Non-linear stability in photogravitational non-planar restricted three body problem with oblate smaller primary

TL;DR

This paper investigates the non-linear stability of the photogravitational non-planar restricted three-body problem with an oblate smaller primary, using Hamiltonian normalization and Arnold's theorem to establish stability criteria.

Contribution

It introduces a stability analysis for a non-planar three-body problem with radiating primaries and oblateness, applying Lie transforms and Birkhoff normal form.

Findings

L6 is stable under the studied conditions.

Graphs of (, D2) form rectangular hyperbolas.

Non-linear stability criteria are derived using Arnold's theorem.

Abstract

We have discussed non-linear stability in photogravitational non-planar restricted three body problem with oblate smaller primary. By photogravitational we mean that both primaries are radiating. We normalised the Hamiltonian using Lie transform as in Coppola and Rand (1989). We transformed the system into Birkhoff's normal form. Lie transforms reduce the system to an equivalent simpler system which is immediately solvable. Applying Arnold's theorem, we have found non-linear stability criteria. We conclude that $L_6$ is stable. We plotted graphs for $(\omega_1, D_2).$ They are rectangular hyperbola.