Pulsating Different Curves of Zero Velocity around Triangular Equilibrium Points in Elliptical Restricted Three-Body Problem

Narayan, A.; Shrivastava, Amit Kumar

doi:10.1155/2013/936859

Cited by 6 publications

(4 citation statements)

References 25 publications

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“…Thus, the coordinate of the triangular equilibrium points has been obtained up to the first order terms in the parameters 1 , 2 , 1 , and 2 , which is represented by (4) referred from [22,29].…”

Section: Equation Of Motionmentioning

confidence: 99%

Existence of Resonance Stability of Triangular Equilibrium Points in Circular Case of the Planar Elliptical Restricted Three-Body Problem under the Oblate and Radiating Primaries around the Binary System

Narayan

Shrivastava

2014

Advances in Astronomy

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This paper analyzes the existence of resonance stability of the triangular equilibrium points of the planar elliptical restricted three-body problem when both the primaries are oblate spheroid as well as the source of radiation under the particular case, whene=0. We have derived Hamiltonian function describing the motion of infinitesimal mass in the neighborhood of the triangular equilibrium solutions taken as a convergent series. Hamiltonian function for the system has been derived and also expanded in powers of the generalized components of momenta. We have used canonical transformation to make the Hamiltonian function independent of true anomaly. The most interesting and distinguishable results of this study are establishing the relation for determining the range of stability at and near the resonanceω2=1/2around the binary system.

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Section: Equation Of Motionmentioning

confidence: 99%

Existence of Resonance Stability of Triangular Equilibrium Points in Circular Case of the Planar Elliptical Restricted Three-Body Problem under the Oblate and Radiating Primaries around the Binary System

Narayan

Shrivastava

2014

Advances in Astronomy

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“…Umar and Singh (2014) investigated the effects of oblateness, radiation and eccentricity of both primaries on the periodic orbits around the triangular Lagrangian points of oblate and luminous binary systems in the framework of the ERTBP. Narayan and Shrivastava (2013,) discussed the oblateness and the photogravitational effects of both the primaries on the location and the stability of the triangular equilibrium points in the ERTBP. They studied the stability of the triangular points under the photogravitational and oblateness effects of both the primaries around the binary systems Achird, Lyeten, Alpha Cen-AB, Kruger 60, and Xi-Bootis.…”

Section: Introductionmentioning

confidence: 99%

Stability of the triangular points in the photogravitational triaxial elliptic RTBP with dissipations

El-Salam

2019

New Astronomy

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“…Over decades, the study of the existence of some families of particular solutions in both circular and elliptic R3BP has received the attention of various researchers like [1][2][3][4][5][6][7][8][9][10][11][12][13] among others.…”

Section: Introductionmentioning

confidence: 99%

Generalized Out-of-Plane Equilibrium Points in the Frame of Elliptic Restricted Three-Body Problem: Impact of Oblate Primary and Luminous-Triaxial Secondary

Hussain

Umar

2019

Advances in Astronomy

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This paper studies the motion of a third body near the 1st family of the out-of-plane equilibrium points, L6,7, in the elliptic restricted problem of three bodies under an oblate primary and a radiating-triaxial secondary. It is seen that the pair of points (ξ0,0,±ζ0) which correspond to the positions of the 1st family of the out-of-plane equilibrium points, L6,7, are affected by the oblateness of the primary, radiation pressure and triaxiality of the secondary, semimajor axis, and eccentricity of the orbits of the principal bodies. But the point ±ζ0 is unaffected by the semimajor axis and eccentricity of the orbits of the principal bodies. The effects of the parameters involved in this problem are shown on the topologies of the zero-velocity curves for the binary systems PSR 1903+0327 and DP-Leonis. An investigation of the stability of the out-of-plane equilibrium points, L6,7 numerically, shows that they can be stable for 0.32≤μ≤0.5 and for very low eccentricity. L6,7 of PSR 1903+0327 and DP-Leonis are however linearly unstable.

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Pulsating Different Curves of Zero Velocity around Triangular Equilibrium Points in Elliptical Restricted Three-Body Problem

Cited by 6 publications

References 25 publications

Existence of Resonance Stability of Triangular Equilibrium Points in Circular Case of the Planar Elliptical Restricted Three-Body Problem under the Oblate and Radiating Primaries around the Binary System

Existence of Resonance Stability of Triangular Equilibrium Points in Circular Case of the Planar Elliptical Restricted Three-Body Problem under the Oblate and Radiating Primaries around the Binary System

Stability of the triangular points in the photogravitational triaxial elliptic RTBP with dissipations

Generalized Out-of-Plane Equilibrium Points in the Frame of Elliptic Restricted Three-Body Problem: Impact of Oblate Primary and Luminous-Triaxial Secondary

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