Cyclic coordinate

Summary

A cyclic coordinate, or ignorable coordinate, of a Lagrangian system is a generalized coordinate on which the Lagrangian does not depend. The Lagrangian may still depend on the velocity of this coordinate. The generalized momentum conjugate to a cyclic coordinate is conserved during the motion. This is the simplest form of the link between symmetries and conservation laws given by Noether's theorem. Cyclic coordinates can be eliminated from the equations, which reduces the number of degrees of freedom.