Based on this pdf
| Coordinate | h1 | h2 | h3 | u1 | u2 | u3 | n1 | n2 | n3 |
|---|
| Cartesian | 1 | 1 | 1 | x | y | z | x^ | y^ | z^ |
| Cylindrical | 1 | s | 1 | s | ϕ | z | s^ | ϕ^ | z^ |
| Spherical | 1 | ρ | ρsinθ | ρ | θ | ϕ | ρ^ | θ^ | ϕ^ |
∇f=hi1∂uifni
∇⋅f=h1h2h31∂ui(hjhkfi)
∇×f=hjhk1εijk∂uj(hkfk)ni
Cartesian
∇f=⟨∂xf,∂yf,∂zf⟩
Cylindrical
Spherical
∇f=∂ρfρ^+ρ1∂θfθ^+ρsinθ1∂ϕfϕ^
∇×f=ρsinθ1[∂θ(fϕsinθ)−∂ϕfθ]ρ^+ρ1[sinθ1∂ϕfρ−∂ρ(ρfϕ)]θ^+ρ1[∂ρ(ρfθ)−∂θfρ]ϕ^