Curvilinear Coordinates -- from Wolfram MathWorld

A coordinate system composed of intersecting surfaces. If the intersections are all at right angles, then the curvilinear coordinates are said to form an orthogonal coordinate system. If not, they form a skew coordinate system. A general metric g_(munu) has a line element ds^2=g_(munu)du^mudu^nu, (1) where Einstein summation is being used. Orthogonal coordinates are defined as those with a diagonal metric so that g_(munu)=delta_nu^muh_mu^2, (2) where delta_nu^mu is the Kronecker...