Accession Number : ADA132820

Title :   Central Configurations of the N-Body Problem.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Pacella,Filomena

PDF Url : ADA132820

Report Date : Jun 1983

Pagination or Media Count : 17

Abstract : An important problem is celestial mechanics is to find the central configurations of the N-body problem. This problem is equivalent to looking for critical points of the relevant potential function over a manifold on which a group of symmetries acts. The so-called collinear problem is well understood. While many important results have been obtained about the N-body problem in the plane, as far as it is known there are no results about this problem in space. In this paper the author use topological methods, in particular Morse theory and the equivalent homology, to obtain a first estimate on the minimal number of spatial central configurations. Then, using known results for the collinear and planar she improves this estimate and is able to give an inferior bound on the number of those central configurations which are not planar in the sense that not all the bodies lie on the same plane.

Descriptors :   *Differential topology, *N body problem, *Celestial mechanics, Configurations, Estimates, Linearity, Potential energy, Kinetic energy, Computations, Inequalities

Subject Categories : Celestial Mechanics
      Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE