  Integrable dynamical systems play an important role in many areas of science,
including accelerator and plasma physics. An integrable dynamical system with
$n$ degrees of freedom (DOF) possesses $n$ nontrivial integrals of motion, and
can be solved, in principle, by covering the phase space with one or more
charts in which the dynamics can be described using action-angle coordinates.
To obtain the frequencies of motion, both the transformation to action-angle
coordinates and its inverse must be known in explicit form. However, no general
algorithm exists for constructing this transformation explicitly from a set of
$n$ known (and generally coupled) integrals of motion. In this paper we
describe how one can determine the dynamical frequencies of the motion as
functions of these $n$ integrals in the absence of explicitly-known
action-angle variables, and we provide several examples.
