TITLE: Billiard dynamics under gravity
QUESTION [38 upvotes]: Has the dynamics of billiards in a polygon subject to gravity been
studied?
What I have in mind is something like this:

          


Still Snell's Law applies so the angle of incidence equals the
angle of reflection, and the collision is perfectly elastic,
but the path followed by the ball between
contacts is a parabola.
I am wondering if such a system can somehow be converted into one
without gravity, so that our understanding of, e.g., the dynamics of
billiards in a square may be applied.
To be specific:

What initial conditions lead to a periodic path in a square?

For example, suppose the square has corners $(0,0)$ and $(1,1)$.
Starting at $p_0=(0,\frac{1}{2})$, with
vertical velocity zero and horizontal velocity that first lands
the ball at $p_1=(\frac{1}{2},0)$
(say, $v_x=\frac{1}{2}$, gravity $=1$),
produces (I believe) a periodic path bouncing
between the three points $\{ p_0, p_1, p_2 \}$, where $p_2=(1,\frac{1}{2})$:

                    


I'd appreciate literature pointers—Thanks!

Addendum.
Following fedja's intriguing comment, here a path when gravity is tilted $30^\circ$:

REPLY [6 votes]: This problem is very similar to what is known in the physics literature (including in real atom-optics experiments) as the "wedge billiard."
Self-edit: Another comment -
Formulas for linear stability of billiards with potentials (such as gravity) are given in
Holger Dullin's paper here:

Holger R Dullin, "Linear stability in billiards with potential."
  Nonlinearity, Volume 11, Number 1,
  11, 151. 1998.
Abstract: A general formula for the linearized Poincaré map of a billiard with a potential is derived. ...