Unperturbed Chandler’s motion and perturbation theory of the rotational motion of the deformable celestial bodies

Barkin, Y.V.

Автор: Barkin Y.V.
Журнал: Astronomical and Astrophysical Transactions
Том: 17
Номер: 3
Год издания: 1998
Издательство: Cambridge Scientific Publishers
Местоположение издательства: Cambridge
Первая страница: 431
Последняя страница: 475
DOI: 10.1080/10556799808232092
Аннотация: 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 classicd 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 8- 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 expressed through full elliptical integrals of the Erst, second and third kinds with modulus which is the defining function of the action variables. It is the principal peculiarity of these series. As an illustration we give a application of this unperturbed theory to the study of the Earth’s rotation (the principal properties of the Earth’s rotation and perturbations). So, the unperturbed motion describes the following phenomena of the Earth’s rotation: (1) Chandler’s motion of the pole of the Earth’s axis of rotation; (2) the ellipticity of the trajectory of the Earth’s pole; (3) the non-uniformity of the pole motion along the elliptical trajectory; (4) the variation with Chandler’s period of the modulus of the‘Earth’s angular velocity.
Добавил в систему: Баркин Юрий Владимирович

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Unperturbed Chandler’s motion and perturbation theory of the rotational motion of the deformable celestial bodiesстатья

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