Direct expression of incompatibility in curvilinear systems

Abstract

With this note, we would like present a method to compute the incompatibility operator in any system of curvilinear coordinates/components. The procedure is independent of the metric in the sense that the expression can be expressed by means of the basis vectors only, which are first defined as normal and tangent to the domain boundary and then extended to the whole domain. It is in some sense an intrinsic method, since the chosen curvilinear system depends solely on the geometry of the domain boundary. As an application, the in extenso expression of incompatibility in a spherical system is given.