Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Central configurations lead to special solutions of the $ n$-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.


References [Enhancements On Off] (What's this?)

  • [Hall] G. R. Hall, Central configurations of the $ 1 + N$ 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 $ {{\mathbf{R}}^2}$ and $ {{\mathbf{R}}^3}$, 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 70F15, 58F05, 58F14

Retrieve articles in all journals with MSC: 70F15, 58F05, 58F14


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-0990414-7
Keywords: $ n$-body problem, central configurations, relative equilibria
Article copyright: © Copyright 1990 American Mathematical Society