Open AccessPhotogravitational perturbations in the infinitesimal orbits around the libration points in the oblate RTBP
Author(s) -
S. E. Abd El-Bar,
F. A. Abd El-Salam
Publication year - 2019
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2019411
Subject(s) - infinitesimal , hamiltonian (control theory) , classical mechanics , lagrangian point , physics , libration (molecule) , conjugate points , oblate spheroid , point particle , hamiltonian system , point (geometry) , mathematical analysis , mathematics , geometry , mathematical optimization
In this paper, the infinitesimal orbits around the libration points in the photogravitational oblate restricted problem are computed. To reach this goal, the Hamiltonian of our dynamical model taking into account the considered perturbing forces is constructed. A lie operator method, as a method of solution, is outlined. The Hamiltonian is transferred to any point of the equilibruim point as an origin. The explicit first order as well as the second order solutions for the coordinates and their conjugate momenta of a test particle in an infinitesimal orbit around any equilibrium point are obtained.