### 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) |
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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 |

### 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