Linear stability analysis in tether system using its Hamiltonian function

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 α , 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 α× e .