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Normal forms of Hamiltonian are very important to analyze the nonlinearstability of a dynamical system in the vicinity of invariant objects. Thispaper presents the normalization of Hamiltonian and the analysis of nonlinearstability of triangular equilibrium points in non-resonance case, in thephotogravitational restricted three body problem under the influence ofradiation pressures and P-R drags of the radiating primaries. The Hamiltonianof the system is normalized up to fourth order through Lie transform method andthen to apply the Arnold-Moser theorem, Birkhoff normal form of the Hamiltonianis computed followed by nonlinear stability of the equilibrium points isexamined. Similar to the case of classical problem, we have found that in thepresence of assumed perturbations, there always exists one value of massparameter within the stability range at which the discriminant $D_4$ vanish,consequently, Arnold-Moser theorem fails, which infer that triangularequilibrium points are unstable in nonlinear sense within the stability range.Present analysis is limited up to linear effect of the perturbations, whichwill be helpful to study the more generalized problem.

qualitative theory of dynamical systems

Normalization of Hamiltonian and nonlinear stability of triangular  equilibrium points in the photogravitational restricted three body problem  with P-R drag in non-resonance case