Editing Moving frame (section)

===Uses===

Moving frames are important in [[general relativity]], where there is no privileged way of extending a choice of frame at an event ''p'' (a point in [[spacetime]], which is a manifold of dimension four) to nearby points, and so a choice must be made. In contrast in [[special relativity]], ''M'' is taken to be a vector space ''V'' (of dimension four). In that case a frame at a point ''p'' can be translated from ''p'' to any other point ''q'' in a well-defined way. Broadly speaking, a moving frame corresponds to an observer, and the distinguished frames in special relativity represent [[inertial frame of reference|inertial observers]].

In relativity and in [[Riemannian geometry]], the most useful kind of moving frames are the '''orthogonal''' and '''[[orthonormal frame]]s''', that is, frames consisting of orthogonal (unit) vectors at each point. At a given point ''p'' a general frame may be made orthonormal by [[orthonormalization]]; in fact this can be done smoothly, so that the existence of a moving frame implies the existence of a moving orthonormal frame.