{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T09:53:35Z","timestamp":1772272415342,"version":"3.50.1"},"reference-count":6,"publisher":"American Association of Physics Teachers (AAPT)","issue":"8","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2007,8,1]]},"abstract":"<jats:p>The kinematics of a sphere of radius R and mass m bouncing elastically in a horizontal channel is studied in detail. Explicit expressions for the position and linear and angular velocities of the sphere at any collision are obtained. It is shown that if the moment of inertia I=\u03b3mR2 is such that (1\u2212\u03b3)\u2215(1+\u03b3)=cos2\u03c0\u2215k with k an integer and k\u22654, the motion is periodic, with repetition after k collisions for k even, and after 2k collisions for k odd. The motion of a homogeneous sphere (which is not periodic) is analyzed by investigating the mean properties of its velocities and positions. The analogy between this motion and that of a periodic oscillator is discussed.<\/jats:p>","DOI":"10.1119\/1.2742402","type":"journal-article","created":{"date-parts":[[2007,7,13]],"date-time":"2007-07-13T22:30:48Z","timestamp":1184365848000},"page":"690-695","update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["The elastic bounces of a sphere between two parallel walls"],"prefix":"10.1119","volume":"75","author":[{"given":"J. M.","family":"Tavares","sequence":"first","affiliation":[{"name":"Instituto Superior de Engenharia de Lisboa , Avenida Conselheiro Em\u00ed dio Navarro 1, 1959-007 Lisboa, Portugal"}]}],"member":"3","reference":[{"key":"2023080620590902800_c1","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1119\/1.1975420","article-title":"Kinematics of the ultraelastic rough ball","volume":"37","year":"1969","journal-title":"Am. J. Phys."},{"key":"2023080620590902800_c2","doi-asserted-by":"publisher","first-page":"834","DOI":"10.1119\/1.1975158","article-title":"Matrices and superballs","volume":"36","year":"1968","journal-title":"Am. J. Phys."},{"key":"2023080620590902800_c3","doi-asserted-by":"publisher","first-page":"875","DOI":"10.1119\/1.1701843","article-title":"The kinematics of a superball bouncing between two vertical surfaces","volume":"72","year":"2004","journal-title":"Am. J. Phys."},{"key":"2023080620590902800_c5","first-page":"36","volume-title":"Table of Integrals, Series, and Products","year":"1994","edition":"5th ed."},{"key":"2023080620590902800_c7","first-page":"42","volume-title":"The Physics of Vibrations and Waves","year":"1979","edition":"2nd ed."},{"key":"2023080620590902800_c8"}],"container-title":["American Journal of Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aapt\/ajp\/article-pdf\/75\/8\/690\/7532900\/690_1_online.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aapt\/ajp\/article-pdf\/75\/8\/690\/7532900\/690_1_online.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,6]],"date-time":"2023-08-06T20:59:18Z","timestamp":1691355558000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/ajp\/article\/75\/8\/690\/1042159\/The-elastic-bounces-of-a-sphere-between-two"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,8,1]]},"references-count":6,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2007,8,1]]}},"URL":"https:\/\/doi.org\/10.1119\/1.2742402","relation":{},"ISSN":["0002-9505","1943-2909"],"issn-type":[{"value":"0002-9505","type":"print"},{"value":"1943-2909","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2007,8]]},"published":{"date-parts":[[2007,8,1]]}}}