Singular continuation of planar central configurations with clusters of bodies

Planar central configurations of point masses that have one or more clusters of bodies are created by analytic continuation. The singularity of the gravitational interaction is removed from the continuation equations by algebraic means. The continuation splits a single body into several, and the ini...

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Bibliographic Details
Published in:Physica. D 2014-02, Vol.269, p.120-125
Main Author: O’Neil, Kevin A.
Format: Article
Language:English
Subjects:
Celestial mechanics
Central configuration
Continuation
Relative equilibrium
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Summary:Planar central configurations of point masses that have one or more clusters of bodies are created by analytic continuation. The singularity of the gravitational interaction is removed from the continuation equations by algebraic means. The continuation splits a single body into several, and the initial mass of the single body can be nonzero. Necessary conditions are derived for these continuations that may be useful in addressing the question of finiteness of central configurations. •Central configurations are created by continuation.•Initial mass in the continuation may be zero or nonzero.•The resulting configurations have clusters of point masses.•Two scaling regimes are explored, and existence results proved.•This relates to the finiteness problem for central configurations.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2013.12.001