Stabilization of periodic orbits in a wedge billiard

fixed angle θ with the direction of gravity. Rotational actuation of the edges around their fixed intersection point is used to stabilize one particular orbit of the uncontrolled system. When uncontrolled, the wedge billiard is a rich dynamical model leading to stabilization problems of various complexity. It was realized in [2], [6] that the wedge billiard displays a variety of dynamical phenomena as a function of the angle θ. For θ < 45◦, the phase space exhibits stable and chaotic behavior associated with periodic orbits of any period. For θ > 45◦, the motion appears completely chaotic. The value θ = 45◦ is very special and leads to a completely integrable system with a two-parameter family of unstable periodic orbits.