### Abstract

The method of obtaining the estimates of the maximal t-interval (ω_{-}, ω_{+}) on which the solution of the N-body problem exists and which is such that some fixed mutual distance (e. g. Δ_{12}) exceeds some fixed non-negative lower bound, for all t contained in (ω_{-}, ω_{+}), is considered. For given masses and initial data, the increasing sequences of the numbers γ_{k}, each of which provides the estimate ω_{+} >γ_{k}, are constructed. It appears that if ω_{+} = +∞, then {Mathematical expression}.

Original language | English |
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Pages (from-to) | 43-57 |

Number of pages | 15 |

Journal | Celestial Mechanics |

Volume | 20 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jul 1979 |

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### Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

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*Celestial Mechanics*, vol. 20, no. 1, pp. 43-57. https://doi.org/10.1007/BF01236607

**Existence of the continuations in the N-body problem.** / Babadzanjanz, L. K.

Research output

TY - JOUR

T1 - Existence of the continuations in the N-body problem

AU - Babadzanjanz, L. K.

PY - 1979/7/1

Y1 - 1979/7/1

N2 - The method of obtaining the estimates of the maximal t-interval (ω-, ω+) on which the solution of the N-body problem exists and which is such that some fixed mutual distance (e. g. Δ12) exceeds some fixed non-negative lower bound, for all t contained in (ω-, ω+), is considered. For given masses and initial data, the increasing sequences of the numbers γk, each of which provides the estimate ω+ >γk, are constructed. It appears that if ω+ = +∞, then {Mathematical expression}.

AB - The method of obtaining the estimates of the maximal t-interval (ω-, ω+) on which the solution of the N-body problem exists and which is such that some fixed mutual distance (e. g. Δ12) exceeds some fixed non-negative lower bound, for all t contained in (ω-, ω+), is considered. For given masses and initial data, the increasing sequences of the numbers γk, each of which provides the estimate ω+ >γk, are constructed. It appears that if ω+ = +∞, then {Mathematical expression}.

UR - http://www.scopus.com/inward/record.url?scp=33750683844&partnerID=8YFLogxK

U2 - 10.1007/BF01236607

DO - 10.1007/BF01236607

M3 - Article

AN - SCOPUS:33750683844

VL - 20

SP - 43

EP - 57

JO - Celestial Mechanics and Dynamical Astronomy

JF - Celestial Mechanics and Dynamical Astronomy

SN - 0923-2958

IS - 1

ER -