On clustering in central configurations

Author:
Gregory Buck

Journal:
Proc. Amer. Math. Soc. **108** (1990), 801-810

MSC:
Primary 70F15; Secondary 58F05, 58F14

MathSciNet review:
990414

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Abstract: Central configurations lead to special solutions of the -body problem. In this paper we present a geometric condition that all central configurations must satisfy: a central configuration cannot have too much 'clustering'-they are bounded away from the diagonal in configuration space. An explicit bound is given.

**[Hall]**G. R. Hall,*Central configurations of the**body problem*, preprint.**[Meyer-Schmidt]**K. Meyer and D. Schmidt,*Bifurcation of relative equilibria in the four and five body problem*, preprint.**[Moekel]**Richard Moeckel,*Relative equilibria of the four-body problem*, Ergodic Theory Dynam. Systems**5**(1985), no. 3, 417–435. MR**805839**, 10.1017/S0143385700003047**[Saari]**Donald G. Saari,*On the role and the properties of 𝑛-body central configurations*, Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics (Math. Forschungsinst., Oberwolfach, 1978), Part I, 1980, pp. 9–20. MR**564603**, 10.1007/BF01230241**[Schmidt]**D. Schmidt,*Central configurations in**and*, preprint.**[Shub]**M. Shub,*Appendix to Smale’s paper: “Diagonals and relative equilibria”*, Manifolds – Amsterdam 1970 (Proc. Nuffic Summer School), Lecture Notes in Mathematics, Vol. 197, Springer, Berlin, 1971, pp. 199–201. MR**0278700****[Simo]**Carlos Simó,*Relative equilibrium solutions in the four-body problem*, Celestial Mech.**18**(1978), no. 2, 165–184. MR**510556**, 10.1007/BF01228714**[Smale]**S. Smale,*Problems on the nature of relative equilibria in celestial mechanics.*, Manifolds – Amsterdam 1970 (Proc. Nuffic Summer School), Lecture Notes in Mathematics, Vol. 197, Springer, Berlin, 1971, pp. 194–198. MR**0278699**

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1990-0990414-7

Keywords:
-body problem,
central configurations,
relative equilibria

Article copyright:
© Copyright 1990
American Mathematical Society