### 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 language | English (US) |
---|---|

Pages (from-to) | 73-88 |

Number of pages | 16 |

Journal | Celestial Mechanics and Dynamical Astronomy |

Volume | 50 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1990 |

Externally published | Yes |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Celestial Mechanics and Dynamical Astronomy*, vol. 50, no. 1, pp. 73-88. https://doi.org/10.1007/BF00048987

}

TY - JOUR

T1 - The global solution of the N-body problem

AU - Wang, Qiu-Dong

PY - 1990/3

Y1 - 1990/3

N2 - 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.

AB - 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.

KW - analytic continuation

KW - blowing up transformation

KW - N-body problem

UR - http://www.scopus.com/inward/record.url?scp=34249924049&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249924049&partnerID=8YFLogxK

U2 - 10.1007/BF00048987

DO - 10.1007/BF00048987

M3 - Article

AN - SCOPUS:34249924049

VL - 50

SP - 73

EP - 88

JO - Celestial Mechanics and Dynamical Astronomy

JF - Celestial Mechanics and Dynamical Astronomy

SN - 0923-2958

IS - 1

ER -