Symmetry Theorems for the Newtonian 4- and 5-body Problems with Equal Masses

Jean-Charles Faugère () and Ilias Kotsireas ()
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Jean-Charles Faugère: Universitè Paris, LIP6, CNRS
Ilias Kotsireas: Universitè Paris, LIP6

A chapter in Computer Algebra in Scientific Computing CASC’99, 1999, pp 81-92 from Springer

Abstract: Abstract We present a new proof of the algebraic part of a symmetry theorem for the central configurations of the newtonian planar 4-body problem with equal masses, using Gröbner bases. This approach is used to obtain a new symmetry theorem for the central configurations of the newtonian spatial 5-body problem with equal masses in the convex case. In fact we prove a more general statement of the theorem, valid for a class of potentials defined by functions with increasing and concave derivatives.

Keywords: Equal Mass; Convex Case; Central Configuration; Admissible Order; Oriented Area (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-60218-4_6

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DOI: 10.1007/978-3-642-60218-4_6

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