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We propose geometric tools that are suitable for studying the behavior of abilliard trajectory in a homogeneous force field. Two examples are considered:a vertical plane with an open top and with a parabolic or right angle boundaryat the bottom. In either case, we obtain equations that describe the envelopeof a trajectory. These equations are in good agreement with those found earlierwith the use of other calculation methods. In addition, we present some newgeometric properties of trajectories. We show that in the case of a parabolicboundary the sequence of the trajectory impact points can be easily constructedby multiple reflections of a single ellipse.

Billiards in a gravitational field: A particle bouncing on a parabolic and right angle mirror