Abstract:
Let us consider the motion of a planar (inverted) pendulum in the
presence of a horizontal force, which is not assumed to be bounded
(its magnitude can be arbitrarily large as time tends to infinity). Is
it true that, for any such force, there exists an initial position of
the pendulum such that, being released with zero initial velocity from
this position, the pendulum never falls? If this external force is
periodic, is it true that there exists a periodic non-falling
solution? Do similar statements hold for a spherical inverted
pendulum? We will answer these and a number of other questions in our
talk.
