{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:35:22Z","timestamp":1787236522946,"version":"build-2736575974"},"reference-count":26,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["1180288"],"award-info":[{"award-number":["1180288"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["233145\/2014-1"],"award-info":[{"award-number":["233145\/2014-1"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>The problem of attraction of an infinitesimal particle by the gravitational force induced by a massive body composed of a ring (in the form of a circle) of radius $a$ and a punctual body at the center of the ring is considered. We study the singularity problem of the solutions associated with this problem, and we prove that all the singularities are due to collision. In the planar equatorial case (the plane that contains the ring) we are able to prove that the reciprocal is true. Moreover, we observe that zero angular momentum is a necessary condition in order to have solutions that go or start in collision with the central body or with the ring. Still in the planar case, we give all the possible global phase portraits as a function of the angular momentum. More precisely, we show that inside the ring there are topologically four possible phase portraits according to the variation of the angular momentum, while outside the ring there are topologically five possible phase portraits according to the variation of the angular momentum.<\/jats:p>","DOI":"10.1137\/18m1179274","type":"journal-article","created":{"date-parts":[[2019,1,2]],"date-time":"2019-01-02T11:14:24Z","timestamp":1546427664000},"page":"1-32","source":"Crossref","is-referenced-by-count":3,"title":["Singularities and Dynamics Aspects of a Particle in a Gravitational Field of a Central Punctual Body Surrounded by a Solid Circular Ring"],"prefix":"10.1137","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5991-4208","authenticated-orcid":true,"given":"Angelo","family":"Alberti","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1630-0898","authenticated-orcid":true,"given":"Claudio","family":"Vidal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,1,2]]},"reference":[{"key":"atypb1","unstructured":"A. Alberti,\n                      Din\u00e2mica de uma part\u00edcula no potencial de um fio circular homog\u00eaneo\n                      , Master's thesis, Departamento de Matem\u00e1tica, UFPE, Recife, Brazil, 2003."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s10569-007-9071-z"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2010.26.805"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1515\/ans-2007-0103"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1070\/RD2005v010n02ABEH000307"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1088\/0143-0807\/30\/3\/019"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2011.05.019"},{"key":"atypb8","unstructured":"F. Diacu,\n                      Singularities of the N-body Problem. An Introduction to Celestial Mechanics\n                      , Universit\u00e9 de Montr\u00e9al, Centre de Recherches Math\u00e9matiques, Montreal, QC, 1992."},{"key":"atypb9","first-page":"435","volume":"3","author":"Elipe A.","year":"2003","journal-title":"Int. Math. J."},{"key":"atypb10","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1007\/BF03546290","volume":"51","author":"Elipe A.","year":"2003","journal-title":"J. Astronaut. Sci."},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/s11038-012-9391-1"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(91)90110-U"},{"key":"atypb13","doi-asserted-by":"crossref","unstructured":"O. Kellogg,\n                      Foundations of the Potential Theory\n                      , Dover, New York, 1929.","DOI":"10.1007\/978-3-642-90850-7"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.76.024018"},{"key":"atypb15","unstructured":"W. MacMillan,\n                      The Theory of the Potential\n                      , Dover, New York, 1958."},{"key":"atypb16","first-page":"99","volume":"40","author":"Neslus\u01cen L.","year":"2010","journal-title":"Contributions Astronom. Observatory Skalnat\u00e9 Pleso"},{"key":"atypb17","unstructured":"P. Painlev\u00e9,\n                      Le\\ccons sur la th\u00e9orie analytique des equations diff\u00e9rentielles\n                      , A. Hermann, Paris, 1897."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-2966.2011.18618.x"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008399030624"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/0094-5765(93)90137-L"},{"key":"atypb21","unstructured":"J. Sotomayor,\n                      Li\u00e7o\u0342es de equa\u00e7o\u0342es diferenciais ordin\u00e1rias\n                      , IMPA, R\u00edo de Janeiro, Brazil, 1979."},{"key":"atypb22","first-page":"645","volume":"225","author":"Tresaco E.","year":"2013","journal-title":"Appl. Math. Comput."},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1007\/s10569-011-9371-1"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1046\/j.1365-8711.1998.01564.x"},{"key":"atypb25","unstructured":"A. Wintner,\n                      The Analytical Foundations of Celestial Mechanics\n                      , Princeton Math. Ser. 5, Princeton University Press, Princeton, NJ, 1941."},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.2307\/2946572"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1179274","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:45:07Z","timestamp":1787233507000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1179274"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/18M1179274"],"URL":"https:\/\/doi.org\/10.1137\/18m1179274","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}