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Finiteness of relative equilibria of the four-body problem. (English) Zbl 1083.70012

Summary: 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.

MSC:

70F10 \(n\)-body problems
70-08 Computational methods for problems pertaining to mechanics of particles and systems
68W30 Symbolic computation and algebraic computation
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