# Curvilinear coordinate systems and periodic coordinates

 P: 625 Hello, we can consider a generic system of curvilinear coordinates in the 2d plane: $$\rho = \rho(x,y)$$ $$\tau = \tau(x,y)$$ Sometimes, it can happen that one of the coordinates, say $\tau$, represents an angle, and so it is "periodic". This clearly happens for example, in polar coordinates. What are the families of curvilinear coordinates systems in 2d, that have one or more coordinates that are angles? I hope the question is not too vague to be answered. Thanks.