Збурені рухи твердого тіла з рухомою масою в середовищі з опором

Abstract

Various cases of the rigid body motion having internal degrees of freedom was studied. In particular, the motions of a body carrying masses which are attached to it by means of elastic forces with linear damping was investigated. This situation simulates the presence of loosely fixed components on a spacecraft, having a significant influence on its motion about its center of mass. The development of research in dynamics of rigid body motions about its center of mass goes in the direction of taking into account the fact that these bodies are not perfectly rigid but are rather close to perfect models. The need for the analysis of the influence of various deviations from perfectness is caused by growing accuracy requirements in space exploration, gyroscopy, etc. The influence of imperfections can be revealed using asymptotic methods of nonlinear mechanics (averaging, singular perturbations and others). This influence reduces the additional terms in the Euler equations of motion of a fictitious rigid body. In the space flight, there arises sometimes a necessity to suppress the chaotic rotation that occurs for one reason to another. Тo this end, the relative displacements of movable masses are used. A number of works are devoted to the analysis of various problems of the dynamics of space vehicles containing internal masses. The issues of stability and instability and the problems of control and stabilization of motions have been studied. In [1, 6] vector equation which describes the change of vector in the system of coordinates connected with the body was obtained. Function in the right-hind side of this equation is a polynomial containing the fourth and fifth powers of . We study the problem of the motion in a resistive medium of a dynamically symmetric rigid body carrying a movable point mass, connected with the body by an elastic coupling in the presence of viscous friction. By means of asymptotic approach equations of motion of body with mass are simplified. Nonlinear evolution of angular motions of the body is analyzed using averaged equations and numerical integration. Results summed up in this paper make it possible to analyze angular motions of artificial satellites under the influence of small internal perturbation torques.