On the instability of ?folded? equilibria of a flexible nonstretchable thread attached to the satellite in a circular orbit

Abstract

The author considers a problem of Lyapunov's stability of relative equilibria of a flexible nonstretchable thread attached to the satellite moving in a circular Keplerian orbit in the first approximation. When it is in the position of relative equilibrium, the thread is known to be situated either along the radius vector of the orbit (the “radial” equilibrium) or along the circular orbit (the “tangential” equilibrium) and in each case the thread can be in a “folded” state. The author shows that “folded radial” equilibria of the thread are always unstable while “tangential” ones are unstable if the thread is sufficiently short in comparison with the radius of the orbit. The generalized Chetaev functional has been constructed to prove the instability.