Rigorous results on Hill Stability for the classical <italic>N</italic> -body problem are in general unknown for <italic>N</italic> ≥ 3, due to the complex interactions that may occur between bodies and the many different outcomes which may occur. However, the addition of finite density for the bodies along with a rigidity assumption on their mass distribution allows for Hill stability to be easily established. In this note we generalize results on Hill stability developed for the Full 3-body problem and show that it can be applied to the Full <italic>N</italic> -body problem. Further, we find that Hill Stability concepts can be applied to identify types of configurations which can escape and types which cannot as a function of the system energy.
%0 Journal Article
%1 scheeres2015stability
%A Scheeres, D J
%D 2015
%J Proceedings of the International Astronomical Union
%K astronomy hills_mechanism
%N S318
%P 128-134
%R 10.1017/S174392131500719X
%T Hill Stability of Configurations in the Full N-Body Problem
%U https://www.cambridge.org/core/product/identifier/S174392131500719X/type/journal_article
%V 10
%X Rigorous results on Hill Stability for the classical <italic>N</italic> -body problem are in general unknown for <italic>N</italic> ≥ 3, due to the complex interactions that may occur between bodies and the many different outcomes which may occur. However, the addition of finite density for the bodies along with a rigidity assumption on their mass distribution allows for Hill stability to be easily established. In this note we generalize results on Hill stability developed for the Full 3-body problem and show that it can be applied to the Full <italic>N</italic> -body problem. Further, we find that Hill Stability concepts can be applied to identify types of configurations which can escape and types which cannot as a function of the system energy.
@article{scheeres2015stability,
abstract = {Rigorous results on Hill Stability for the classical <italic>N</italic> -body problem are in general unknown for <italic>N</italic> ≥ 3, due to the complex interactions that may occur between bodies and the many different outcomes which may occur. However, the addition of finite density for the bodies along with a rigidity assumption on their mass distribution allows for Hill stability to be easily established. In this note we generalize results on Hill stability developed for the Full 3-body problem and show that it can be applied to the Full <italic>N</italic> -body problem. Further, we find that Hill Stability concepts can be applied to identify types of configurations which can escape and types which cannot as a function of the system energy.},
added-at = {2024-05-08T21:51:08.000+0200},
author = {Scheeres, D J},
biburl = {https://www.bibsonomy.org/bibtex/2f94e1b040ff7c48f70e974c4be072745/tabularii},
doi = {10.1017/S174392131500719X},
interhash = {e77fa1225c1525769c4f8857cbc4cc54},
intrahash = {f94e1b040ff7c48f70e974c4be072745},
journal = {Proceedings of the International Astronomical Union},
keywords = {astronomy hills_mechanism},
number = {S318},
pages = {128-134},
timestamp = {2024-05-10T12:00:19.000+0200},
title = {Hill Stability of Configurations in the Full N-Body Problem},
url = {https://www.cambridge.org/core/product/identifier/S174392131500719X/type/journal_article},
volume = 10,
year = 2015
}