{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T13:26:45Z","timestamp":1778592405270,"version":"3.51.4"},"reference-count":63,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2012,11,1]],"date-time":"2012-11-01T00:00:00Z","timestamp":1351728000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p>Impact happens when two or more bodies collide, generating very large impulsive forces in a very short period of time during which kinetic energy is first absorbed and then released after some loss. This paper introduces a state transition diagram to model a frictionless multibody collision. Each state describes a different topology of the collision characterized by the set of instantaneously active contacts. A change of state happens when a contact disappears at the end of restitution, or when a disappeared contact reappears as the relative motion of two bodies goes from separation into penetration. Within a state, (normal) impulses are coupled differentially subject to relative stiffnesses at the active contact points and the strain energies stored there. Such coupling may cause restart of compression from restitution during a single impact. Impulses grow along a bounded curve with first-order continuity, and converge during the state transitions. To solve a multibody collision problem with friction and tangential compliance, the above impact model is integrated with a compliant impact model. The paper compares model predictions to a physical experiment for the mass\u00e9 shot, which is a difficult trick in billiards, with a good result.<\/jats:p>","DOI":"10.1177\/0278364912461539","type":"journal-article","created":{"date-parts":[[2012,11,2]],"date-time":"2012-11-02T02:32:09Z","timestamp":1351823529000},"page":"84-114","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":28,"title":["Multiple impacts: A state transition diagram approach"],"prefix":"10.1177","volume":"32","author":[{"given":"Yan-Bin","family":"Jia","sequence":"first","affiliation":[{"name":"Department of Computer Science, Iowa State University, Ames, IA, USA"}]},{"given":"Matthew T","family":"Mason","sequence":"additional","affiliation":[{"name":"School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, USA"}]},{"given":"Michael A","family":"Erdmann","sequence":"additional","affiliation":[{"name":"School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, USA"}]}],"member":"179","published-online":{"date-parts":[[2012,11,1]]},"reference":[{"key":"bibr1-0278364912461539","first-page":"1836","volume-title":"Proceedings of the MIT Conference on Computational Fluid and Solid Mechanics","author":"Acary V","year":"2003"},{"key":"bibr2-0278364912461539","volume-title":"Proceedings of the Fifth Euromech Nonlinear Dynamics Conference","author":"Acary V","year":"2005"},{"key":"bibr3-0278364912461539","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008292328909"},{"key":"bibr4-0278364912461539","doi-asserted-by":"publisher","DOI":"10.1080\/08905459608905271"},{"key":"bibr5-0278364912461539","doi-asserted-by":"publisher","DOI":"10.1007\/s10035-009-0161-3"},{"key":"bibr6-0278364912461539","doi-asserted-by":"publisher","DOI":"10.1007\/BF01891843"},{"key":"bibr7-0278364912461539","volume-title":"Die Werk von Jakob Bernoulli","author":"Bernoulli J","year":"1969"},{"key":"bibr8-0278364912461539","volume-title":"Mechanized Assembly: Fundamentals of Parts Feeding, Orientation, and Mechanized Assembly","author":"Boothroyd G","year":"1968"},{"key":"bibr9-0278364912461539","first-page":"325","volume":"77","author":"Boulanger G","year":"1939","journal-title":"Revue Scientifique"},{"key":"bibr10-0278364912461539","unstructured":"Brach RM (2007) Design of experiments and parametric sensitivity of planar impact mechanics. 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