# Cyclic coordinates

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Generalized coordinates of a certain physical system that do not occur explicitly in the expression of the characteristic function of this system. When one uses the corresponding equations of motion, one may obtain at once for every cyclic coordinate the integral of motion corresponding to it. For example, if the Lagrange function , where the are generalized coordinates, the generalized velocities, and the time, does not contain explicitly, then is a cyclic coordinate, and the -th Lagrange equation has the form (cf. Lagrange equations (in mechanics)), which at once gives an integral of motion

#### References

 [1] L.D. Landau, E.M. Lifshits, "Mechanics" , Pergamon (1965) (Translated from Russian)