Abstract
Planar central configurations of four different masses are analyzed theoretically and computed numerically. We follow Dziobek’s approach to four-body central configurations with a straightforward implicit (in the masses and distances) method of our own in which the fundamental quantities are each the quotient of a directed area divided by the corresponding mass. We apply a new simple numerical algorithm to construct general four-body central configurations. We use this tool to obtain new properties of the symmetric and non-symmetric central configurations. The explicit continuous connection between three-body and four-body central configurations where one of the four masses approaches zero is clarified. Some cases of coorbital 1+3 problems are also considered.
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Piña, E., Lonngi, P. Central configurations for the planar Newtonian four-body problem. Celest Mech Dyn Astr 108, 73–93 (2010). https://doi.org/10.1007/s10569-010-9291-5
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DOI: https://doi.org/10.1007/s10569-010-9291-5