Effect of oblateness on the non-linear stability of the triangular liberation points of the restricted three-body problem in the presence of resonances

Bifurcation Analysis of Stability of Triangular Equilibrium Points in the Elliptic Restricted Problem of Three Bodies

“…The dependence of ω 1 and ω 2 on µ are given by equations (13 and shown in the graphs (3)(4). The value of mass ratio µ critical for stable equilibrium position and local bifurcation is given by (16).…”

“…The dependence of ω 1 and ω 2 on µ is given in the graph (3)(4). In the region (15), the only parametric resonance ω 2 = …”

“…[26], analysed the stability of equilibrium points and demonstrated that parametric resonance causes instability of equilibrium points. [4] studied the non-linear stability of triangular libration points in the restricted three body problem with bigger oblate primary and concluded that the system is stable for resonant case ω 1 = 3ω 2 and unstable for ω 1 = 2ω 2 . [14] is the extension of their previous study by investigating the case of parametric resonance for elliptic restricted three body problem.…”

Linear stability and resonance of triangular equilibrium points in elliptic restricted three body problem with radiating primary and triaxial secondary

“…The stability of such systems (ER3BP) moving in an elliptic orbits was subject of investigation and was investigated by many authors , Arnold [1] ; Danby [11]; Bennet [4]; Szebehely [25]; Broucke [6]; Katsiaris [19] ; Beauge [5]; Baoyin [3]; Ammar [2]; Biggs [7]; Biggs [8] and many others. The resonance/non-resonance cases of libration points for restricted/elliptic restricted three body problem was studied and analyzed by many authors Kamel [18]; Choudhry [10]; Ferraz [12]; Henrard [15]; Kumar [20]; Henrard [17], Hadjidemetriou [13]; Hadjidemetriou [14]; Subba Rao [24]; Thakur [26]; Beauge [5]; Chandra [9]; Narayan [22] and many others. In the present paper an attempt have been made to study and analyze the linear stability of the system.…”

COMBINED EFFECTS OF OBLATENESS AND RADIATION ON THE NONLINEAR STABILITY OF L4IN THE RESTRICTED THREE-BODY PROBLEM

“…The motions of artificial Earth satellites are examples of this. This enables many researchers to study the restricted problem by taking into account the shapes (oblateness) of the bodies (Subba Rao & Sharma, 1975;Bhatnagar & Chawla, 1979, Elipe & Ferrer, 1985Elipe 1992;Markellos et al 1996;Chandra & Kumar, 2004). …”