The theory of canonical perturbations applied to attitude dynamics and to the Earth rotation. Osculating and nonosculating Andoyer variables

The Hamiltonian theory of Earth rotation, known as the Kinoshita-Souchay theory, operates with nonosculating Andoyer elements. This situation parallels a similar phenomenon that often happens (but seldom gets noticed) in orbital dynamics, when the standard Lagrange-type or Delaunay-type planetary equations unexpectedly render nonosculating orbital elements. In orbital mechanics, osculation loss happens when a velocity-dependent perturbation is plugged into the standard planetary equations. In attitude mechanics, osculation is lost when an angular-velocity-dependent disturbance is plugged in the standard dynamical equations for the Andoyer elements. We encounter exactly this situation in the theory of Earth rotation, because this theory contains an angular-velocity-dependent perturbation (the switch from an inertial frame to that associated with the precessing ecliptic of date).
While the osculation loss does not influence the predictions for the figure axis of the planet, it considerably alters the predictions for the instantaneous spin-axis' orientation. We explore this issue in great detail.