Abstract
This paper studies resonance motions of a tethered satellite system (TSS) in elliptical orbits. A perturbation analysis is carried out to obtain all possible resonance types and corresponding parameter relations, including internal resonances and parametrically excited resonances. Besides, a resonance parametric domain is given to provide a reference for the parameter design of the system. The bifurcation behaviors of the system under resonances are studied numerically. The results show that resonant cases more easily enter chaotic motion than nonresonant cases. The extended time-delay autosynchronization (ETDAS) method is applied to stabilize the chaotic motion to a periodic one. Stability analysis shows that the stable domains become smaller in resonance cases than in the nonresonance case. Finally, it is shown that the large amplitudes of periodic solutions under resonances are the main reason why the system is difficult to control.
Highlights
Tethered satellite system is a promising new type of spacecraft [1,2,3]
The researches on the dynamic behavior of the tethered satellite system under nonresonance mainly focus on the steady-state solutions and stabilities
The mass of the main satellite is assumed to be much greater than the mass of the subsatellite, such that the center of mass of the system can be assumed to coincide with the main satellite that moves in an unperturbed Kepler elliptical orbit of semimajor axis a and eccentricity ratio e
Summary
Tethered satellite system is a promising new type of spacecraft [1,2,3]. It has great potential in applications such as space debris capture [4], space elevator [5], and orbital transfer [6]. Takeichi et al [7] studied the periodic solution of the librational motion of a tethered system in elliptic orbit via the Lindstedt perturbation method. The same control method is employed by Peláez and Lorenzini [13] to control an electrodynamic tethered system in inclined orbit This control law does not stabilize the unstable periodic orbit for reasonable values of the control parameters. Additional, Kojima et al [16] applied a model-following, decoupling-control method combining with the delayed feedback control method in a new approach to control the librational motion of the tethered satellite system in elliptic orbits.
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