In this article we obtain the Andoyer equations for noncollinear planar central configurations taking into account the center of mass of the system. We apply these equations to study two configurations. In the first one we prove that it is not possible to put a square central configuration and an equilateral triangle central configuration as a cocircular central configuration. In the second one we give the central configurations for the noncollinear planar $4$-body problem with one pair of equal positive masses and two null masses.
FERNANDES, ANTONIO CARLOS and MELLO, LUIS FERNANDO
"Andoyer equations for noncollinear planar central configurations,"
Turkish Journal of Mathematics: Vol. 41:
3, Article 5.
Available at: https://journals.tubitak.gov.tr/math/vol41/iss3/5