In my, er, studies I've encountered descriptions of what I understand to be various ways to go from global to local coordinates. These are: tetrads, Riemann Normal Coordinates and Fermi Normal coordinates. Until now I haven't investigated much further than that, mostly because I've not been able to really see where I would want to chose any one over the others. I am reasonably OK with getting orthonormal tetrads from a metric, but even then I'm not really sure where to go next. I only understand RNC as some kind of local polar-ish coordinate sytem, and I have only really been alerted to FNC via a recent comment by pervect on a thread here. Anyway, the question is: Is there a reasonably snappy way of describing what sort of problems or applications each technique is most suited to?