The rolling ball problem on the plane revisited

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dc.contributor.authorBiscolla, Laura M. O. [UNESP]
dc.contributor.authorLlibre, Jaume
dc.contributor.authorOliva, Waldyr M.
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionUniv Sao Judas Tadeu
dc.contributor.institutionUniv Autonoma Barcelona
dc.contributor.institutionUniv Tecn Lisboa
dc.contributor.institutionUniversidade de São Paulo (USP)
dc.date.accessioned2014-12-03T13:09:01Z
dc.date.available2014-12-03T13:09:01Z
dc.date.issued2013-08-01
dc.description.abstractBy a sequence of rollings without slipping or twisting along segments of a straight line of the plane, a spherical ball of unit radius has to be transferred from an initial state to an arbitrary final state taking into account the orientation of the ball. We provide a new proof that with at most 3 moves, we can go from a given initial state to an arbitrary final state. The first proof of this result is due to Hammersley ( 1983). His proof is more algebraic than ours which is more geometric. We also showed that generically no one of the three moves, in any elimination of the spin discrepancy, may have length equal to an integral multiple of 2 pi.en
dc.description.affiliationUniv Estadual Paulista, BR-04026002 Sao Paulo, Brazil
dc.description.affiliationUniv Sao Judas Tadeu, BR-03166000 Sao Paulo, Brazil
dc.description.affiliationUniv Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain
dc.description.affiliationUniv Tecn Lisboa, CAMGSD, ISR, Inst Super Tecn, P-1049001 Lisbon, Portugal
dc.description.affiliationUniv Sao Paulo, Dept Matemat Aplicada, Inst Matemat & Estat, BR-05508900 Sao Paulo, Brazil
dc.description.affiliationUnespUniv Estadual Paulista, BR-04026002 Sao Paulo, Brazil
dc.description.sponsorshipMICINN/FEDER
dc.description.sponsorshipAGAUR
dc.description.sponsorshipICREA Academia
dc.description.sponsorshipFCT (Portugal)
dc.description.sponsorshipIdMICINN/FEDERMTM 2008-03437
dc.description.sponsorshipIdAGAUR2009SGR 410
dc.description.sponsorshipIdFCT (Portugal)POC-TI/FEDER
dc.description.sponsorshipIdFCT (Portugal)PDCT/MAT/56476/2004
dc.format.extent991-1003
dc.identifierhttp://dx.doi.org/10.1007/s00033-012-0279-8
dc.identifier.citationZeitschrift Fur Angewandte Mathematik Und Physik. Basel: Springer Basel Ag, v. 64, n. 4, p. 991-1003, 2013.
dc.identifier.doi10.1007/s00033-012-0279-8
dc.identifier.issn0044-2275
dc.identifier.urihttp://hdl.handle.net/11449/111838
dc.identifier.wosWOS:000321977600006
dc.language.isoeng
dc.publisherSpringer
dc.relation.ispartofZeitschrift fur Angewandte Mathematik und Physik
dc.relation.ispartofjcr1.711
dc.relation.ispartofsjr0,828
dc.rights.accessRightsAcesso restrito
dc.sourceWeb of Science
dc.subjectControl theoryen
dc.subjectRolling ballen
dc.subjectKendall problemen
dc.subjectHammersley problemen
dc.titleThe rolling ball problem on the plane revisiteden
dc.typeArtigo
dcterms.licensehttp://www.springer.com/open+access/authors+rights?SGWID=0-176704-12-683201-0
dcterms.rightsHolderSpringer
unesp.author.orcid0000-0002-7292-0231[3]
unesp.author.orcid0000-0002-9511-5999[2]

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