The chaotic oscillations of the spacecraft with a vertical elastic tether

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 Lagranges 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.