ИСТИНА

It is known from everyday experience that an inverted pendulum is unstable. The same observation is also valid for the pendulum suspended to the Moon. However, for a "very, very long" pendulum it is not the case: if the pendulum length exceeds certain value, then the pendulum extended along the Earth - Moon straight line is stable in sense of Lyapunov. It means, that there exist other, unstable equilibria in the Earth - Moon orbital plane. It turns out, that there exist also equilibria located outside the orbital plane. These equilibria were verified to be unstable in the secular sense. The necessary conditions of spatial stability for librations/rotations of the Lunar pendulum moving in the orbital plane are also under investigation. An alternation of stable and unstable motions depending on libration amplitude or angular velocity of rotation was found numerically. Similar alternation of stability for the satellite in the circular orbit planar oscillations is well known (Markeev, Sidorenko \& Neustadt).