  In the paper we consider systems in oscillating force fields such that the
classical method of averaging can be applied. We present sufficient conditions
for the existence of forced oscillations in such systems and study the
asymptotic behaviour of some solutions. In particular, we show that for an
inverted pendulum with a horizontally moving pivot point in an oscillating
gravity field there exists a solution along which the pendulum never falls.

Dynamical Systems;Classical Analysis and ODEs