Escape distribution for an inclined billiard

TL;DR

This paper derives an analytical escape distribution for h-orbits in an inclined billiard model, enhancing understanding of chaotic scattering phenomena relevant to satellite encounters and Hill's problem.

Contribution

It provides the first analytical expression for the escape distribution of h-orbits in an inclined billiard, complementing previous numerical studies.

Findings

Analytical escape distribution derived for h-orbits.

Comparison confirms analytical results match numerical simulations.

Discussion on applications to Hill's problem and chaotic scattering.

Abstract

H${\acute{e}}$non [8] used an inclined billiard to investigate aspects of chaotic scattering which occur in satellite encounters and in other situations. His model consisted of a piecewise mapping which described the motion of a point particle bouncing elastically on two disks. A one parameter family of orbits, named h-orbits, was obtained by starting the particle at rest from a given height. We obtain an analytical expression for the escape distribution of the h-orbits, which is also compared with results from numerical simulations. Finally, some discussion is made about possible applications of the h-orbits in connection with Hill's problem.