Trolleys have wheels which can choose the direction of their rolling. Studying the
motion of a wheel like this, we can often find periodic motions ('shimmy') or even
chaotic ones. It has also been experienced that the chaotic motions sometimes disappear
quite unexpectedly. A strongly simplified model of these systems is analysed in the
paper by means of the methods of bifurcation theory. Analytical and numerical results
are shown to characterize the system, including simulation results. Similar behaviour
can be found in more complicated systems as well, like the trailers or the nosegears
of aeroplanes. The development of the so-called transient chaotic motion is explained
in these systems.
