11. A simple example is Euclidean ( flat ) space expressed in curvilinear coordinates . 12. In general relativity, local curvilinear coordinates in a local basis must be used. 13. In curvilinear coordinates , such as alternative expressions. 14. The formalism of curvilinear coordinates provides a unified and general description of the standard coordinate systems. 15. Despite the use of partial derivatives, these equations are invariant under arbitrary curvilinear coordinate transformations. 16. Curvilinear coordinates are coordinates in which the angles between axes can change from point to point.17. In general relativity, the metric tensor is given by much more general expressions for curvilinear coordinates . 18. Instead of inertial frames, these accelerated motions can also be described using accelerated or curvilinear coordinates . 19. In " n "-dimensional general curvilinear coordinates , the square of arc length is: 20. Another example is his work on the conduction of heat which led him to his theory of curvilinear coordinates .
