The Perturbed Rotational Motion Equations of a Celestial Body with Variable Mass Geometry in Andoyer’s Variables

• Main Author: M. Yu. Barkin
• Format: Article
• Language: Russian
• Published: MGTU im. N.È. Baumana 2017-01-01
• Series: Matematika i Matematičeskoe Modelirovanie
• Subjects: andoyer variables; liouville problem; euler angles; earth; weakly deformed body
• Online Access: https://www.mathmelpub.ru/jour/article/view/50

The paper deals with deriving the rotational motion equations of the lightly deformed planet (Earth) with variable geometry of mass in canonical Andoyer’s variables (a Liouville problem). Presents a new method developed to study the rotational motion of the lightly deformed body with dynamic structure being close to the axially symmetric one and provides the applications to explore the Earth's pole motion. A characteristic feature of the model is a conical motion of the rate vector in the planet body with a constant specified initial value of the semi-opening angle . Classical papers, which investigate a disturbed motion of the Earth pole, usually, assume a polar axis of inertia instead of the specified cone (with ). Thus, we have obtained a new form of the motion equations to solve the Liouville problem in canonical Andoyer’s variables. Their right-hand side is expressed directly through the time variations of geo-potential coefficients and the components of a kinetic moment vector of the relative particles motion of the variable Earth.Using the motion equations in Andoyer’s variables opens up new opportunities for researchers of the perturbed rotational motions of the celestial bodies with variable geometry of mass. The developed approach allows direct use of space geodesy data on variations in the geometry of the Earth's mass directly from the observed variations in the geo-potential coefficients. These observation data are perpetually enriched. Thus, methods of space geodesy and research methods of perturbed motions of the Earth pole and variations of its axis of rotation act as a single tandem and allow us to obtain new results. In the first place, these results are of interest to study how redistribution of the celestial body mass impacts on the motion of their poles and on the daily axial rotation.The obtained results are of important interest for research in celestial mechanics and geodynamics. The perturbation theory of rotational motion of a celestial body contains effects that have been never described. They allow us to discover new effects in the pole motion and daily rotation not only of the Earth, but also of other planets and asteroids.