Bs. Bardin et Ap. Markeyev, THE STABILITY OF THE EQUILIBRIUM OF A PENDULUM FOR VERTICAL OSCILLATIONS OF THE POINT OF SUSPENSION, Journal of applied mathematics and mechanics, 59(6), 1995, pp. 879-886
The motion of a pendulum, the point of suspension of which is subject
to vertical harmonic oscillations of arbitrary frequency and amplitude
, is considered. A complete rigorous solution of the non-linear proble
m of the stability of the relative positions of equilibrium of the pen
dulum along the vertical is given.