The motion of constrained system may be described in terms of the non-independent state functions. Suppose the action integral and constraint conditions of this system are invariant under the symmetry transformations of the time-space points and state functions, then we can generalize the Noether's theorem to this constrained system. In general, it does not yield the conservation laws as ordinary Noether's theorem. However, when the system only subjects to finite constraint, the generalized Noether's theorem can reduce to the results as ordinary Noether's theorem.
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