Available in electronic format
Available in print format		 Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

The number of planar central configurations is finite when $N-1$ mass positions are fixed

Author(s): Peter W. Lindstrom
Journal: Trans. Amer. Math. Soc. 353 (2001), 291-311.
MSC (2000): Primary 70F10
Posted: September 18, 2000
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract:

In this paper, it is proved that for $n>2$ and $n\not=4$, if $n-1$ masses are located at fixed points in a plane, then there are only a finite number of $n$-point central configurations that can be generated by positioning a given additional $n$th mass in the same plane. The result is established by proving an equivalent isolation result for planar central configurations of five or more points. Other general properties of central configurations are established in the process. These relate to the amount of centrality lost when a point mass is perturbed and to derivatives associated with central configurations.

References:

1.
G. Buck, On clustering in central configurations, Proc. Amer. Math. Soc. 108 (1990), 801-810. MR 90f:70016

2.
L. Euler, De moto rectilineo trium corporum se mutuo attahentium, Novi Comm. Acad. Sci. Imp. Petrop. 11 (1767), 144-151.

3.
J. L. Lagrange, Ouvres, Volume 6, Paris, 1873, 272-292.

4.
K. R. Meyer, and G. R. Hall, Introduction to Hamiltonian Dynamical Systems and the $N$-Body Problem, Springer-Verlag, 1992. MR 93b:70002

5.
R. Moeckel, On central configurations, Math. Z. 205 (1990), 499-517. MR 96d:70015

6.
R. Moeckel, Relative equilibria of the four-body problem, Ergodic Theory and Dynamical Systems 5 (1985), 417-435. MR 87b:70011

7.
F. R. Moulton, The straight line solutions of the problem of $N$ bodies, Ann. Math., II. Ser. 12, 1910, 1-17.

8.
D. Saari, On the role and properties of $n$ body central configurations, Celest. Mech. 21 (1980), 9-20. MR 81a:70016

9.
S. Smale, Mathematical problems for the next century, The Mathematical Intelligencer 20 (1998), 7-15. MR 99h:01033

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 70F10

Retrieve articles in all Journals with MSC (2000): 70F10

Additional Information:

Peter W. Lindstrom
Affiliation: Department of Mathematics, Saint Anselm College, Manchester, New Hampshire 03102

DOI: 10.1090/S0002-9947-00-02568-X
PII: S 0002-9947(00)02568-X
Received by editor(s): December 18, 1998
Posted: September 18, 2000
Copyright of article: Copyright 2000, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google