NON-LINEAR STABILITY OF OBLATE INFINITESIMAL IN THE NEIGHBOURHOOD OF TRIANGULAR EQUILIBRIUM POINTS FOR TRIAXIAL PRIMARIES IN ELLIPTIC RESTRICTED THREE BODY PROBLEM
By
Poonam Duggad1, Shilpi Dewangan2 and A. Narayan3
1Research Scholar, Shri Shankaracharya Technical Campus, Bhilai, Durg, Chhattisgarh, India-490020.
2Department of Mathematics and Statistics, MGM University, Aurangabad, Maharashtra, India-431003.
3Department of Mathematics, Darbhanga College of Engineering, Darbhanga, Department of Science and Technology, Government of Bihar, India-846001.
Email: pariduggad91@gmail.com,shilpi.mahesh2003@gmail.com, ashutoshmaths.narayan@gmail.com.
(Received: July 25, 2023; In format: November 23, 2023; Revised: July 18, 2024; Accepted: September 13, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54204
Abstract
The present work deals with the non- linear stability of the oblate infinitesimal in the neighbourhood of triangular equilibrium point for triaxial primaries in the Elliptical restricted Three Body Problem under the presence of third and fourth order resonance; when the bigger and smaller primaries are taken as triangular rigid body and the third body of infinitesimal mass is taken as an oblate. The stability has been analysed for the resonance case as well as non- resonance cases around ω1 = 2ω2 and ω1 = 3ω2. It was observed that in the third order resonance case the motion of the infinitesimal system shows unstable behaviour however in the fourth order resonance case. The stability shown for some mass parameter whereas the motion in the non- resonance case was found to be unstable.
2020 Mathematical Sciences Classification: 70F15, 37N05, 70F07.
Keywords: Triaxial, Oblateness, Hamiltonian, Elliptic Restricted Three Body Problem.