Comment on “Matrix representations for vector differential operators in general orthogonal coordinates” by Š. Višňovský

Abstract

In a recent tutorial paper Vǐsňovský [1] presented the correct matrix representations of some well-known vector differential operators valid in arbitrary orthogonal curvilinear coordinates. In a real tour de force he showed, inter alia, that the Laplacian of the vector field can be obtained as either the divergence of the dyadic ∇A or via the matrix representation of the right-hand side of the differential vector identity ∇ · (∇A) = ∇(∇ ·A)−∇× (∇×A) , but also applying the Laplacian operator, ∇ · ∇ ≡ ∇2, to the vector field (compare, e. g., [2]). The key point in Vǐsňovský’s analysis is the equation giving the partial derivative of the unit vectors in arbitrary orthogonal curvilinear coordinates (Eq. (25 ) in [1]; in this Comment all notation in italics will be that of [1]):