Matrix Representations for Vector Differential Operators in General Orthogonal Coordinates

Abstract

The restrictions in arbitrary orthogonal coordinates to a unified matrix presentation of vector operations using generalized differential matrix operators [Y. Chen et al.: IEEE Trans. on Educ., Vol. 41, (1998), p. 61] are pointed out. The corrected matrix representation for the operations ∇⋅(∇A) and B⋅(∇A) valid in arbitrary orthogonal curvilinear coordinates are obtained and shown to be consistent with the calculation using the dyadic technique. The presentation is accessible to undergraduate students.