Central configurations of N-body problem with general attraction. II - The numbers and the shapes of the central configurations when N = 2-4

Astronomy and Astrophysics – Astronomy

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Many Body Problem, Orbital Mechanics, Four Body Problem, Three Body Problem, Two Body Problem, Two Dimensional Models

Scientific paper

This paper is a sequel to one in which central configurations of n-body (n = 2, 3, 4) were studied. Some theoretical results about 1D central configurations show that Moulton's theorem does not apply to the situation when k (parameter in the general force function) is less than zero. Also given are the theoretical results concerning the qualitative properties of the shapes of four-body 2D central configurations. By means of classification, these properties are expressed succinctly. Furthermore, numerical explorations are invoked for illustrating how the numbers and the shapes of central configurations of n-body (n = 3, 4) depend on the parameter k.

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