Analysis of the process of deployment of a lunar tether system taking into account the Earth's gravity

The development of space transport systems for the delivery of payloads and the study of the lunar surface is an important scientific and technical challenge. The article considers a near-lunar space tether system consisting of a station and a microsatellite. The station is considered as a rigid body having a cylindrical shape, and the microsatellite is considered as a spherical rigid body. The tether is considered as a weightless inextensible rod of variable length. The station moves in a near-lunar orbit, which is influenced by the Earth's gravity. The process of deployment of a radially directed near-lunar tether system is considered. The equations of motion of the space tether system are obtained using Newton's second law and the theorem on the change in the angular momentum. To release the tether and bring the orbital tether system to a working state, the article proposes to use the control program of tethers tension force, which ensures the deployment of the tether system to a position close to the vertical. A comparison of the motion of the tether system along the unperturbed lunar orbit and along the perturbed one, taking into account the gravitational influence of the Earth, is made. To substantiate the theoretical results, a numerical simulation was carried out, based on the results of which a conclusion was made about the influence of the Earth's gravity on the amplitude of oscillations of the microsatellite relative to the local vertical.

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.

Feed-forward control of total retrieval of the space tether from vertical position

This paper presents the results of studies of the feasibility of total and safe retrieval of a space tether of two bodies connected by an elastic, massless cable. The purpose of the research is to build up the control for the mode of the total and safe retrieval of the tether, which is one of the basic modes of its functioning. It allowed the development of the feed-forward control of the tether length or tension that provides demanded change of the angular momentum of the tether under the effect of the gravitational torque. The novelty of the research results consists also in the novel approach to the control of underactuated mechanical systems, which have the number of the control channels less than their degrees of freedom. Here the constraints on the tether angular motion relative to the pitch axis are introduced. They reduce the number of the system degrees of freedom and allow realizing the necessary mode of motion. For this control, only the remaining degree of freedom is used. The numerical simulation of the effect of the mode parameters on the tether motion is carried out for the tether in the chosen ranges of the parameters. The numerical example demonstrates the simplicity of the application of the method in practice. Plots illustrate the analysis of the results.

Control for the Space Tether System Motion

This paper proposed a study of a spatial tether system (STS), composed by two satellite (a main satellite and a subsatellite), with the objective of developing a control system in which the motion of the subsatellite is limited in the orbital plane of the main satellite. The linear quadratic regulator (LQR) method is used to implement this control, which is an optimal control with state feedback to predict the linearization of the equations of motion to calculate the feedback gain, using the resolution of Riccati equation. The results show an effective control, with the motion of the subsatellite limited only to the stretch of the cable that links both satellites. However, it is necessary to introduce an auxiliary torque, since the linearized equation associated with the second variation of the angle out of the plan does not have a term independent of the state vector.