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The system is equivalent to a billiard problem on a cylinder. It is shown that the system is integrable if and only if the body is a disk with its center of mass coincident with the geometric center. More specifically, for any other convex planar body with a smooth boundary, the existence of chaotic sets and Cantor circles on high-energy surfaces is proved. Additionally, the phenomenon of rigidity in more general rigid body impact systems is also discussed.<\/jats:p>","DOI":"10.1063\/5.0326314","type":"journal-article","created":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T12:51:45Z","timestamp":1783515105000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Integrability and chaos in the bouncing convex body model"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1332-7665","authenticated-orcid":false,"given":"Xiaoming","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mechanics and Aerospace Engineering, Southwest Jiaotong University , Chengdu, Sichuan 611756,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,7,8]]},"reference":[{"issue":"2","key":"2026070808513779100_c1","doi-asserted-by":"publisher","first-page":"025003","DOI":"10.1088\/1361-6544\/ad953b","article-title":"Time-dependent billiards, variational method, and invariant tori","volume":"38","year":"2025","journal-title":"Nonlinearity"},{"issue":"5369","key":"2026070808513779100_c2","doi-asserted-by":"publisher","first-page":"1556","DOI":"10.1126\/science.280.5369.1556","article-title":"High-power directional emission from microlasers with chaotic resonators","volume":"280","year":"1998","journal-title":"Science"},{"issue":"7299","key":"2026070808513779100_c3","doi-asserted-by":"publisher","first-page":"696","DOI":"10.1038\/465696a","article-title":"Chaotic billiard lasers","volume":"465","year":"2010","journal-title":"Nature"},{"issue":"2","key":"2026070808513779100_c4","doi-asserted-by":"publisher","first-page":"719","DOI":"10.1121\/1.2946714","article-title":"Application of Hamiltonian of ray motion to room acoustics","volume":"124","year":"2008","journal-title":"J. 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