{"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":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"470 ","pages":"Article 134385"},"PeriodicalIF":2.7000,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica D: Nonlinear Phenomena","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S016727892400335X","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍：
Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.
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