Linear stability of the triangular equilibrium points in the photogravitational elliptic restricted problem, II

Markellos, V. V.; Perdios, E. A.; Georghiou, Costas

doi:10.1007/bf00612974

Cited by 16 publications

(7 citation statements)

References 6 publications

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“…In the photo-gravitational version, when we consider a case that preserves symmetry with respect to both coordinate axes, that is when q 1 = q 2 = q, the triangular points are still located on the y-axis of the synodic coordinate system and their y-coordinate is given by the relation (Perdios 1996;Markellos et al 1993aMarkellos et al , 1993b,…”

Section: In-plane Stationary Solutions and Their Variation With Radiamentioning

confidence: 99%

On some new aspects of the photo-gravitational Copenhagen problem

Kalvouridis

2008

Astrophys Space Sci

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We deal with some new aspects of the photogravitational Copenhagen case of the restricted three-body problem; more particularly, the distribution and the attracting domains of the stationary solutions of small particles that move in the neighborhood of two major bodies with equal masses when one or both primaries are radiation sources with constant luminosity. Under these conditions, each particle is subjected not only to gravitational forces but to the radiation emitted from the primaries as well.

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Section: In-plane Stationary Solutions and Their Variation With Radiamentioning

confidence: 99%

On some new aspects of the photo-gravitational Copenhagen problem

Kalvouridis

2008

Astrophys Space Sci

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“…To describe and analyze more systems in stellar dynamics, primaries were also considered as source of radiation. The elliptic restricted three body problem has been described in considerable detail by various authors, see [5], [23], [13], [8], [15], [14], [3]. In their study, authors have studied about the linear as well as the non-linear stability of motion near the triangular libration points.…”

Section: Introductionmentioning

confidence: 99%

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

Usha¹,

Narayan²

2017

Int. J. of Pure and Appl. Math.

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This paper analyses the local bifurcation of linear stability of motion near the triangular equilibrium points in the neighborhood of parametric resonance frequency ω2 = for circular and elliptic orbits, respectively. The Hamiltonian is made independent of time using canonical transformations.It is found that the values of mass ratio, µ are less than the critical value µc in resonant case, for both orbits. The boundary of the stability region are found in form of equations for both orbits, circular and elliptic (for small values of e). The regions of stability and instability are plotted in the graphs. There is a shift in the bifurcation points of mass ratio,µ from the critical value µc as a result of increase in values of radiation pressure(δ), triaxiality parameters(σ1 and σ2).

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“…In classical problems the primaries are taken strictly as spheres but some planets and stars are sufficiently oblate to make departure from sphericity significant in the study of celestial systems. The influence of eccentricity of the orbit of the primaries with or without radiation pressure, oblateness and triaxiality of the primaries was studied by many authors [1,3,7,13,15,16,18,20,21,24,29,34,36] and others. Kumar and Ishwar [16] investigated the stability of the collinear liberation points when both the primaries are oblate and radiating whereas Singh and Aishetu [30] studied the stability of the triangular equilibrium points when both the primaries are oblate and radiating.…”

Section: Introductionmentioning

confidence: 99%

Existence of Resonance Stability of Triangular Equilibrium Points for an Oblate Infinitesimal in Elliptical Restricted Three Body Problem with Radiating Oblate Primaries

Narayan¹,

Chakraborty²,

Dewangan³

2017

MMC_B

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The present paper models the restricted three body problem, considering the generalization that the orbits of the primaries are taken to be elliptic and the two primaries are considered to be sources of radiation and all three participating bodies are considered as oblate spheroids. Hamiltonian of the problema is derived and then normalized using well-established normalization techniques. The range of values of µ and e for the linear stability of triangular equilibrium points have been found in presence of resonance. The stability of some of the cases of third order resonances has been simulated and explored graphically. The linear stability is observed in the resonance cases 3λ2 = −1, 3λ2 = −2 and λ1 + 2λ2 = 0, where as the triangular points are found to be linearly unstable in the case λ1 − 2λ2 = 2.

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Linear stability of the triangular equilibrium points in the photogravitational elliptic restricted problem, II

Cited by 16 publications

References 6 publications

On some new aspects of the photo-gravitational Copenhagen problem

On some new aspects of the photo-gravitational Copenhagen problem

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

Existence of Resonance Stability of Triangular Equilibrium Points for an Oblate Infinitesimal in Elliptical Restricted Three Body Problem with Radiating Oblate Primaries

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