CANONICAL STRUCTURE OF SYMMETRY TRANSFORMATIONS IN CLASSICAL MECHANICS - NONDEGENERATE THEORIES

The classical structure of Noether symmetries is considered in classic al mechanics with a nondegenerate action functional. It is shown that the set of symmetry transformations is isomorphic, module symmetries v anishing on the manifold specified by the equations of motion, to the set of the canonical symmetries of the physical action functional. It is established that any canonical symmetry of the physical action func tional can be extended to the symmetry that holds for the total action functional and which is canonical for the phase-space variables. In g eneral, the generator of canonical symmetry depends on the Lagrangian multipliers.