Morse Theory and Central Configurations in the Spatial N-body Problem |
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Authors: | John Conrad Merkel |
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Affiliation: | (1) Department of Mathematics, Morehouse College, 830 Westview Drive, SW Atlanta, GA 30314, USA |
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Abstract: | In the spirit of Palmore and Pacella, Morse Theory is used to obtain a lower bound for the number of central configurations in the spatial N-body problem. The homology of the configuration ellipsoid with the collision and collinear manifolds removed and the SO(3) symmetry quotiented out is calculated. As intermediate steps, homology calculations are carried out for several additional manifolds naturally arising in the N-body problem. |
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Keywords: | N-body problem Central configuration Morse theory Celestial mechanics |
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