Homographic solutions of the n-body problem in E4 |
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Authors: | Julian I Palmore |
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Affiliation: | Department of Mathematics, University of Illinois, Urbana, Illinois 61801 U.S.A. |
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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)?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. |
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