We give a futher development on previous articles Suppose the Lag- rangian of generalized mechanics involving High Order of generalized derivativse coordinates

This System Subject to a Constraint Whose Motion May be Des- cribed in Terms of non-Indepdent Generalzed Coordinates.Under the Symmetry Transformation of the Time and Generalized Coordinates We Can Generalize Noether's Theorem to This Constrained System and Give a Condition Such That Gene ralized Noether's Theorem may Reduce to Classical Noether's The- orem.Using This Formalism We Can Easily Generalize Saletan—Cromer's Therem.At Same Time Wc Give a Generalization of Riahi's results. We Start from General Transformation properties of Constrained System

One obtain gnenra lized Poinsares Invaraint.