https://doi.org/10.1140/epjs/s11734-023-01022-0
Regular Article
Linear stability analysis in tether system using its Hamiltonian function
1
Aeronautical Engineering Department, São Paulo State University, UNESP-FESJ, Street, São João da Boa Vista, 1387, São Paulo, Brazil
2
Exact Sciences Department, Federal University of Paraíba, Rio Tinto, Paraíba, Brazil
3
Environmental Engineering Department, São Paulo State University, UNESP-ICT, São José dos Campos, São Paulo, Brazil
Received:
16
May
2023
Accepted:
9
November
2023
Published online:
8
December
2023
The aim of this work is to study the behavior of a tether system, which consists of two point masses connected each other by a cable, in a Keplerian orbit around a Newtonian center of attraction, with no external forces acting on the system. To do so, after some reductions in the equations of motion of the problem, an Hamiltonian function related to these equations is obtained. Four stationary solutions are found, two of them stable, in which we investigate the parametric linear stability, regarding the parameter of the eccentricity of the elliptical orbit, named e, and a parameter, called 
, related to the angle formed between the projection of the tether and the plane of the orbit. Using the Deprit–Hori method and numerical computations, we plot curves separating regions of stability and instability in the plane of parameters 
.
José Laudelino de Menezes Neto, Vinicius Tavares Azevedo and Jorge Kennety Silva Formiga have contributed equally to this work.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
