On the regularization of impact without collision: the Painlevé paradox and compliance
We consider the problem of a rigid body, subject to a unilateral constraint, in the presence of Coulomb friction. We regularize the problem by assuming compliance (with both stiffness and damping) at the point of contact, for a general class of normal reaction forces. Using a rigorous mathematical a...
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| Veröffentlicht in: | Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2017-06, Vol.473 (2202), p.20160773-20160773 |
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| container_end_page | 20160773 |
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| container_issue | 2202 |
| container_start_page | 20160773 |
| container_title | Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences |
| container_volume | 473 |
| creator | Hogan, S. J. Kristiansen, K. Uldall |
| description | We consider the problem of a rigid body, subject to a unilateral constraint, in the presence of Coulomb friction. We regularize the problem by assuming compliance (with both stiffness and damping) at the point of contact, for a general class of normal reaction forces. Using a rigorous mathematical approach, we recover impact without collision (IWC) in both the inconsistent and the indeterminate Painlevé paradoxes, in the latter case giving an exact formula for conditions that separate IWC and lift-off. We solve the problem for arbitrary values of the compliance damping and give explicit asymptotic expressions in the limiting cases of small and large damping, all for a large class of rigid bodies. |
| doi_str_mv | 10.1098/rspa.2016.0773 |
| format | Article |
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J. ; Kristiansen, K. Uldall</creator><creatorcontrib>Hogan, S. J. ; Kristiansen, K. Uldall</creatorcontrib><description>We consider the problem of a rigid body, subject to a unilateral constraint, in the presence of Coulomb friction. We regularize the problem by assuming compliance (with both stiffness and damping) at the point of contact, for a general class of normal reaction forces. Using a rigorous mathematical approach, we recover impact without collision (IWC) in both the inconsistent and the indeterminate Painlevé paradoxes, in the latter case giving an exact formula for conditions that separate IWC and lift-off. We solve the problem for arbitrary values of the compliance damping and give explicit asymptotic expressions in the limiting cases of small and large damping, all for a large class of rigid bodies.</description><edition>Royal Society (Great Britain)</edition><identifier>ISSN: 1364-5021</identifier><identifier>EISSN: 1471-2946</identifier><identifier>DOI: 10.1098/rspa.2016.0773</identifier><identifier>PMID: 28690403</identifier><language>eng</language><publisher>England: The Royal Society Publishing</publisher><subject>Compliance ; Coulomb friction ; Damping ; Impact Without Collision ; Painlevé Paradox ; Paradoxes ; Regularization ; Rigid structures ; Rigid-body dynamics ; Stiffness</subject><ispartof>Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, 2017-06, Vol.473 (2202), p.20160773-20160773</ispartof><rights>2017 The Authors.</rights><rights>Copyright The Royal Society Publishing Jun 2017</rights><rights>2017 The Authors. 2017</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c462t-a5cc2110108b36f97c4e1b0a079760582528981783d657d08b789db4cb9b6dcf3</citedby><cites>FETCH-LOGICAL-c462t-a5cc2110108b36f97c4e1b0a079760582528981783d657d08b789db4cb9b6dcf3</cites><orcidid>0000-0001-6012-6527</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,27923,27924</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/28690403$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Hogan, S. 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We solve the problem for arbitrary values of the compliance damping and give explicit asymptotic expressions in the limiting cases of small and large damping, all for a large class of rigid bodies.</description><subject>Compliance</subject><subject>Coulomb friction</subject><subject>Damping</subject><subject>Impact Without Collision</subject><subject>Painlevé Paradox</subject><subject>Paradoxes</subject><subject>Regularization</subject><subject>Rigid structures</subject><subject>Rigid-body dynamics</subject><subject>Stiffness</subject><issn>1364-5021</issn><issn>1471-2946</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNptkU1rFTEUhoMotla3LmXAjZu5nkwy-XAhSPELCnWhuAyZTKY3JZOMSaZ6_Uf-Dv-Yud5aqrhK4Dx53xwehB5j2GCQ4nnKi950gNkGOCd30DGmHLedpOxuvRNG2x46fIQe5HwJALIX_D466gSTQIEco8_noSlb2yR7sXqd3HddXAxNnBo3L9qU5qsr27iWxkTvXa6zF7_5D9oFb69-_mgWnfQYvzU6jBWaF-90MPYhujdpn-2j6_MEfXrz-uPpu_bs_O3701dnraGsK63ujekwBgxiIGyS3FCLB9DAJWfQi67vhBSYCzKyno-V4kKOAzWDHNhoJnKCXh5yl3WY7WhsKEl7tSQ367RTUTv19yS4rbqIV6qnkkiKa8Cz64AUv6w2FzW7bKz3Oti4ZoUl5qx2A1T06T_oZVxTqOtVSlAiKOtlpTYHyqSYc7LTzWcwqL0ztXem9s7U3ll98OT2Cjf4H0kVIAcgxV0ti8bZsrvV_f_YX8QKpXM</recordid><startdate>20170601</startdate><enddate>20170601</enddate><creator>Hogan, S. 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Uldall</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c462t-a5cc2110108b36f97c4e1b0a079760582528981783d657d08b789db4cb9b6dcf3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Compliance</topic><topic>Coulomb friction</topic><topic>Damping</topic><topic>Impact Without Collision</topic><topic>Painlevé Paradox</topic><topic>Paradoxes</topic><topic>Regularization</topic><topic>Rigid structures</topic><topic>Rigid-body dynamics</topic><topic>Stiffness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hogan, S. J.</creatorcontrib><creatorcontrib>Kristiansen, K. Uldall</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><collection>PubMed Central (Full Participant titles)</collection><jtitle>Proceedings of the Royal Society. 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| ispartof | Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, 2017-06, Vol.473 (2202), p.20160773-20160773 |
| issn | 1364-5021 1471-2946 |
| language | eng |
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| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; Alma/SFX Local Collection |
| subjects | Compliance Coulomb friction Damping Impact Without Collision Painlevé Paradox Paradoxes Regularization Rigid structures Rigid-body dynamics Stiffness |
| title | On the regularization of impact without collision: the Painlevé paradox and compliance |
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