Deployment and stabilization of the motion of a space tethered system in a lunar orbit

The motion of a space tether system, consisting of a constellation of two microsatellites and a space station, is investigated. The station moves in a circular undisturbed circular lunar orbit. The process of deployment of tethers to bring the system into a working near-vertical condition is considered. A program for controlling the tether tension force that ensures the deployment of tethers to the required length and stabilizes the system in the vertical position is proposed. A study of the stability of the equilibrium position of a mechanical system is carried out. It is shown that the motion carried out during the deployment of a tethered system according to the program proposed in the work is asymptotically stable.

Hamiltonian formulation and energy-based control for space tethered system deployment and retrieval

Usually, the dynamic equations of tethered systems are derived using Lagrangian formulation. However, Hamiltonian formulation is also widely used for mechanical systems because of its well-known symplectic structure property. In this paper, the dynamic equations of the tethered system are deduced using Hamiltonian formulation. The goodness of the Hamiltonian formulation is intuitive to reveal the energy balance property that corresponds to the passive property. Furthermore, the Hamiltonian function of the tethered system is employed to facilitate the design of the controller. The energy-based control is to achieve the tether deployment/retrieval with suppressing the tether liberation. Numerical simulations are used to demonstrate the effectiveness of the designed controller.