Computing exact symmetries of dynamical systems from their reduced system of equations can be interesting

The symmetry analysis of differential equations in the context of Lie point and nonlocal symmetries is rich in the literature. In this paper we present the computation of the exact symmetry transformations of dynamical systems from their reduced systems using the Kepler problem as vehicle. We also note that this computational technique is applicable to systems that can be reduced to couple oscillator(s) and a conservation law.