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

In: Computer Algebra in Scientific Computing CASC’99

Author

Listed:
  • Jean-Charles Faugère

    (Universitè Paris, LIP6, CNRS)

  • Ilias Kotsireas

    (Universitè Paris, LIP6)

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.

Suggested Citation

  • Jean-Charles Faugère & Ilias Kotsireas, 1999. "Symmetry Theorems for the Newtonian 4- and 5-body Problems with Equal Masses," Springer Books, in: Victor G. Ganzha & Ernst W. Mayr & Evgenii V. Vorozhtsov (ed.), Computer Algebra in Scientific Computing CASC’99, pages 81-92, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-60218-4_6
    DOI: 10.1007/978-3-642-60218-4_6
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