Unrestricted planar problem of a symmetric body and a point mass. Triangular libration points and their stability

We present an analysis of the model introduced by Kokoriev and Kirpichnikov (1988) for the study of unrestricted planar motion of a point mass and a s ymmetric rigid body whose gravity field is approximated by two point masses (a dumb-bell model). To show possible generalization of the model, we give a systematic derivation of equations of motion for a more general unrestri cted problem of a point and a rigid body possessing a plane of dynamical sy mmetry. We give a simple description of bifurcation of triangular libration points, and we perform an analysis of their linear stability. We propose t o extend the model of Kokoriev and Kirpichnikov (1988) to a case when the s ymmetric body is oblate. In the proposed model the gravity field of moving and rotating body is approximated by two complex masses at complex distance (a complex dumb-bell model). An analysis of bifurcation of the triangular libration points in this model is also presented.