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

Usha, Tune; Narayan, A.

doi:10.14419/ijaa.v4i2.6536

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2017

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“…The resonance cases of libration points for restricted/elliptic restricted three body problem was analyzed by many authors: Henrard and Caranicolas [10][11][12], Hadjidemetriou [8], SubbaRao and Sharma [32], Thakur and Singh [33], Beauge´ etal. [2], Usha and Narayan [35] and many others.…”

Section: Introductionmentioning

confidence: 96%

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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