No-slip billiards with particles of variable mass distribution

Astute variations in the geometry of mathematical billiard tables have been and continue to be a source of understanding their wide range of dynamical behaviors, from regular to chaotic. Viewing standard specular billiards in the broader setting of no-slip (or rough) collisions, we show that an equally rich spectrum of dynamics can be called forth by varying the mass distribution of the colliding particle. We look at three two-parameter families of billiards varying both the geometry of the table and the particle, including as special cases examples of standard billiards demonstrating dynamics from integrable to chaotic, and show that markedly divergent dynamics may arise by changing only the mass distribution. Furthermore, for certain parameters, billiards emerge, which display unusual dynamics, including examples of full measure periodic billiards, conjectured to be nonexistent for the standard billiards in Euclidean domains.

Automated summary

The geometry variations of mathematical billiard tables can result in various dynamical behaviors, and changing the mass distribution of the colliding particle can also lead to a rich spectrum of dynamics. The study explores different families of billiards with varying table geometry and particle, showing that divergent dynamics can arise solely from changes in mass distribution. Moreover, for certain parameters, billiards with unusual dynamics, including periodic billiards, are observed, which are conjectured to be nonexistent in standard billiards in Euclidean domains.