Orthogonal Curvilinear Coordinate Systems

Orthogonal curvilinear coordinates occupy a special place among general coordinate systems, due to their special properties. There exists a number of such coordinate systems where the Laplace or Helmholtz equations may be separable, thus yielding a powerful tool to solve them. Operations like gradients, divergence, Laplacian take on much simpler forms in orthogonal coordinates. In this chapter the summation convention will not be used.