ON THE PLOTTING OF THE STABILITY DOMAIN BORDER OF TRIANGULAR LIBRATION POINTS FOR PLANE BOUNDED ELLIPTICAL THREE-BODY PROBLEM
In the article, the plane bounded elliptical three-body problem is considered. The authors study the problem of plotting the border of stability domain of triangular libration points in the parameter plane: the eccentricity and the parameter of mass. As the main method of solving the problem, the method of M. Rozo for studying the stability of linear differential equations with periodic coefficients is proposed. It is shown that this formulation leads to the formation of resonance problem. To transform it to non-resonant form, a transition matrix was constructed, using the properties of the linearized problem. In solution of the main problem, the ideas of the small parameter method and methods of the theory of stability of solutions of Hamiltonian systems were applied as well. The main result is the development of a new scheme for plotting of the tangents to the stability boundaries of the of triangular libration points. The proposed scheme was formulated as algorithms and approximate equations for solving the problem of the stability regions plotting. The scheme can be modified to calculate the approximate formulas of the stability domain borders of triangular libration points of a higher order, as well as to study the problems of bifurcation scenarios of the behavior of solutions of the three-body problem for parameters passing through the borders of stability regions.