Differential Operators

Differential Operators:

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