Abstract:
In the talk, we will discuss some general properties of the vector
field of an inverted pendulum with a horizontally moving pivot point and
will show how these properties can be used to prove the existence of a
forced oscillation in the system and to explain the impossibility of
global stabilization of the pendulum in the vertical upward position. We
will also spend some time discussing further generalizations of the
considered methods and ideas. For instance, similarly to the case of one
inverted pendulum, it can be shown that there exists a forced
oscillation in the system of a chain of strongly coupled pendulums with
non-local interaction in a periodic field.
