The global solution of the N-body problem

Research output: Contribution to journalArticle

39 Citations (Scopus)

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

Fingerprint

N-body Problem
many body problem
Angular momentum
Angular Momentum
Global Solution
angular momentum
celestial mechanics
Celestial Mechanics
Blowing-up
blowing
Zero
Blow molding
series expansion
Series Expansion
mechanics
Mechanics
Valid
Generalise

Keywords

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

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

The global solution of the N-body problem. / Wang, Qiu-Dong.

In: Celestial Mechanics and Dynamical Astronomy, Vol. 50, No. 1, 03.1990, p. 73-88.

Research output: Contribution to journalArticle

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