테더가 있는 인공위성의 동적 분석

Abstract

In this study, the dynamic behavior of three-body tethered satellite system with moving mass and deployment of tether are analyzed. The previous studies neglected the variation of orbital radius of system because they assumed that the mass center of system is always in circular orbit. However, the movement of mass center, deploying ratio of tether and orbit eccentricity make change the center of mass. Thus, present study considering the orbital radius is more accurate than previous studies. In addition, the equations of motion of three-body tethered satellites system derived from two dynamic models. One is two tethers are dependent case and the other model is described tethered system deploying two tethers independently. Furthermore, I can derive the equations of gravity-gradient force and calculate the tension of tether with time variation when the satellite system performs the deployment and retrieval of tether. First of all, this paper presents dynamic analysis of a tethered satellite system with a moving mass. A dynamic model with four degrees of freedom, i.e., a two-piece dumbbell model, is established for tethered satellites conveying a mass between them along the tether length. This model includes two satellites and a moving mass, treated as particles in a single orbital plane, which are connected by massless, straight tethers. The equations of motion are derived by using Lagrange’s equations. From the equations of motion, the dynamic response of the system when the moving mass travels along the tether connecting the two satellites is computed and analyzed. I investigate the global tendencies of the libration angle difference (between the two sections of tether) with respect to the changes in the system parameters, such as the initial libration angle, size (i.e. mass) of the moving mass, velocity of the moving mass, and tether length. I also present an elliptic orbit case and show that the libration angles and their difference increase as orbital eccentricity increases. Finally, our results show that a one-piece dumbbell model is qualitatively valid for studying the system under certain conditions, such as when the initial libration angles, moving mass velocity and moving mass size are small, the tether length is large, and the mass ratio of the two satellites is large. Next, this paper discusses a dynamic behavior of three-body tethered satellites system with deploying and retrieval. A dynamic model with six degrees of freedom, i.e., a three-body dumbbell model, is constructed for tethered satellites having the deployment and retrieval of tether. This model includes three satellites, treated as particles in-plane orbital plane, which are consisted with two massless, straight tethers. The equations of motion are derived by applying Lagrange’s equations. From the dynamic equations, the dynamic behaviors of the system when the tether length increases and decreases are computed and analyzed. I investigate the configuration analysis for four initial configuration cases with constant and deploying tether. I also examine the dynamic responses of in-plane libration and tension varying the masses of satellites, mass ratio of satellites and orbital eccentricity. Finally, our results present that the three-body tethered satellites system is stabilized as tether is deployed. However, the three-body system goes to unstable when tether has retrieval.