# Three-dimensional multi-tethered satellite formation with the elements moving along Lissajous curves

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## Abstract

This note presents a novel approach to maintain three-dimensional multi-tethered satellite formation in space. For a formation consisting of a main body connected by tethers with several deputy satellites (the so-called “hub-and-spoke” configuration) we demonstrate that under proper choice of the system’s parameters the deputy satellites can move along Lissajous curves in the plane normal to the local vertical with all tethers stretched; the total force due to the tension forces acting on the main satellite is balanced in a way allowing it to be in relative equilibrium strictly below or strictly above the system’s center of mass. We analyze relations between the system’s essential parameters and obtain conditions under which the proposed motion does take place. We also study analytically the motion stability for different configurations and whether the deputy satellites can collide or the tethers can entangle. Our theoretical findings are corroborated and validated by numerical experiments.

## Keywords

Tethered satellite system Hub-and-spoke configuration Perturbation theory Collision Tethers entanglement Stability## Notes

### Acknowledgments

The authors first conceived the idea of the motion described in this paper during the dynamical analysis of the rotating multi-tethered satellite system (Alary et al. 2015), and the authors sincerely thank their collaborators Didier Alary, Kirill Andreev, Pavel Boyko, Elena Ivanova, and Cyrille Tourneur for the warm and stimulating atmosphere of that study. The work of one of the authors (DY) on the present paper was supported by Russian Science Foundation (Project 14-50-00150).

## Supplementary material

Supplementary material 1 (avi 24262 KB)

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