  It is shown that all spherical symmetric potentials are capable of producing
dynamical symmetries in classical one-body motions, thanks to the inevitable
existence of symmetry axes associated with turning points for corresponding
trajectories. This will definitely expand the class of maximally
superintegrable one-body motions in central potentials that until now was
considered to include only the Newtonian and Hookean cases. A simple method is
proposed to identify and characterize these dynamical symmetries.
