Infinitesimal velocity‐dependent symmetry mappings of second‐order dynamical systems (a) Ei
, were studied in considerable detail in a previous paper [J. Math. Phys. 2X
, xxxx (198X), the first of this series]. Among the results developed in that paper was a procedure for determining the characteristic functional structure of symmetry mappings for such second‐order systems. In this present companion paper it is shown that a similar procedure may be used to obtain the characteristic functional structure of infinitesimal symmetry mappings (b) I
, for systems of first‐order differential equations (d) EI
. This characteristic structure is the same for all first‐order systems (d) and is explicitly dependent upon constants of motion of the system. For the special case in which (d) is a system of N
equations derived from a system of n
second‐order equations (a) it is shown how the respective symmetry equations based upon these two equivalent dynamical descriptions are related and how their symmetry solutions are correlated. Two examples are given.