A dynamieal system of classical mechanics subjgect to a constra. int whose motion may be described in terms of non - independent generalized coordinates. Suppose the action integral of the Systom and constraint conditions are invariant under the symmetry trans. formations of the time and these generalized coordinates. We can generalize Noether theorem to this dynamical system. For the non_ holonomic systen

In general

Symmetry transformations Do noty ielb the conseryation laws as usual Noether theorem. At the Same time

We Can generalize the PoinCare's - Cartan invariant to this constr ained system