The global solution of theN-body problem

✍ Scribed by Wang Qiu-Dong

• Publisher: Springer Netherlands
• Year: 1991
• Tongue: English
• Weight: 552 KB
• Volume: 50
• Category: Article
• ISBN-13: 9789812770820
• ISSN: 1572-9478
• DOI: 10.1007/bf00048987

✦ Synopsis

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 MeGehee'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.