“…It has been shown that resonances of the third order exist under the range of linear stability. This paper is in continuation of the paper ( Usha [27] and Narayan [23]). The study of linear stability in presence of resonance makes the work different from the other works.…”
Section: Introductionmentioning
confidence: 54%
“…al. [27] and given in the following equation (1). The notations in principle follow the book of Szebehely [25], with some minor modifications in the notation being done for adapting to the present problem, presented as: …”
The present paper studies the linear stability of the triangular equilibrium points of the system. The system comprises of a radiating primary and a triaxial secondary in elliptic restricted three body problem. The existence of third order resonances has been shown and the linear stability has been analyzed for these resonance cases. For the resonance case, 3 2 = 1 and 2 1 + 2 = 0, the conditions of the linear stability are satisfied and the system is stable. But, for the resonance cases 2 1 + 2 = 1 and 1 − 2 2 = 2 the system is unstable.
“…It has been shown that resonances of the third order exist under the range of linear stability. This paper is in continuation of the paper ( Usha [27] and Narayan [23]). The study of linear stability in presence of resonance makes the work different from the other works.…”
Section: Introductionmentioning
confidence: 54%
“…al. [27] and given in the following equation (1). The notations in principle follow the book of Szebehely [25], with some minor modifications in the notation being done for adapting to the present problem, presented as: …”
The present paper studies the linear stability of the triangular equilibrium points of the system. The system comprises of a radiating primary and a triaxial secondary in elliptic restricted three body problem. The existence of third order resonances has been shown and the linear stability has been analyzed for these resonance cases. For the resonance case, 3 2 = 1 and 2 1 + 2 = 0, the conditions of the linear stability are satisfied and the system is stable. But, for the resonance cases 2 1 + 2 = 1 and 1 − 2 2 = 2 the system is unstable.
“…Let R 1 and R 2 be the dimensionless distance between the primaries. The equation of motion of the system with the minor modification as solved by [17,21]) is given as: In equation (2.5), the second term in the left hand side represents the Coriolisacceleration. The complex position vectors z 1 and z 2 are the location of the primaries, which are permanent on the real axis (x ̅, y ̅)of the system, we have:…”
Section: Equation Of Motionmentioning
confidence: 99%
“…Many authors such as [1][2][3][4][5] have studied the elliptical restricted three body problem in detail. The influence of eccentricity of orbits of the primaries with or without radiation pressure,oblateness and triaxiality of the primaries are studied by [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. The present study is an attempt to derive the differential equation governing the motion of the triangular equilibrium points on the assumption that both the primaries are oblate triaxial rigid body.…”
This paper explore pulsating Curves of zero velocityof the infinitesimal mass around the triangular equilibrium points with oblate and triaxial rigid body in the elliptical restricted three body problem(ER3BP).
“…[20],Usha, T., Narayan, A., Ishwar, B. [21],Zimvoschikov, A.S., Thkai, V.N. [22] , have studied the effects of radiation pressure on the motion of the infinitesimal body by taking one or both primaries as a source of radiation.…”
This Paper deals with the effects of the radiation pressure and triaxiality of primaries on the stability of infinitesimal motion about triangular equilibrium points [ 4 , 5 ] in the elliptical restricted three body problem (ER3EB) around binary system. For determining the characteristic exponents of variational equations with periodic coefficient, we have used analytical method, described by Bennet in [3,4]. This analytical method is based on Floquet's theory. The stability of equilibrium points has been discussed under the assumption thatboth the primaries are radiating and triaxial. For this we have drawn transition cureves in μ-e plane. And it is seen that system is stable outside the transition curves, while system is Unstable within the transition curves.
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