Integrable billiards model important integrable cases of rigid body dynamics

Abstract—A generalized billiard is considered, in which a point moves on a locally flat surface obtained by isometrically gluing together several plane domains along boundaries being arcs of confocal quadrics. Under this motion, a point moves from one domain to another, passing through the glued boundaries. Many integrable cases of rigid body dynamics with appropriate parameter values at certain levels of integrals are modeled by classical or generalized billiards; in the paper, Liouville equivalence is proved by comparing Fomenko–Zieschang invariants.