Linearization of the Hamiltonian around the triangular equilibrium points in the generalized photogravitational Chermnykh's problem

TL;DR

This paper analyzes the linear stability of triangular equilibrium points in a generalized photogravitational Chermnykh's problem, considering radiation and oblateness effects, and derives the Hamiltonian's normal form.

Contribution

It introduces a normal form of the Hamiltonian around equilibrium points considering radiation and oblateness, with analytical and numerical stability analysis.

Findings

Radiation pressure affects stability conditions.

Gravitational potential from the belt influences equilibrium.

Normal form of the Hamiltonian facilitates stability analysis.

Abstract

Linearization of the Hamiltonian is being performed around the triangular equilibrium points in the generalized photogravitational Chermnykh's problem. The bigger primary is being considered as a source of radiation and small primary as an oblate spheroid. We have found the normal form of the second order part of the Hamiltonian. For this we have solved the aforesaid set of equations. . The effect of radiation pressure, gravitational potential from the belt on the linear stability have been examined analytically and numerically.