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