Higher order resonance stability of triangular libration points for radiating primaries in ER3BP

Abstract

The main aim of this paper is to study the existence of resonance and stability of the triangular equilibrium points in the framework of ER3BP when both the attracting bodies are sources of radiation atin both circular and elliptical cases .A practical application of this model could be seen in the case of binary systems ( Achird, Luyten, α Cen-AB, Kruger 60, Xi Bootis). The study is carried out both analytically and numerically by considering various values of radiation pressures and around binary systems .In both cases (CR3BP and ER3BP) it is found that 12   corresponds to the boundary region of the stability for the system, whereas the other two cases 1 2 1 2 2 , 3correspond to the resonant cases. In order to investigate the stability, the Hamiltonian is normalized up to the fourth order by using linear canonical transformation of variables. Then KAM theorem is applied to investigate the stability for different values of radiation pressures in general and around the binary systems in particular. Finally, simulation technique is applied to study the correlation between radiation pressures and mass ratio in circular case; mass ratio and eccentricity in elliptical case. It is found that all the binary systems considered are stable. Also, it is found that except for some values of the radiation pressure parameters and for 0.0385209; c   the triangular equilibrium points are stable.

Analysis on nonlinear stability of the triangular libration points for radiating and oblate primaries in ER3BP

“…Recently [32] studied nonlinear stability of the triangular points considering both the primaries as radiating in ER3BP in non-resonance case .It was found that the except for some values of radiation pressure the triangular points are stable. The resonance condition was also studied by [33] considering only radiating primaries and observed that the motion is stable for third order resonance but unstable for fourth order resonance.…”

Nonlinear Stability of the Triangular Libration Points for Radiating and Oblate Primaries in CR3BP in Nonresonance Condition

“…The stability of the triangular equilibrium points in CR3BP is investigated when both primaries are radiating and oblate, under the nonresonance case using KAM theory. Recently Narayan and Singh [5] studied nonlinear stability considering both primaries as radiating in ER3BP and found that the binary systems are stable. It has been observed that in general the stability character remains the same even if oblateness factor is considered apart from radiation factor in circular cases.…”

“…The nonlinear stability of the triangular Lagrangian points, considering the bigger primary as oblate spheroid in circular case, was examined by Markellos et al [4]. Recently Narayan and Singh [5] studied the nonlinear stability of higher order for both radiating primaries and found that binary systems are stable.…”

“…The detailed description and the behavior of equilibrium points in ER3BP are touched upon by Danby [6], Bennett [7], Szebebely [8], Markeev [9], Selaru and Cucu-Dumitrescu [10], and Hallan and Rana [11]. The influence of the eccentricity of the orbits of the primaries with or without radiation pressure on the existence and stability of the equilibrium points was studied by Györgyey [12], Grebenikov [13], Kumar and Choudhry [2,14], Markellos [4,15], Sahoo and Ishwar [16], Roberts [17], Zimovshchikov and Tkhai [18], Ammar [19],Érdi et al [20], Kumar and Ishwar [21], Singh and Umar [22,23], Usha et al [24], and Narayan and Singh [5,25,26].…”