The main idea is to develop a suitable notion of the connection forms and curvature using moving frames adapted to the particular geometrical problem at hand.
32.
A key feature of the general method is that a preferred moving frame, provided it can be found, gives a complete kinematic description of the curve.
33.
Note for example how the unit directions of latitude and longitude on the Earth's surface break down as a moving frame at the north and south poles.
34.
Here \ rho is the mass-energy density measured in a momentary co-moving frame, u _ a is the fluid's 4-velocity vector field, and p is the pressure.
35.
To show that this definition is equivalent to the others above, one must introduce a suitable notion of a moving frame for the bundle " E ".
36.
Later, moving frames were developed extensively by �lie Cartan and others in the study of submanifolds of more general homogeneous spaces ( such as projective space ).
37.
In their view, synchronous consideration of forces should only be used for the object's rest frame, while in moving frames the same forces should be considered asynchronously.
38.
The theory of Cartan connections was developed by �lie Cartan, as part of ( and a way of formulating ) his method of moving frames ( "'rep�re mobile "').
39.
He used the moving frame method with success only matched by its inventor; he preferred in complex manifold theory to stay with the geometry, rather than follow the potential theory.
40.
The famous Michelson Morley experiment of 1887 showed that the then-accepted Lorentz FitzGerald contraction is not measurable in a co-moving frame, because these theories were based on the Lorentz transformation.
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