Vector calculus in cyclic coordinates

In physical calculations containing angular momenta, cyclic coordinates are frequently employed [379]. Cyclic unit vectors are introduced according to the following rules  

Any vector A may be resolved over cyclic unit vectors eM  

The quantities A thus defined are called contragredient components of the vector A. 

In addition to Eq. (A.3) one may also apply cogredient expansion of A. Then 

In this case the connections between the cogredient Ay, contragredient 

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