Periodic Billiard Trajectories in Right Triangle

This paper is dedicated to periodic billiard trajectories in right triangles and right-angled tetrahedra. We construct a specific type of periodic trajectories and show that the trajectories of this type fill the right triangle entirely. Then we establish the instability of all known types of periodic trajectories in right triangles. Finally, some of these results are generalized to the $n$-dimensional case and are given a mechanical interpretation.