
Velocity Potential or Electrical Potential or Gravitational Potential:
Using chain rules this becomes,
Then the gradient of f, on orthogonal curvilinear coordinates, is