Vector Differential Operators in arbitrary coordinates: a general approach

arXiv:2508.18309v1 Announce Type: new
Abstract: We present a method for calculating the results of operation of differential operators operating on components of vector in generalized coordinates not restricted to orthogonal one. For this we use the relationships between covariant, contravariant and physical components of a vector and the idea of covariant differentiation. This not only simplifies vector calculus in common curvilinear coordinates, e.g., cylindrical or spherical polar, but also provides a deeper understanding of these operators in coordinate independent form.