On the classification of pyramidal central configurations
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- by Nelly Fayçal PDF
- Proc. Amer. Math. Soc. 124 (1996), 249-258 Request permission
Abstract:
We present some results associated with the existence of central configurations (c.c.’s) in the classical gravitational $N$-body problem of Newton. We call a central configuration of five bodies, four of which are coplanar, a $pyramidal$ central configuration (p.c.c). It can be shown that there are only three types of p.c.c.’s, admitting one or more planes of symmetry, viz. (i) the case where the planar bodies lie at the vertices of a regular trapezoid, (ii) the case where the bodies lie at the vertices of a kite-shaped quadrilateral, and (iii) the case where the bodies lie at the vertices of a rectangle. In this paper we classify all p.c.c.’s with a rectangular base and, in fact, prove that there is only one such c.c., namely, the square-based pyramid with equal masses at the corners of the square. The classification of all p.c.c.’s satisfying either (i) or (ii) will be discussed in subsequent papers.References
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Additional Information
- Nelly Fayçal
- Affiliation: Carleton University, Department of Mathematics and Statistics, Ottawa, Ontario, Canada K1S 5B6
- Received by editor(s): July 25, 1994
- Additional Notes: This research was partially supported by an NSERC, PGS3 Scholarship
- Communicated by: Hal L. Smith
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 249-258
- MSC (1991): Primary 70F15, 70F10
- DOI: https://doi.org/10.1090/S0002-9939-96-03135-8
- MathSciNet review: 1301024