The global solution of the N-body problem

Research output: Contribution to journalArticlepeer-review

46 Scopus citations

Abstract

The problem of finding a global solution for systems in celestial mechanics was proposed by Weierstrass during the last century. More precisely, the goal is to find a solution of the n-body problem in series expansion which is valid for all time. Sundman solved this problem for the case of n = 3 with non-zero angular momentum a long time ago. Unfortunately, it is impossible to directly generalize this beautiful theory to the case of n > 3 or to n = 3 with zero-angular momentum. A new 'blowing up' transformation, which is a modification of McGehee's transformation, is introduced in this paper. By means of this transformation, a complete answer is given for the global solution problem in the case of n > 3 and n = 3 with zero angular momentum.

Original languageEnglish (US)
Pages (from-to)73-88
Number of pages16
JournalCELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
Volume50
Issue number1
DOIs
StatePublished - Mar 1990
Externally publishedYes

Keywords

  • N-body problem
  • analytic continuation
  • blowing up transformation

ASJC Scopus subject areas

  • Modeling and Simulation
  • Mathematical Physics
  • Astronomy and Astrophysics
  • Space and Planetary Science
  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'The global solution of the N-body problem'. Together they form a unique fingerprint.

Cite this