Investigation of stability in certain problems of non-linear mechanics

Abstract The generalized Liapunov second method /1/ is used to investigate the stability of resonance modes in a non-linear multifrequency system. The results are used to study the oscillations of a pendulum whose point of suspension performs small harmonic two-frequency motions in resonance with the natural oscillation of the pendulum and, also, the two-frequency problem of the motion of a satellite relative to the centre of mass. In estimating the small denominators in these problems no reduction to systems with a lower number of frequencies was achieved.