Evolution of motions in a resistive medium of a body with a movable mass

Abstract

The problem of a rigid body motion about a fixed point is one of the classical problems of mechanics. The interest in the problem of the rigid body dynamics has increased in the second half of the XX century in connection with the development or rocket and space technologies. The study of the motion of a satellite about center of mass is important for creating systems of orientation control, stabilization of motion and for solving the practical problems of astronautics. The paper develops an approximate solution by means of an averaging method for the motion in a resistive medium of a nearly dynamically spherical rigid body containing a viscoelastic element. The numerical integration of the averaged system of equations is conducted for the body motion. The graphical presentations of the solutions are represented and discussed. We received the system of motion equations in standard form, which refined in square approximation by small parameter. The asymptotic approach permits to obtain some qualitative results and to describe evolution of rigid body motion using simplified averaged equations and numerical solution. The paper can be considered as mainstreaming of previous works for the problem of rigid body motion under the action of small torques (cavity filled with a fluid of high viscosity, moving mass, constant body-fixed torques). The advantage of this work is in receiving the original asymptotic and numerical calculations, as well as solutions that describe the evolution of rigid body motion with a moving mass in a resistive medium over an infinite time interval with an asymptotically small error. The paper presents a contribution in the problems of spacecraft motion, and the activities of crew members about the vehicles. The importance of the results is in the moving mass control, and the motions of spinning projectiles.