{"title":"非平面五体中心构型的非平面极限","authors":"Alain Albouy, Antonio Carlos Fernandes","doi":"10.1007/s00205-023-01949-7","DOIUrl":null,"url":null,"abstract":"<div><p>Moeckel (Math Z 205:499–517, 1990), Moeckel and Simó (SIAM J Math Anal 26:978–998, 1995) proved that, while continuously changing the masses, a 946-body planar central configuration bifurcates into a spatial central configuration. We show that this kind of bifurcation does not occur with 5 bodies. Question 17 in the list (Albouy et al. in Celest Mech Dyn Astr 113:369–375, 2012) is thus answered negatively.</p></div>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Limit of Nonplanar 5-Body Central Configurations is Nonplanar\",\"authors\":\"Alain Albouy, Antonio Carlos Fernandes\",\"doi\":\"10.1007/s00205-023-01949-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Moeckel (Math Z 205:499–517, 1990), Moeckel and Simó (SIAM J Math Anal 26:978–998, 1995) proved that, while continuously changing the masses, a 946-body planar central configuration bifurcates into a spatial central configuration. We show that this kind of bifurcation does not occur with 5 bodies. Question 17 in the list (Albouy et al. in Celest Mech Dyn Astr 113:369–375, 2012) is thus answered negatively.</p></div>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-01-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00205-023-01949-7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00205-023-01949-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
A Limit of Nonplanar 5-Body Central Configurations is Nonplanar
Moeckel (Math Z 205:499–517, 1990), Moeckel and Simó (SIAM J Math Anal 26:978–998, 1995) proved that, while continuously changing the masses, a 946-body planar central configuration bifurcates into a spatial central configuration. We show that this kind of bifurcation does not occur with 5 bodies. Question 17 in the list (Albouy et al. in Celest Mech Dyn Astr 113:369–375, 2012) is thus answered negatively.
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