Rotation Formation Flying of Three Satellites Using Tethers

The feasibility of rotating formation flying of satellites using flexible tethers is explored. The system is composed of three satellites connected through tethers and located at the vertices of a triangle-like configuration. The satellites are modeled as point masses, and tethers are considered massless. The general formulation of the governing equations of motions of the system moving in an elliptic orbit and including different satellite masses and tether lengths is obtained through a Lagrangian approach. The open-loop tether deployment and retrieval laws have been developed. Results of numerical simulations of the nonlinear governing equations of motion of the proposed constrained system and an equilibrium analysis indicate the feasibility of achieving formation flying of three satellites in the orbital plane. Furthermore, the equilibrium analysis leads to useful design criteria in the form of inequality constraints on the system parameters. In the case when three satellites have equal masses, the critical minimum value of spin rate for system steady-spin motion in the orbital plane is found to be 0.58 times the orbital rate. Finally, the effects of various system parameters as well as the tether deployment and retrieval on the system response have been investigated.