Abstract
We prove the existence of many homographic solutions of the n-body problem in E4 by topological methods. Homographic solutions are associated with relative equilibria. Homothetic solutions always give rise to central configurations. In Euclidean space E4 central configurations are a proper subset of the relative equilibria for any n ≥ 3 and for any (mi)ε{lunate}R+n. We compare the existence and classification of homographic solutions of the n-body problem in E3 with the Newtonian potential and that of homographic solutions of the n-body problem in E4. Classifying relative equilibria leads to classifying homographic solutions.
Original language | English (US) |
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Pages (from-to) | 279-290 |
Number of pages | 12 |
Journal | Journal of Differential Equations |
Volume | 40 |
Issue number | 2 |
DOIs | |
State | Published - May 1981 |
ASJC Scopus subject areas
- Analysis
- Applied Mathematics