Unperturbed chandler motion and perturbation theory of the rotation motion of deformable celestial bodies

Abstract

Abstract New unperturbed motions are suggested for the study of the rotational motion of deformable celestial bodies. This motion describes the rotation of an isolated celestial body deformed by its own rotation. By some natural simplifications and by using special forms of canonical variables (similar to Andoyer's variables) the problem is reduced to the classical Euler-Poinsot problem for a rigid body, but with different moments of inertia. The suggested unpertubed motion describes Chandler's pole motion and we shall call it Chandler or Euler-Chandler motion. The development of the unperturbed theory is described in this paper. The solution of the Chandler problem (Andoyer's variables, components of angular velocity of the body's axes, and their direction cosines) is presented in elliptical and θ- functions, and in the form of Fourier series in the angle-action variables. Similar Fourier series were obtained for products and squares of the diraction cosines. The coefficients of these series are expresse...