  We use the action-angle variables to describe the geodesic motions in the
$5$-dimensional Sasaki-Einstein spaces $Y^{p,q}$. This formulation allows us to
study thoroughly the complete integrability of the system. We find that the
Hamiltonian involves a reduced number of action variables. Therefore one of the
fundamental frequency is zero indicating a chaotic behavior when the system is
perturbed.
