This paper analyzes the dynamical evolution of
satellites formed by two masses connected by a cable—
tethered satellites. We derive the Lagrangian equations of
motion in the neighborhood of the collinear equilibrium
points, especially for the L 2 , of the restricted problem of
three bodies. The rigid body configuration is expanded in
Legendre polynomials up to fourth degree. We present some
numerical simulations of the influence of the parameters
such as cable length, mass ratio and initial conditions in
the behavior of the tethered satellites. The equation for
the collinear equilibrium point is derived and numerically
solved. The evolution of the equilibria with the variation of
the cable length as a parameter is studied. We also present
a discussion of the linear stability around these equilibria.
Based on this analysis calculate some unstable Lyapunov
orbits associated to these equilibrium points. We found pe-
riodic orbits in which the tether travels parallel to itself
without involving the angular motion. The numerical appli-
cations are focused on the Earth–Moon system. However,
the general character of the equations allows applications to
the L 1 equilibrium and obviously to systems other than the
Earth–Moon.

EB00000003929K

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• Dynamics of tethered satellites in the vicinity of the Lagrangian point L 2 of the Earth–Moon system