Non-linear stability zones around triangular equilibria in the plane circular restricted three-body problem with oblateness

Markellos, V. V.; Papadakis, K. E.; Perdios, E. A.

doi:10.1007/bf00637811

Cited by 61 publications

(40 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The linear stability region and corresponding main resonance curves in µ − q 1 parameter space are shown in figure ( 12) the doted lines are corresponding to A 2 = 0.02, the curve corresponding to k = 1, (q 1 = 1, A 2 = 0, µ 1 = µ Routh = 0.038521) is actual boundary of the stability region these results are similar to Markellos, Papadakis, and Perdios (1996) and others. The critical values of mass parameter µ are given in the tables ( 4, 5) for various values of q 1 , A 2 .…”

Section: Linear Stability Without P-r Effectsupporting

confidence: 77%

The effect of radiation pressure on the equilibrium points in the generalized photogravitational restricted three body problem

Kushvah¹

2008

Astrophys Space Sci

View full text Add to dashboard Cite

The existence of equilibrium points and the effect of radiation pressure have been discussed numerically. The problem is generalized by considering bigger primary as a source of radiation and small primary as an oblate spheroid. We have also discussed the PoyntingRobertson(P-R) effect which is caused due to radiation pressure. It is found that the collinear points L 1 , L 2 , L 3 deviate from the axis joining the two primaries, while the triangular points L 4 , L 5 are not symmetrical due to radiation pressure. We have seen that L 1 , L 2 , L 3 are linearly unstable while L 4 , L 5 are conditionally stable in the sense of Lyapunov when P-R effect is not considered. We have found that the effect of radiation pressure reduces the linear stability zones while P-R effect induces an instability in the sense of Lyapunov.

show abstract

Section: Linear Stability Without P-r Effectsupporting

confidence: 77%

The effect of radiation pressure on the equilibrium points in the generalized photogravitational restricted three body problem

Kushvah¹

2008

Astrophys Space Sci

View full text Add to dashboard Cite

show abstract

“…These expressions of the perturbed mass ratio have similar form to that of [36], [37], [38], [39] and [28], obtained in case of triangular equilibrium points under specific assumptions. Numerically, the perturbed mass ratio are obtained at different values of q 1 and A 2 (Table 3).…”

Section: Resonance Casessupporting

confidence: 53%

“…have studied different aspects of restricted three body problem (RTBP), by taking one or both primary as source of radiation or oblate spheroid or both and have discussed their effects on the motion of infinitesimal mass. [27] have found non-linear stability zones around triangular equilibrium point in the RTBP with oblateness. [11], [12] have studied generalized photogravitational Chermnykh-like problem with P-R drag and found that triangular points are stable under Routh's condition but collinear equilibrium points are unstable whereas, [28] have discussed about linear stability of triangular equilibrium point and resonances.…”

Section: Introductionmentioning

confidence: 94%

See 1 more Smart Citation

The Linear Stability of Collinear Equilibrium Points and Resonances

Kishor¹,

Kushvah²

2017

AdAp

View full text Add to dashboard Cite

The stability properties, dynamical processes and factors affecting these are very important aspects to describing the behaviour of a dynamical system because these play a significant role in the study of their past evolution. The present article discuss about the existence of collinear equilibrium points, their computation and stability analysis in the Chermnykh-Like problem under the influence of perturbations in the form of radiation pressure, oblateness and a disc. In the presence of the disc, there exists a new collinear equilibrium point in addition to the three points of the classical problem. We examine the linear stability of the collinear equilibrium points with respect to disc's outer radius b instead of mass parameter µ and it is found that all the collinear equilibrium points are unstable except L3 which is stable for b ∈ (1.3312, 1.5275) provided that remaining parameters are fixed. Further, we obtain stability regions and perturbed mass ratio in the case of three main resonances for L3 under appropriate approximations. We analyze the effect of the perturbations numerically and it is observed that they significantly affect the motion of infinitesimal mass. The results are limited up to the regular symmetric disc and the radiation effect of the bigger primary but further it can be extended for more generalized cases.

show abstract

“…[10]; El-Shaboury [11]; Bhatnagar et al [12]; Selaru D. et.al. [13]; Markellos et al [14]; Subbarao and Sharma [15]; Khanna and Bhatnagar [16,17]; Roberts G.E. [18]; Oberti and Vienne [19]; Sosnytskyi [20]; Perdiou et.…”

Section: Introductionmentioning

confidence: 99%

A general solution to non-collinear equilibria in terms of largest root (κ) of confocal oblate spheroid

Idrisi¹

2016

IJAA

View full text Add to dashboard Cite

This paper deals with the existence of non-collinear equilibria in restricted three-body problem when less massive primary is an oblate spheroid and the potential of oblate spheroid is in terms of largest root of confocal oblate spheroid. This is found that the non-collinear equilibria are the solution of the equations r 1 = n -2/3 and κ = 1 -a 2 , where r 1 is the distance of the infinitesimal mass from more massive primary, n is mean-motion of primaries, a is semi axis of oblate spheroid and κ is the largest root of the equation of confocal oblate spheroid passes through the infinitesimal mass.

show abstract

Non-linear stability zones around triangular equilibria in the plane circular restricted three-body problem with oblateness

Cited by 61 publications

References 12 publications

The effect of radiation pressure on the equilibrium points in the generalized photogravitational restricted three body problem

The effect of radiation pressure on the equilibrium points in the generalized photogravitational restricted three body problem

The Linear Stability of Collinear Equilibrium Points and Resonances

A general solution to non-collinear equilibria in terms of largest root (κ) of confocal oblate spheroid

Contact Info

Product

Resources

About