Central Configurations of the N-Body Problem.

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.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1983
Accession Number
ADA132820

Entities

People

  • Filomena Pacella

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algebraic Topology
  • Bodies
  • Celestial Mechanics
  • Contracts
  • Differential Equations
  • Energy
  • Inequalities
  • Mathematics
  • Mechanics
  • N Body Problem
  • North Carolina
  • Potential Energy
  • Symmetry
  • Three Dimensional
  • United States
  • Universities
  • Wisconsin

Readers

  • Electromagnetic Wave Scattering and Antenna Radiation Engineering
  • Parallel and Distributed Computing.
  • Quantum Dot Semiconductor Device Photonics and Graphene Optoelectronic Materials and THz Physics.

Technology Areas

  • Space