Hidden symmetries and Killing tensors

Just as a Killing vector of the kinetic energy metric of a classical mechanical system can generate a symmetry of the system (an “obvious” symmetry), and thus a constant of the motion, so can a Killing tensor generate a symmetry and a constant of the motion. In the latter case the symmetry is “hidden”: for example the well-known hidden symmetries for a single particle moving under an inverse-square central force, and for the harmonic oscillator, arise in this way.