{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:31:12Z","timestamp":1787232672425,"version":"build-2736575974"},"reference-count":17,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>We study the dynamics of an extremely idealized model of a planetary ring. In particular, we study the motion of an infinitesimal particle moving under the gravitational influence of a large central body and a regular n-gon of smaller bodies as n tends to infinity. Our goal is to gain insight into the structure of thin, isolated rings.<\/jats:p>","DOI":"10.1137\/090771582","type":"journal-article","created":{"date-parts":[[2010,6,9]],"date-time":"2010-06-09T18:05:21Z","timestamp":1276106721000},"page":"634-658","source":"Crossref","is-referenced-by-count":5,"title":["A Limit Case of the \u201cRing Problem\u201d: The Planar Circular Restricted $1+n$ Body Problem"],"prefix":"10.1137","volume":"9","author":[{"given":"E.","family":"Barrab\u00e9s","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J. M.","family":"Cors","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"G. R.","family":"Hall","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,6,9]]},"reference":[{"key":"R1","unstructured":"E. Barrab\u00e9s, J. M. Cors, and G. R. Hall,\n                      Numerical Exploration of the Limit Ring Problem\n                      , preprint, 2009."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1038\/25684"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1023\/B:CELE.0000043569.25307.ab"},{"key":"R4","unstructured":"A. M. Fridman and N. N. Gorkavyi,\n                      Physics of Planetary Rings: Celestial Mechanics of Continuous Media\n                      , Springer-Verlag, New York, 1994."},{"key":"R5","unstructured":"G. R. Hall,\n                      Central Configurations in the Planar $1+n$ Body Problem\n                      , preprint, 1988."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1023\/A:1001739018698"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/s10569-008-9149-2"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(85)90024-5"},{"key":"R9","unstructured":"L. Lovett, J. Horavath, and J. Cuzzi,\n                      Saturn: A New View\n                      , Harry N. Abrams, New York, 2006."},{"key":"R10","unstructured":"J. C. Maxwell,\n                      On the stability of the motion of Saturn's rings\n                      , in The Scientific Papers of James Clerk Maxwell, Cambridge University Press, Cambridge, UK, 1890, pp. 288\u2013376."},{"key":"R11","doi-asserted-by":"crossref","unstructured":"K. R. Meyer and G. R. Hall,\n                      \n                        Introduction to Hamiltonian Dynamical Systems and the\n                        N\n                        -Body Problem\n                      \n                      , Appl. Math. Sci. 90, Springer-Verlag, New York, 1992.","DOI":"10.1007\/978-1-4757-4073-8"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1007\/BF02219187"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"C. Murray and S. Dermott,\n                      Solar System Dynamics\n                      , Cambridge University Press, Cambridge, UK, 1999.","DOI":"10.1017\/CBO9781139174817"},{"key":"R14","unstructured":"G. E. Roberts,\n                      \n                        Existence and Stability for Relative Equilibria in the\n                        N\n                        -Body Problem\n                      \n                      , Ph.D. thesis, Boston University, Boston, MA, 1999."},{"key":"R15","doi-asserted-by":"crossref","unstructured":"G. E. Roberts,\n                      Linear stability in the $1+n$-gon relative equilibrium\n                      , in Hamiltonian Systems and Celestial Mechanics (P\u00e1tzcuaro, 1998), World Sci. Monogr. Ser. Math. 6, World Scientific Publishers, River Edge, NJ, 2000, pp. 303\u2013330.","DOI":"10.1142\/9789812792099_0018"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"D. G. Saari,\n                      \n                        Collisions, Rings, and Other Newtonian\n                        N\n                        -Body Problems\n                      \n                      , CBMS Regional Conf. Ser. in Math. 104, AMS, Providence, RI, 2005.","DOI":"10.1090\/cbms\/104"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(99)00211-0"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/090771582","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:14:26Z","timestamp":1787231666000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/090771582"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":17,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/090771582"],"URL":"https:\/\/doi.org\/10.1137\/090771582","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}