ANALYTICAL INVESTIGATION OF NONLINEAR STABILITY OF THE LAGRANGIAN POINT-L(4) AROUND THE COMMENSURABILITY-1 2/

The problem of stability of the Lagrangian point L(4) in the circular restricted problem of three bodies is investigated close to the 1 : 2 commensurability of the long and short period libration. By stability we define boundedness of the solution for a given initial finite displ acement from the equilibrium point as function of the mass parameter m u close to the commensurability. A rigorous treatment close to the res onance condition is possible using a transformation that diagonalizes the matrix related to the linear part of the equations of motion. The so obtained equations are further transformed to action angle type var iables. Then using an isolated resonance approach, only the slowly var ying terms are kept in the equations and two independent isolating fir st integrals can be found. These integrals finally enable us to solve the stability problem in an exact way. The so obtained results are com pared to numeric integration of the equations of motion and are found to be in perfect agreement.