  Both orbital and rotational dynamics employ the method of variation of
parameters. We express, in a non-perturbed setting, the coordinates (Cartesian,
in the orbital case, or Eulerian in the rotation case) via the time and six
adjustable constants called elements (orbital elements or rotational elements).
If, under disturbance, we use this expression as ansatz and endow the
"constants" with time dependence, then the perturbed velocity (Cartesian or
angular) will consist of a partial derivative with respect to time and a
so-called convective term, one that includes the time derivatives of the
variable "constants." Out of sheer convenience, the so-called Lagrange
constraint is often imposed. It nullifies the convective term and, thereby,
guarantees that the functional dependence of the velocity upon the time and
"constants" stays, under perturbation, the same as it used to be in the
undisturbed setting.
  When the dynamical equations, written in terms of the "constants," are
demanded to be symplectic (and the "constants" make conjugated pairs $ Q, P$),
these "constants" are called Delaunay elements, in the orbital case, or Andoyer
elements, in the rotational case. The Andoyer and Delaunay sets of elements
share a feature not visible with a naked eye: in certain cases, the standard
equations render these elements non-osculating.
  Hence, even though the Andoyer variables in the Kinoshita-Souchay theory are
introduced in a precessing frame of the Earth orbit, they nevertheless return
the angular velocity relative to an inertial frame.
