On the problem of constructing intermediate trajectories in the theory of elastic-Earth rotation around a center of mass

A Celestial Mechanics Model of Oscillations of the Poles of a Deformable Earth

“…Thus, according to (5), the Earth-Moon system is considered as "almost" binary planet, however, the contribution of the motion with respect to barycenter is relatively small (~5%).…”

“…After a number of simple transformations and averaging over the fast variables ϕ 2 and ϑ the Routh functional R* in the intermediate problem for deformable Earth is represented (correct to a nonessential constant) in the form [5] …”

“…An intermediate model problem is considered at the preliminary stage of studying the Chandler motion of the poles and their evolution under the action of disturbing moments [5]. It is assumed that a deformable planet (the Earth) and a point satellite (the Moon) execute mutual translational-rotational motion around their common center of mass (barycenter).…”

“…The body is considered to be two-layered and consisting of a perfectly rigid core (sphere) and a viscoelastic mantle (spherical layer) [4,5]. There are no displacements of particles of the mantle at the inner boundary, and its outer boundary is free.…”

“…High-precision data of experimental observations and measurements of the trajectory of motion of the Earth's poles testify that very complex dynamical processes take place in the Earth-Moon-Sun system [1][2][3][4][5][6][7][8][9]. The creation of an adequate mathematical model which would allow one to describe satisfactorily the actual trajectories of the rotational axis (instantaneous positions of the angular velocity vector) in some convenient frame of reference associated with the Earth is an interesting problem of theoretical and celestial mechanics.…”