For the study of nonlinear stability of a dynam-
ical system, normalized Hamiltonian of the system is very
important to discuss the dynamics in the vicinity of invari-
ant objects. In general, it represents a nonlinear approxima-
tion to the dynamics, which is very helpful to obtain the
information as regards a realistic solution of the problem.
In the present study, normalization of the Hamiltonian and
analysis of nonlinear stability in non-resonance case, in the
Chermnykh-like problem under the influence of perturba-
tions in the form of radiation pressure, oblateness, and a
disc is performed. To describe nonlinear stability, initially,
quadratic part of the Hamiltonian is normalized in the neigh-
borhood of triangular equilibrium point and then higher or-
der normalization is performed by computing the fourth or-
der normalized Hamiltonian with the help of Lie transforms.
In non-resonance case, nonlinear stability of the system is
discussed using the Arnold–Moser theorem. Again, the ef-
fects of radiation pressure, oblateness and the presence of
the disc are analyzed separately and it is observed that in the
absence as well as presence of perturbation parameters, tri-
angular equilibrium point is unstable in the nonlinear sense
within the stability range 0 < μ < μ 1 = μ̄ c due to failure of
the Arnold–Moser theorem. However, perturbation param-
eters affect the values of μ at which D 4 = 0, significantly.
This study may help to analyze more generalized cases of
B R. Kishor
kishor.ram888@gmail.com
B.S. Kushvah
bskush@gmail.com
1 Department of Mathematics, Central University of Rajasthan,
NH-8, Bandarsindari, Kishangarh, Ajmer 305817, Rajasthan,
India
2 Department of Applied Mathematics, Indian School of Mines,
Dhanbad 826004, Jharkhand, India
the problem in the presence of some other types of perturba-
tions such as P-R drag and solar wind drag. The results are
limited to the regular symmetric disc but it can be extended
in the future.

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• Normalization of Hamiltonian and nonlinear stability of the triangular equilibrium points in non-resonance case with perturbations