Libration Points of the Generalized Restricted Circular Problem of Three Bodies in the case of imaginary distance between attracting centers

A particle steady motions in vicinity of dynamically symmetric precessing rigid body are studied in assumption that the body gravitational field is modeled as gravitational field of two centers being on imaginary distance. Such particle motion equations are a variant of motion equations of the Generalized Restricted Circular Problem of Three Bodies (GRCP3B). The number of Coplanar Libration Points, i.e. the particle equilibria in the plane passing through the body axis of dynamical symmetry and through the axis of precession are established. (This number is odd and can be equal to 5, 7 or 9). CLPs evolution are studied at changing values of the considered system parameters. Moreover, two Triangular Libration Points, i. e. the particle equilibria in the axis crossing the body mass center orthogonally to axes of precession and dynamical symmetry are found.