Динамические эффекты во вращении Земли, вызванные годовыми и полугодовыми циклическими перераспределениями масс планеты

Abstract

The paper deals with development of the theory of perturbed rotational motion of a celestial body with variable geometry of the masses. Its main task is to study the impact of annual and semi-annual variations of the Earth's mass geometry (a component of its inertia tensor), as well as a component of its relative angular momentum, on the movement of the Earth's poles and its axial rotation. The body is considered to be a free (isolated), and the problem formulation corresponds to the classical Liouville problem on rotation of a variable body. Euler conical movement of the axially symmetric body with an arbitrary constant half-angle  is assumed as the unperturbed motion. In the classical theory of the Earth's rotation this angle is usually assumed to be zero. In the last 20 years, accuracy to determine the Earth rotation parameters owing to using methods of space geodesy and method of Very Long Baseline Interferometry (VLBI) has increased by about three orders of magnitude and has made about  i.e., in angle measure it is about 10 - 20 arc-microseconds. According to experts, the theory of the Earth's rotation with such precision is not created yet. The paper is focused just on the new dynamic studies of the Earth rotation at a higher level of accuracy than has been done in previous studies, using a new approach to the problem, based on the new forms of the equations of motion (in the Andoyer variables) and the analytical methods of perturbation theory (small parameter method). The problem of perturbed rotational motion with variable geometry and variable mass relative angular momentum in the first approximation is solved in Andoyer variables and projections of the angular velocity of the planet rotation. The analytical solution allows us to run applications to study dynamic effects from above factors for various bodies in the solar system, including the Earth. The solution allowed us to obtain the following parameters of the fundamental effects in the Earth's rotation: the annual and semi-annual fluctuations of the axis pole of Earth's rotation, annual and semiannual variations in the axial Earth's rotation. The theoretical values of the parameters are in good agreement with modern observation data of the Earth's rotation and the cyclical variations in the geo-potential coefficients.