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The tangent frame bundle (or simply the frame bundle) of a smooth manifold is the frame bundle associated with the tangent bundle of . The frame bundle of M {\displaystyle M} is often denoted F M {\displaystyle FM} or G L ( M ) {\displaystyle \mathrm {GL} (M)} rather than F ( T M ) {\displaystyle F(TM)} .
A rotating frame of reference is a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth. (This article considers only frames rotating about a fixed axis. For more general rotations, see Euler angles.)
A panel (alternatively known as frame or box) [6] is one drawing on a page, [7] and contains a segment of action. A page may have one or many panels, and panels are frequently, but not always, [ 6 ] surrounded by a border or outline, [ 8 ] whose shape can be altered to indicate emotion, tension or flashback sequences. [ 9 ]
In this setting, a frame carries the geometric idea of a basis of a vector space over to other sorts of geometrical spaces (Klein geometries). Some examples of frames are: [3] A linear frame is an ordered basis of a vector space. An orthonormal frame of a vector space is an ordered basis consisting of orthogonal unit vectors (an orthonormal basis).
The interpretation of this equation is as follows: the acceleration of the particle in frame A consists of what observers in frame B call the particle acceleration a B, but in addition, there are three acceleration terms related to the movement of the frame-B coordinate axes: one term related to the acceleration of the origin of frame B, namely ...
The Darboux frame is an example of a natural moving frame defined on a surface. With slight modifications, the notion of a moving frame can be generalized to a hypersurface in an n-dimensional Euclidean space, or indeed any embedded submanifold. This generalization is among the many contributions of Élie Cartan to the method of moving frames.