  Wojtkowski's system of $N$, $N \geq 2$, falling balls is a nonuniformly
hyperbolic smooth dynamical system with singularities. It is still an open
question whether this system is ergodic. We contribute towards an affirmative
answer, by proving the non-contraction property, conditioned by the assumption
of strict unboundedness. For a certain mass ratio the configuration space can
be unfolded to a billiard table where the daunting proper alignment condition
is satisfied. We prove, that the aforementioned unfolded system with three
degrees of freedom is ergodic.
