Эволюция вращательного движения спутника с гибкими вязкоупругими стержнями на эллиптической орбите

Abstract

The rotational motion of an artificial satellite in the central Newtonian force field is investigated. The satellite is modeled as a symmetric solid with rigid viscoelastic rods rigidly attached along the symmetry axis and with a spherical inertia tensor. A limited statement of the problem is considered: the center of mass of the satellite moves along a given Keplerian elliptic orbit. As is known, some artificial Earth satellites (AES) have whip radio antennas for a length of hundreds of meters. The problem considered in this paper is a model for studying the rotational motion of this type of satellites. To solve this problem, the method of separation of motions and averaging is used for mechanical systems with an infinite number of degrees of freedom. We obtain an averaged system of differential equations in the Andoyer variables, which describes the evolution of the satellite's rotational motion. Partial solutions of the evolutionary system of the equations are found. For each such class of solutions phase portraits are built. It is shown that in the process of dissipative evolution caused by energy dissipation in rods, the angle between the vector of the angular momentum of the satellite's rotational motion and the normal to the orbital plane decreases to zero. Besides, new classes of stationary motions are found: the axis of symmetry of the satellite makes an arbitrary angle with the normal to the orbit plane, or the module of the angular velocity of the satellite rotation does not depend on the orbital angular velocity of the radius vector of its center of mass.