Glashov, Sheldon Lee; Mittag, Laurence Three rods on a ring and the triangular billiard. (English) Zbl 0952.70501 J. Stat. Phys. 87, No. 3-4, 937-941 (1997). Summary: We demonstrate the equivalence of two seemingly disparate dynamical systems. One consists of three hard rods, sliding along a frictionless ring and making elastic collisions. The other consists of one ball moving on a frictionless triangular table with elastic rails. Several applications of this result are discussed. Cited in 7 Documents MSC: 70F99 Dynamics of a system of particles, including celestial mechanics 70F35 Collision of rigid or pseudo-rigid bodies 37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010) Keywords:billiards; hard rods; impact phenomena; tonks gas PDF BibTeX XML Cite \textit{S. L. Glashov} and \textit{L. Mittag}, J. Stat. Phys. 87, No. 3--4, 937--941 (1997; Zbl 0952.70501) Full Text: DOI References: [1] L. Onsager, Unpublished lectures, Yale University (1965); Ya. G. Sinai,Introduction to Ergodic Theory (Princeton University Press, Princeton, New Jersey, 1976). [2] S. Tabachnikov, Billiards: Panoramas and syntheses,Soc. Math. France (1995) · Zbl 0833.58001 [3] E. Gutkin, Biliards in polygons: Survey of recent results,J. Stat. Phys. 81:7 (1996). · Zbl 1081.37525 · doi:10.1007/BF02183637 [4] G. Galperin, T. Krüger, and S. Troubetskoy, Local instability of orbits in polygonal and polyhedral billiards,Commun. Math. Phys. 169:463 (1995). · Zbl 0924.58043 · doi:10.1007/BF02099308 [5] S. L. Glashow and L. Mittag,The Physics of Billiards. in preparation. [6] H. Masur, Closed trajectories for quadratic differentials with an application to billiards,Duke Math. J. 53:307 (1986); M. Boshernitzan, G. Galperin, T. Krüger, and S. Trobetsckoy, Periodic billiard orbits are dense in rational polygons, preprint (1996). · Zbl 0616.30044 · doi:10.1215/S0012-7094-86-05319-6 [7] S. Kerckhoff, H. Masur, and J. Smille, Ergodicity of biliard flows and quadratic differentials,Ann. Math. 124:293 (1986). · Zbl 0637.58010 · doi:10.2307/1971280 [8] C. Boldrighini, M. Keane, and F. Marchetti, Billiards in polygons.,Ann. Prob. 6:532 (1978). · Zbl 0377.28014 · doi:10.1214/aop/1176995475 [9] L. Tonks, The complete equation of state of one, two, and three dimensional gases of hard spheres,Phys. Rer. 50:955 (1936) see also D. W. Jepson, Dynamics of a simple manybody system of hard rods,J. Math. Phys. 6:405 (1965). · Zbl 0015.33503 · doi:10.1103/PhysRev.50.955 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.