**X1-015 (2003/03/21)**

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Symmetry and the Lagrangian formulation, I
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Symmetries and constants of motion are investigated. It is shown that each Noetherian symmetry-generator of a system corresponding to an action of at most first order, leads to a local constant-of-motion; and each local constant-of-motion of a system corresponding to an action of at most first order, leads to a Noetherian symmetry-generator.