This paper aims to investigate the non-linear stability of the triangular libration point in the restricted three-body problem (R3BP). The model, we use for our problem consists of a primary body as a heterogeneous spheroid with N-layers having different densities of each layer and a secondary body as a point mass that is producing the modified Newtonian Potential. We determine the equation of motion of the smallest body which is under the influence of the above-mentioned perturbations and also influenced by Coriolis as well as Centrifugal forces and then evaluated the Lagrangian for the evaluated system of equations. Afterwards, we write the first and second-order normalization of the Hamiltonian of the problem. By implying KAM theorem and the techniques used by Bhatnagar and Hallan, we discuss the non-linear stability analytically.
Singh, Bhawna; Shalini, Kumari; Prasad, Sada Nand; and Ansari, Abdullah A.
(R1985) Study the Effect of Modified Newtonian Force on the Restricted 3-body Configuration in Non-Linear Sense,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 17,
2, Article 10.
Available at: https://digitalcommons.pvamu.edu/aam/vol17/iss2/10