Victor Szebehely

Theory and Application of Motion Around Equilibrium Positions

Abstract The motion associated with equilibrium configurations of dynamical systems is treated. The general results are then applied to astronomy and to space dynamics. The theory of libration points in the restricted problem of three bodies is presented in two parts, showing the essentially different dynamical properties associated with collinear and triangular Lagrangian points. The next branch point in the general theory occurs at a special value of the mass parameter at which the stability character of the equilateral points changes. The nonlinear effects are considered at this point, and it is shown how the linear approach must be modified to arrive at meaningful results for motions of finite amplitude. The actual physical picture is scrutinized, and the validity of the assumptions of the restricted problem of three bodies is assessed. A critical review of the literature, is included, with mention of the basic contributions as well as the recent engineering developments.