Coplanar libration points of the generalized restricted circular problem of three bodies for conjugate complex masses of attracting centers

A particle relative equilibria near a rigid body in the plane passing through the body axes of precession and of dynamical symmetry are studied in assumption that the body gravitational field can be composed as gravitational field of two conjugate complex masses being on imaginary distance. Using terminology of the Generalized Restricted Circular Problem of Three Bodies, these equilibria are called Coplanar Libration Points (CLP). One can show that CLP set is divided into three subsets dependently on CLPs type of evolution. There are 2 “external” CLPs going from infinity to the rigid body if precession angular velocity goes from zero to infinity, from 2 to 6 “internal” CLPs between axis of precession and axis of dynamical symmetry, and from 0 to 3 “central” CLPs near singular points of gravitational potential. Numerical-analitical algorithm of CLPs coordinates computation is suggested. This algorithm is based on some special trigonometrical transformations of coordinates and parameters.