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Erschienen in:
1999 | OriginalPaper | Buchkapitel
Symmetry Theorems for the Newtonian 4- and 5-body Problems with Equal Masses
verfasst von : Jean-Charles Faugère, Ilias Kotsireas
Erschienen in: Computer Algebra in Scientific Computing CASC’99
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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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.