Stability and control of transversal oscillations of a tethered satellite system

The tethered satellite system is characterized by weak nonlinearities but it practically works in conditions of internal resonance which produces unstable oscillations. The effect of a longitudinal control force is investigated. Since the displacement component in the orbit plane is always present in the motion due to the nonlinear coupling, the control force is assumed depending only on this component and also when a prevailing out-of-plane oscillation is considered. The harmonic balance method and numerical solutions of amplitude modulated equations are used to obtain stationary and nonstationary oscillations, respectively; the Floquet theory is followed in the stability analysis. The assumed control force is shown to be effective in reducing the primary and secondary instability regions of oscillations perturbed by internally resonant disturbance components.

[1]  Darryll J. Pines,et al.  Two Nonlinear Control Approaches for Retrieval of a Thrusting Tethered Subsatellite , 1990 .

[2]  V. J. Modi,et al.  A general dynamical model for the Space Shuttle based tethered subsatellite system , 1980 .

[3]  Wilhelm Dipl.-Ing. Dr. techn Schneider,et al.  Trends in applications of mathematics to mechanics , 1991 .

[4]  Liu Liangdong,et al.  Effect of tether flexibility on the tethered Shuttle subsatellite stability and control , 1989 .

[5]  Vimal Singh,et al.  Perturbation methods , 1991 .

[6]  V. V. Beletskii,et al.  Dynamics of the orbital cable system , 1983 .

[7]  Vinod J. Modi,et al.  On the control of the space shuttle based tethered systems , 1982 .

[8]  Noel C. Perkins,et al.  Three-dimensional oscillations of suspended cables involving simultaneous internal resonances , 1995, Nonlinear Dynamics.

[9]  P. M. Ku.  ASME winter annual meeting , 1978 .

[10]  A. Luongo,et al.  NON-LINEAR FREE PERIODIC OSCILLATIONS OF A TETHERED SATELLITE SYSTEM , 1994 .

[11]  One-to-one autoparametric resonances in infinitely long cylindrical shells , 1990 .

[12]  Ali H. Nayfeh,et al.  Modal Interactions in Dynamical and Structural Systems , 1989 .

[13]  Angelo Luongo,et al.  Three-dimensional vibrations of tethered satellite systems , 1991 .

[14]  A. H. Von Flotow.  Some approximations for the dynamics of spacecraft tethers , 1988 .

[15]  A. K. Bajaj,et al.  On the amplitude dynamics and crisis in resonant motion of stretched strings , 1992, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.