Oscillations of a Spacecraft with a Vertical Elastic Tether

Abstract

The motion about a centre of mass of a spacecraft with a vertical elastic tethered system under the action of the gravitational moment and small periodic tethered force at a circular orbit is studied. The mathematical model is derived using Lagrange's equations including tether vibrations and oscillations of the spacecraft relatively of the proper mass center. The paper contains bifurcation analysis, phase space study, and analytic solutions for separatrixes. The considered mechanical system performs chaotic motion near separatrixes under the influence of small disturbances. The Melnikov method gives a criterion for homo/heteroclinic chaos in terms of system parameters. Results of the study can be useful for the analysis of gravitational stabilization systems with space tethers and for studying the behavior of a spacecraft with a deployed tether.

The effect of the elasticity of an orbital tether system on the oscillations of a satellite

“…8 On the other hand, an elastic tether also causes chaos in the case of the motion of a satellite in a circular orbit. 4 We note that Eq. (4.1) is an extension of the equation obtained earlier for an elastic tether (Ref.…”

Anti-sway control of tethered satellite systems using attitude control of the main satellite

“…In this model, satellites are free to undergo three dimensional attitude motions. In [26] oscillation of the main satellite due to tether is studied, but it is assumed that the mass of sub-satellite, i.e. the satellite which is attached to the main satellite through a tether, is negligible and center of gravity of the whole system is approximated with the center of gravity of the main satellite.…”