Characteristic functional structure of infinitesimal symmetry mappings of classical dynamical systems. III. Systems with cyclic variables

Abstract

This paper is a continuation of previous papers I and II with similar titles [J. Math. Phys. 26, 3080, 3100 (1985)]. In those papers a theory was developed that described the characteristic functional structures of infinitesimal symmetry mappings of systems of first- or second-order dynamical equations. Now an investigation is made of how cyclic variables of the dynamical equations affect the symmetry equations and thereby propagate through the theory to influence the form of the characteristic functional structure of the symmetries. These special symmetries, which have a particularly simple form, are characterized by infinitesimal point mappings in which only cyclic coordinates are varied, with the variation essentially determined by constants of motion of the dynamical system. For Lagrangian systems with cyclic coordinates these special symmetry mappings include the well-known Noether symmetries characterized by constant variation of the cyclic coordinates.