تجزیه و تحلیل سیستم های ماهواره ای محدود شده - مورد دو بعدی و دینامیک منظم

The study on tethered satellite system (TSS) in two-dimensional in-planar motion is restricted in that the tether is assumed to be massless. The equations of motion are given in a spherical coordinate system to describe the magnitude (tether length) and direction angle of the position vector between the satellites. A length rate control algorithm is adopted, and the controlled motion of the directional angle by the algorithm will have a stable equilibrium state. The equilibrium state is a fixed point if the orbit of the base-satellite is circular, and a limit cycle if the orbit is elliptic. The value and stability of the equilibrium state are determined by the parameters of the control algorithm, and the bifurcation analysis is also given. Two typical TSS missions have been simulated.

The concept of a tethered satellite system (TSS) for space shuttle mission was put forward in 1974 [1]. According to this concept, a base-satellite and a subsatellite are connected by a flexible tether cable. The subsatellite can be deployed from the base-satellite through a tether reeling mechanism, be station-kept and retrieved back to the base-satellite. Many projects of using TSS in space concerning microgravity, atmospheric probe, spacecraft maneuver, electrodynamic tether, solar power station, etc., have been proposed since then [2], [3], [4] and [5]. In this connection, innumerable literature have been published to investigate the dynamics and control of TSS [6], [7], [8], [9], [10], [11] and [12]. Among them a very impressive job has been done by Beletsky and Levin [6], and Rupp has proposed a valuable tether tension control law [7], Ivanov and Sitarsky gave very interesting treatment of the dynamics of TSS, based on the qualitative methods of the nonlinear differential equations [8]. The world is witness of the joint NASA-ASI project on TSS-1 which has been flown or to be reflown to verify the control techniques. A detailed analysis of TSS-1 is given in [9]. The space flights so far are mainly the flights of single spacecraft or of multiple spacecraft tightly docked together like the space stations. The flight of an ensemble of the soft connected spacecraft like TSS is perhaps the next step of space era. The dynamics of such flight is more complicated and has not been sufficiently investigated. Therefore, it should not be surprised that the first flight of TSS-1 was not successful. This paper is first of the three consecutive papers on TSS study by the author. The other two papers to be published are related to the chaotic dynamics in three-dimensional motion and the dynamics of massive tether system. The controlled motion of TSS is treated by using a single spherical coordinate system and an unique tether length rate control algorithm. Both nonlinear dynamic system theory and linearization techniques are extensively used in these papers to develop the methods and algorithms to analyze the dynamics and stability of TSS.

The analysis of the simplified model of TSS provides many important ideas such as the range rate control algorithm, regular dynamics of the fixed point and limit cycle in the controlled motion, iterative method of computing the limit cycle based on the linearization techniques, etc. The methodology adopted and the results obtained in this paper are insightful to the study of more complicated models and application of TSS; they are also helpful and, in some cases, completed for the research on two-satellite system motion such as the satellite rendezvous and group flight.