Method for judging on-orbit tethered satellite chaos caused by radial micro-amplitude oscillation of elastic tether

The invention discloses a method for judging in-orbit tethered satellite chaos caused by a radial micro-amplitude of an elastic tether. The method comprises the following steps: (1) finding an unstable saddle point and heteroclinic orbits of a tethered satellite system from an undisturbed system by converting a kinetic equation of the tethered satellite system under radial micro-amplitude oscillation of a tether into a state equation form; (2) judging whether the tethered satellite system has a cross-section heteroclinic point generated by cross-section intersection of the heteroclinic orbits under perturbations or not through a Melnikov method; and (3) if the cross-section heteroclinic point exists, judging that chaotic behaviors exist. According to the method, the kinetic equation capable of describing influences of the radial micro-amplitude oscillation of the elastic tether on the on-orbit two-body tethered satellite system can be constructed, and whether the micro-amplitude oscillation can cause chaos of