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Saari's conjecture for the collinear  -body problem |
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| Authors: | Florin Diacu Ernesto Pé rez-Chavela Manuele Santoprete |
| Institution: | Pacific Institute for the Mathematical Sciences and Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045 STN CSC, Victoria, British Columbia, Canada V8W 3P4 ; Departamento de Matemáticas, Universidad Autónoma Metropolitana-Iztapalapa, Apdo. 55534, México, D.F., México ; Department of Mathematics, University of California, Irvine, 294 Multipurpose Science & Technology Building, Irvine, California 92697 |
| Abstract: | In 1970 Don Saari conjectured that the only solutions of the Newtonian  -body problem that have constant moment of inertia are the relative equilibria. We prove this conjecture in the collinear case for any potential that involves only the mutual distances. Furthermore, in the case of homogeneous potentials, we show that the only collinear and non-zero angular momentum solutions are homographic motions with central configurations. |
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