Finiteness of relative equilibria of the four-body problem

• 成果类型: Article
• 署名作者: Hampton, M; Moeckel, R
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-005-0461-0
• 发表日期: 2006
• 页码: 289-312
• 关键词: integral manifolds; configurations

摘要

We show that the number of relative equilibria of the Newtonian four-body problem is finite, up to symmetry. In fact, we show that this number is always between 32 and 8472. The proof is based on symbolic and exact integer computations which are carried out by computer.