Va. Borokhov et Iv. Tyutin, CANONICAL STRUCTURE OF SYMMETRY TRANSFORMATIONS IN CLASSICAL MECHANICS - NONDEGENERATE THEORIES, Physics of atomic nuclei, 61(9), 1998, pp. 1603-1613
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.