A note on a Lagrangian formulation for motion about the collinear points

A Lagrangian formulation for the three-dimensional motion of a satellite in the vicinity of the collinear points of the circular-restricted problem is reconsidered. It is shown that the influence of the primaries can be expressed in the form of two third-body disturbing functions. By use of this approach, the equations for the Lagrangian and for the motion itself are readily developed into highly compact expressions. All orders of the non-linear developments are shown to be easily obtainable using well-known recursive relationships. The resulting forms for these equations are well suited for use in the initial phase of canonical or non-canonical investigations.