{"title":"桑德曼定理重温","authors":"Andrei D. Werkhausen, Heyder Hey","doi":"10.1016/j.physd.2024.134385","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we revisit Sundman’s Theorem on the three-body problem. We provide a simple example demonstrating that the requirement on the total angular momentum <span><math><mi>L</mi></math></span> (bounded away from zero) can be relaxed for a particular set of initial conditions, allowing double shocks. We present an explicit solution for the exact triple-collision scenario through a Sundman-like formal regularization.</div></div>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sundman theorem revisited\",\"authors\":\"Andrei D. Werkhausen, Heyder Hey\",\"doi\":\"10.1016/j.physd.2024.134385\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we revisit Sundman’s Theorem on the three-body problem. We provide a simple example demonstrating that the requirement on the total angular momentum <span><math><mi>L</mi></math></span> (bounded away from zero) can be relaxed for a particular set of initial conditions, allowing double shocks. We present an explicit solution for the exact triple-collision scenario through a Sundman-like formal regularization.</div></div>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-09-21\",\"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://www.sciencedirect.com/science/article/pii/S016727892400335X\",\"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://www.sciencedirect.com/science/article/pii/S016727892400335X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
摘要
在本文中,我们重温了关于三体问题的桑德曼定理。我们提供了一个简单的例子,证明对于一组特定的初始条件,可以放宽对总角动量 L 的要求(远离零的边界),允许双冲击。我们通过类似桑德曼的形式正则化,提出了精确三体碰撞情形的明确解法。
In this paper, we revisit Sundman’s Theorem on the three-body problem. We provide a simple example demonstrating that the requirement on the total angular momentum (bounded away from zero) can be relaxed for a particular set of initial conditions, allowing double shocks. We present an explicit solution for the exact triple-collision scenario through a Sundman-like formal regularization.