Answer:
For a given system, there can be particular transformations for which the explicit equations of motion are the same for both the old and new variables. Transformations for which the equations of motion are invariant, are called invariant transformations. It will be shown that if the Lagrangian does not explicitly contain a particular coordinate of displacement qi, then the corresponding conjugate momentum, pi, is conserved. This relation is called Noether’s theorem which states “For each symmetry of the Lagrangian, there is a conserved quantity".